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Those are the slides for the book: Visual Computing: Geometry, Graphics, and Vision. by Frank Nielsen (2005) http://www.sonycsl.co.jp/person/nielsen/visualcomputing/ http://www.amazon.com/Visual-Computing-Geometry-Graphics-Charles/dp/1584504277
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copy 2011 Frank Nielsen Lecture 1
INF555
Fundamentals of 3D
Lecture 1 Abstract Data Structures
Stacks queues and hashing withapplications in visual computing
Mercredi 14 Septembre 2011
copy 2011 Frank Nielsen Lecture 1
INF555 Fundamentals of 3D
L1 Abstract data structures L2 Transformations and coordinate pipelines L3 Advanced transformations L4 Images and colors L5 Meshes L6 Animation L7 Randomized algorithms L8 High-dimensions for 3D L9 Robustness
rarr Examen 20 min oral en Deacutecembre
copy 2011 Frank Nielsen Lecture 1
Deacuteboucheacutes de la filiegravere Image (4A)middotmiddotFormation complementaire inteacutegreacutee (FCI) avec lmiddotmiddotEacutecole des Ponts ParisTech
Master II middotmiddotMatheacutematiques Vision Apprentissage (MVA)
Master II agrave lmiddotmiddotEacutecole Polytechnique Feacutedeacuterale de Lausanne (EPFL) Suisse Master II dinformatique Master II de robotique et systegravemes autonomes
middotmiddotTeacuteleacutecom ParisTech (ENST) + Master middotmiddotspeacutecialiteacute imagerie du vivant (IMA) + Master middotmiddotIntelligence Artificielle et Deacutecision (IAD) agrave UPMC
Cadre du Corps de lArmement (filiegravere recherche) middotmiddotRoyal Institute of Technology (KTH Stockholm Sueacutede )
Master agrave leacutetranger (notamment aux Etats-Unis et au Japon) Master agrave Columbia University USA en infographieMaster en Electrical and Computer Engineering Cornell University USA
Master II middotmiddotMaster Parisien de Recherche en Informatique (MPRI) Master II middotmiddotMatheacutematiques Vision Apprentissage (MVA) middotmiddotENSIMAG middotmiddotENSTA Masters europeacuteens
Master middotmiddotETH Zuumlrich middotmiddotTU Munchen Computer Science Dept Master in middotmiddotBiomedical Engineering agrave Oxford
middot Masters internationaux Eacutetats-Unis Japon middot etc
httpwwwlixpolytechniquefr~nielsenINF555devenirhtml
copy 2011 Frank Nielsen Lecture 1
Notations et projets
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2008HF2008-Pjhtmlhttpwwwlixpolytechniquefr~nielsenINF555indexhtml
bull 30 rendus des programmes TDs bull 20 controle de connaissance par questions orales (lors de la soutenance
du projet) bull 50 soutenance de projet
copy 2011 Frank Nielsen Lecture 1
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2009
Dehazing(anti-brouillard)
Stippling(pointillisme)
TextureShop(retextureacute les photos)
Face recognitioncompression(algorithmique du visage)
Out of bound photo(effet photo 3D)
copy 2011 Frank Nielsen Lecture 1
Reference textbook
httpwwwsonycslcojppersonnielsenvisualcomputing
Disponible agrave la bibliothegraveque en 5 exemplairesAllez lemprucircnter
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
INF555 Fundamentals of 3D
L1 Abstract data structures L2 Transformations and coordinate pipelines L3 Advanced transformations L4 Images and colors L5 Meshes L6 Animation L7 Randomized algorithms L8 High-dimensions for 3D L9 Robustness
rarr Examen 20 min oral en Deacutecembre
copy 2011 Frank Nielsen Lecture 1
Deacuteboucheacutes de la filiegravere Image (4A)middotmiddotFormation complementaire inteacutegreacutee (FCI) avec lmiddotmiddotEacutecole des Ponts ParisTech
Master II middotmiddotMatheacutematiques Vision Apprentissage (MVA)
Master II agrave lmiddotmiddotEacutecole Polytechnique Feacutedeacuterale de Lausanne (EPFL) Suisse Master II dinformatique Master II de robotique et systegravemes autonomes
middotmiddotTeacuteleacutecom ParisTech (ENST) + Master middotmiddotspeacutecialiteacute imagerie du vivant (IMA) + Master middotmiddotIntelligence Artificielle et Deacutecision (IAD) agrave UPMC
Cadre du Corps de lArmement (filiegravere recherche) middotmiddotRoyal Institute of Technology (KTH Stockholm Sueacutede )
Master agrave leacutetranger (notamment aux Etats-Unis et au Japon) Master agrave Columbia University USA en infographieMaster en Electrical and Computer Engineering Cornell University USA
Master II middotmiddotMaster Parisien de Recherche en Informatique (MPRI) Master II middotmiddotMatheacutematiques Vision Apprentissage (MVA) middotmiddotENSIMAG middotmiddotENSTA Masters europeacuteens
Master middotmiddotETH Zuumlrich middotmiddotTU Munchen Computer Science Dept Master in middotmiddotBiomedical Engineering agrave Oxford
middot Masters internationaux Eacutetats-Unis Japon middot etc
httpwwwlixpolytechniquefr~nielsenINF555devenirhtml
copy 2011 Frank Nielsen Lecture 1
Notations et projets
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2008HF2008-Pjhtmlhttpwwwlixpolytechniquefr~nielsenINF555indexhtml
