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Computer Vision at IPMComputer Vision at IPM
Mehrdad ShahshahaniMehrdad Shahshahani
Institute for Studies in Theoretical Physics Institute for Studies in Theoretical Physics and Mathematicsand Mathematics
International Workshop on Computer VisionInternational Workshop on Computer VisionApril 26-30, Tehran,IranApril 26-30, Tehran,Iran
Computer Vision GroupComputer Vision Group
Masoud AlipourMasoud Alipour Somayeh DanafarSomayeh Danafar Ali FarhadiAli Farhadi Hanif MohammadiHanif Mohammadi Nima RazaviNima Razavi Azad ShadmanAzad Shadman Lila TaghaviLila Taghavi Ali-Reza TavakoliAli-Reza Tavakoli
Scope of EffortScope of Effort
Limited to the Analysis of A Single ImageLimited to the Analysis of A Single Image
Object DifferentiationObject Differentiation
SegmentationSegmentation
Conspicuously Absent: Use of a Data BankConspicuously Absent: Use of a Data Bank
MethodologiesMethodologies
Emphasis on Experimental MethodsEmphasis on Experimental Methods
Statistical Analysis Statistical Analysis – Higher Order StatisticsHigher Order Statistics– SVD TransformsSVD Transforms– Application of Methods of Computational GeometryApplication of Methods of Computational Geometry
Memory/PriorsMemory/Priors
Variation of Correlations (cont.)Variation of Correlations (cont.)
Variation of Correlations (cont.)Variation of Correlations (cont.)
Variation of Correlations (cont.)Variation of Correlations (cont.)
Rough Classification of ImagesRough Classification of Images
Rough Classification of Images Rough Classification of Images (cont.)(cont.)
DetectionDetection
Detection (cont.)Detection (cont.)
Detection (cont.)Detection (cont.)
General ConclusionGeneral Conclusion
Analysis of local correlations in a single image Analysis of local correlations in a single image allows the detection of an extraneous object in a allows the detection of an extraneous object in a texture environment.texture environment.
SegmentationSegmentation
Application of analysis of correlations to segmentation of Application of analysis of correlations to segmentation of imagesimages
Requires more elaborate analysisRequires more elaborate analysis
Roughly Speaking, two step process:Roughly Speaking, two step process:
– 1. Identification of regions (windows) containing object.1. Identification of regions (windows) containing object.– 2. Determination of the boundary of the object.2. Determination of the boundary of the object.
Segmentation (cont.)Segmentation (cont.)
Segmentation (cont.)Segmentation (cont.)
Segmentation (cont.)Segmentation (cont.)
Segmentation (cont.)Segmentation (cont.)
General ConclusionGeneral Conclusion By analysis of local correlations segmentation can By analysis of local correlations segmentation can
be achieved on the basis of local structure of be achieved on the basis of local structure of textures.textures.
Not necessary to make use of memory.Not necessary to make use of memory.
Analysis is based on a single image.Analysis is based on a single image.
Complexity of algorithm is O(N).Complexity of algorithm is O(N).
A Test CaseA Test Case
How can one tell the difference How can one tell the difference between a cat and a dog?between a cat and a dog?
The question can be viewed from a The question can be viewed from a neurophysiologic or image processing point of neurophysiologic or image processing point of
viewview..
Can measures of statistical variability be used in Can measures of statistical variability be used in distinguishing between dogs and cats?distinguishing between dogs and cats?
LPC Surfaces LPC Surfaces
One canonically constructs a surface (LPC surface)One canonically constructs a surface (LPC surface)
from the analysis of local correlations of an image.from the analysis of local correlations of an image.
LPC Surfaces (cont.)LPC Surfaces (cont.)
LPC Surfaces (cont.)LPC Surfaces (cont.)
LPC Surfaces (cont.)LPC Surfaces (cont.)
LPC surfaces are highly non-differentiable.LPC surfaces are highly non-differentiable.
Discrete geometry of LPC surfaces.Discrete geometry of LPC surfaces.
Curvature of a triangulated surface.Curvature of a triangulated surface.
Triangulation of a SurfaceTriangulation of a Surface
Curvature of a triangulationCurvature of a triangulation
Curvature at a vertex v isCurvature at a vertex v is
6 – number of edges incident on v6 – number of edges incident on v
General Conclusion: Count the number of triangles General Conclusion: Count the number of triangles to obtain measure of statistical variability of the to obtain measure of statistical variability of the surface.surface.
Counting trianglesCounting triangles
Counting TrianglesCounting Triangles
Statistical Variability of textures of cats and dogs Statistical Variability of textures of cats and dogs reflected in discrete curvature LPC surfaces.reflected in discrete curvature LPC surfaces.
It can be achieved more simply by a judicious It can be achieved more simply by a judicious method for counting triangles per unit area.method for counting triangles per unit area.
Can tell the difference between a Can tell the difference between a REALREAL dog and dog and
a a REALREAL cat! cat!
Singular Value DecompositionSingular Value Decomposition
SVD decomposition of sliding windowsSVD decomposition of sliding windows
S=UDVS=UDV
Diagonal entries positive and in decreasing order.Diagonal entries positive and in decreasing order.
Do the diagonal matrices D contain significant Do the diagonal matrices D contain significant
information about structural content of an image?information about structural content of an image?
SVD (continued)SVD (continued)
SVD (continued)SVD (continued)
SVD (continued)SVD (continued)
SVD (continued)SVD (continued)
SVD TransformsSVD Transforms
From Diagonal entries of SVD decomposition of From Diagonal entries of SVD decomposition of sliding windows on an image we construct the SVD sliding windows on an image we construct the SVD transform or SVD surface.transform or SVD surface.
SVD Transform (cont.)SVD Transform (cont.)
SVD TransformSVD Transform
Application of SVD TransformsApplication of SVD Transforms
1. Detection of objects in a texture background.1. Detection of objects in a texture background.
2. Detection of fractures or defects.2. Detection of fractures or defects.
3. Segmentation of Images.3. Segmentation of Images.
4. Determination of location of eyes.4. Determination of location of eyes.
DetectionDetection
Detection (continued)Detection (continued)
Detection (continued)Detection (continued)
Detection of FracturesDetection of Fractures
SegmentationSegmentation
Segmentation (continued)Segmentation (continued)
Effect of change in lighting and blurring on Effect of change in lighting and blurring on segmentationsegmentation
Segmentation (continued)