bull 30 rendus des programmes TDs bull 20 controle de connaissance par questions orales (lors de la soutenance
du projet) bull 50 soutenance de projet
copy 2011 Frank Nielsen Lecture 1
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2009
Dehazing(anti-brouillard)
Stippling(pointillisme)
TextureShop(retextureacute les photos)
Face recognitioncompression(algorithmique du visage)
Out of bound photo(effet photo 3D)
copy 2011 Frank Nielsen Lecture 1
Reference textbook
httpwwwsonycslcojppersonnielsenvisualcomputing
Disponible agrave la bibliothegraveque en 5 exemplairesAllez lemprucircnter
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Deacuteboucheacutes de la filiegravere Image (4A)middotmiddotFormation complementaire inteacutegreacutee (FCI) avec lmiddotmiddotEacutecole des Ponts ParisTech
Master II middotmiddotMatheacutematiques Vision Apprentissage (MVA)
Master II agrave lmiddotmiddotEacutecole Polytechnique Feacutedeacuterale de Lausanne (EPFL) Suisse Master II dinformatique Master II de robotique et systegravemes autonomes
middotmiddotTeacuteleacutecom ParisTech (ENST) + Master middotmiddotspeacutecialiteacute imagerie du vivant (IMA) + Master middotmiddotIntelligence Artificielle et Deacutecision (IAD) agrave UPMC
Cadre du Corps de lArmement (filiegravere recherche) middotmiddotRoyal Institute of Technology (KTH Stockholm Sueacutede )
Master agrave leacutetranger (notamment aux Etats-Unis et au Japon) Master agrave Columbia University USA en infographieMaster en Electrical and Computer Engineering Cornell University USA
Master II middotmiddotMaster Parisien de Recherche en Informatique (MPRI) Master II middotmiddotMatheacutematiques Vision Apprentissage (MVA) middotmiddotENSIMAG middotmiddotENSTA Masters europeacuteens
Master middotmiddotETH Zuumlrich middotmiddotTU Munchen Computer Science Dept Master in middotmiddotBiomedical Engineering agrave Oxford
middot Masters internationaux Eacutetats-Unis Japon middot etc
httpwwwlixpolytechniquefr~nielsenINF555devenirhtml
copy 2011 Frank Nielsen Lecture 1
Notations et projets
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2008HF2008-Pjhtmlhttpwwwlixpolytechniquefr~nielsenINF555indexhtml
bull 30 rendus des programmes TDs bull 20 controle de connaissance par questions orales (lors de la soutenance
du projet) bull 50 soutenance de projet
copy 2011 Frank Nielsen Lecture 1
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2009
Dehazing(anti-brouillard)
Stippling(pointillisme)
TextureShop(retextureacute les photos)
Face recognitioncompression(algorithmique du visage)
Out of bound photo(effet photo 3D)
copy 2011 Frank Nielsen Lecture 1
Reference textbook
httpwwwsonycslcojppersonnielsenvisualcomputing
Disponible agrave la bibliothegraveque en 5 exemplairesAllez lemprucircnter
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Notations et projets
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2008HF2008-Pjhtmlhttpwwwlixpolytechniquefr~nielsenINF555indexhtml
bull 30 rendus des programmes TDs bull 20 controle de connaissance par questions orales (lors de la soutenance
du projet) bull 50 soutenance de projet
copy 2011 Frank Nielsen Lecture 1
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2009
Dehazing(anti-brouillard)
Stippling(pointillisme)
TextureShop(retextureacute les photos)
Face recognitioncompression(algorithmique du visage)
Out of bound photo(effet photo 3D)
copy 2011 Frank Nielsen Lecture 1
Reference textbook
httpwwwsonycslcojppersonnielsenvisualcomputing
Disponible agrave la bibliothegraveque en 5 exemplairesAllez lemprucircnter
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
httpwwwlixpolytechniquefrLaboFrankNielsenINF555HallFamePj2009
Dehazing(anti-brouillard)
Stippling(pointillisme)
TextureShop(retextureacute les photos)
Face recognitioncompression(algorithmique du visage)
Out of bound photo(effet photo 3D)
copy 2011 Frank Nielsen Lecture 1
Reference textbook
httpwwwsonycslcojppersonnielsenvisualcomputing
Disponible agrave la bibliothegraveque en 5 exemplairesAllez lemprucircnter
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Reference textbook
httpwwwsonycslcojppersonnielsenvisualcomputing
Disponible agrave la bibliothegraveque en 5 exemplairesAllez lemprucircnter
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Abstract Data Structures
Concepts encapsulated into an interface
Multiple implementations (various trade-offs)
rarr Good for code reuse (APIs) rarr Actual implementation is hidden
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Outline of Abstract DS
Abstract data-structures in Java
Area Flood filling (larr stacks and larr queues)
Any segment pair intersection (larr dictionary)
Image segmentation (larr union-find disjoint elements)
Object recognition (larr geometric hashing)
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
I Abstract Data Structures Stack
Interface (method prototypes)isEmptypush(Element)pop (or pull)
For example two implementations Array Linked list
public static void main(String [] args)
Stack myStack=new Stack()int ifor(i=0ilt10i++)
myStackPush(i)
for(i=0ilt15i++)
Systemoutprintln(myStackPull())
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
class StackArrayint nbmaxint indexint [ ] array
ConstructorsStackArray(int n)thisnbmax=narray=new int[nbmax] index=-1Systemoutprintln(Succesfully created a stack array object)
Methods INTERFACEvoid Push(int element)if (indexltnbmax-1)
array[++index]=element
int Pull()if (indexgt=0 ) return array[index--]else return -1
Stack (array)
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Stack (linked list)class StackList listStack()list=null
void Push(int el)if (list=null) list=listinsertHead(el)
else list=new
List(elnull)
int Pull()int valif (list=null)
val=listelement list=listnext else val=-1
return val
class Listint elementList next
ConstructorList(int el List tail)thiselement=elthisnext=tail
List insertHead(int el)return new List(elthis)
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
httpjavasuncomj2se142docsapijavautilStackhtml
Java documentation of interfaces
Commentez vos programmes avec JavaDoc (sous Eclipse)ou Doxygen (incluant des formules latex par exemple)httpwwwstacknl~dimitridoxygen
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
II Computer Graphics Area Flood Filling
Basic coloring application
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling
Tint filling
Tint fill+pattern fill
Gradient filling
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Application Vectorization of Cartoon Animation
rarr Rendering to multi-size displaysrarr Interaction with image semantic
Vectorizing Cartoon AnimationsJulyAugust 2009 (vol 15 no 4)pp 618-629
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Area Flood FillingImages as large graphs (million pixels)Image (pixel) connectivity 4- or 8-connectivity (but also hexagonal etc)
Example of flood filling (cartoon animation etc)
httpwww-graphicsstanfordedu~levoysands_awardhtml
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Area Flood Filling Recursive Algorithm
Use an abstract data-structure Stack
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a stackHandle recursion explicitly with the stack
Depth first order
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Area flood filling using a queue
Properties of abstract queues
Breadth first order
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Stack(depth search)
Queue(breadth search)
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
3 Abstract dictionariesStore items indexed by keysAxiomatic semantic
Unordered (collection) or ordered dictionaries (rarr augmented dictionaries)
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
IV Dictionaries Detecting Any Segment Pair Intersection Naive quadratic time algorithm
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
S2 intersects S4 At some position they become y-adjacent
Sweeping line combinatorial algorithm 2n extremities onlyrarr 2n events so swap from left to right(A preliminary computational geometric algorithm)
A structural propertyrarr Sweeping combinatorial events
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Ordered dictionary
For a given query (ey) report the line segment immediately above and below (ey)
Dynamic insertiondeletion of line segment extremities
Implementation using binary trees (red-black AVL etc)
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Shamos-Hoey intersection detection algorithmDoes a pair of segment intersect Yes or No
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Priority queues
(INF311 Implementation using implicit heaps stored in an array)
For the line sweep 3 kinds of events type 1 Begin extremity type 2 End extremity type 3 Intersection point
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm (extend Shamos-Hoey)Complexity O((n+I) log n)
Initialization
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Bentley-Ottman algorithm Handling events
Interesting caseSwap manually order at intersection points
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
httpenwikipediaorgwikiBentleyE28093Ottmann_algorithm
Collision detection for 3D games
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
IV Union-Find abstract data-structuresManage disjoint sets very efficiently under union
Example Image segmentation (let a robot see)
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
Each region is a setInitially each pixel defines a region
Merging regions=merging disjoint sets
For a given element find the set that contains it
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Union-Find abstract data-structures
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Path compressionAlmost linear-size data-structure(inverse of Ackermann function)
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Union find DS for labelling connected components
Much easier problem than segmentation
Disjoint set data-structure
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Segmentation clustering and tone mapping
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
V Hashing
Hashing and collision (INF3x1 du Tronc Commun) Open address Linked chains
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
For each feature pair of pointsFor each feature pair of points
bullbull Define a local coordinate Define a local coordinate basisbasis on this pair on this pair
bullbull Compute and quantize all other feature points in this coordinate basisCompute and quantize all other feature points in this coordinate basis
bullbull Record (model basis) in a hash tableRecord (model basis) in a hash table
V Geometric hashing Preprocessing(for a point set)
httpenwikipediaorgwikiGeometric_hashinghttpwwwseasgwuedu~simhawebcs151lecturesmodule4module4html
larr Quadratic time preprocessing
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
1 Pick 1 Pick arbitraryarbitrary ordered pair of scene ordered pair of sceneCompute the other points using this pair as a frame Compute the other points using this pair as a frame basisbasis
2 For all the transformed points vote all records (model basis) appear 2 For all the transformed points vote all records (model basis) appear in the corresponding entry in the hash table and in the corresponding entry in the hash table and histogramhistogram them them
(= frequency histogram)(= frequency histogram)3 Matching candidates (model basis) pairs with 3 Matching candidates (model basis) pairs with large number of voteslarge number of votes
4 Recover the transformation that results in the best least-squares match 4 Recover the transformation that results in the best least-squares match between all corresponding feature pointsbetween all corresponding feature pointsTransform the features and verify against the input image features Transform the features and verify against the input image features (if fails repeat this procedure with another pair)(if fails repeat this procedure with another pair)
Geometric hashing Recognition
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Geometric hashing (2D rigid motion)
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Geometric hashing
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Geometric hashing Object recognition
Object Recognition from Local Scale-Invariant Features (SIFT)
Scalable recognition
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Further readingshttpwwwlixpolytechniquefr~nielsenINF555indexhtml
Wolfson HJ amp Rigoutsos I (1997) Geometric Hashing An Overview IEEE Computational Science and Engineering 4(4) 10-21
Andrew S Glassner Fill Er Up IEEE Computer Graphics and Applications 21(1) 78-85 (2001)
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Java IO ImageSeveral APIs
public Image(String filename) javaawtImage img = ToolkitgetDefaultToolkit()getImage(filename) if (img = null) PixelGrabber pg = new PixelGrabber(img 0 0 -1 -1 true) try pggrabPixels() catch (InterruptedException e) raster = (int[]) pggetPixels() height = pggetHeight() width = pggetWidth() else throw new IllegalArgumentException(Error opening file
+ filename)
Can use alsoprocessingorg
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
Java IO Image public int getBlue(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return (raster[y width + x] amp 0xFF)
public int getGreen(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF00) gtgt 8)
public int getRed(int x int y) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() return ((raster[y width + x] amp 0xFF0000) gtgt 16)
Alpha Red Green Blue
Opacity is 255 (0xFF)
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
public void setGreen(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt8) public void setRed(int x int y int value) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | ((valueamp0xff)ltlt16) public void setBlue(int x int y int value ) if (x lt 0 || x gt= width || y lt 0 || y gt= height) throw new IllegalArgumentException() raster[y width + x] = raster[y width + x] | (valueamp0xff)
Java IO Image Alpha Red Green Blue
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
copy 2011 Frank Nielsen Lecture 1
public void writeBinaryPPM(String filename) String lineStringTokenizer st int i try DataOutputStream out =new DataOutputStream(
new BufferedOutputStream(new FileOutputStream(filename))) outwriteBytes(P6n) outwriteBytes( INF555 Ecole Polytechniquen) outwriteBytes(width+ +height+n255n)
for (int y = 0 y lt height y++) for (int x = 0 x lt width x++)
int rgbr=getRed(xy)g=getGreen(xy)b=getBlue(xy)
outwriteByte((byte)r)outwriteByte((byte)g)outwriteByte((byte)b)
outclose() catch(IOException e)
PPM Image
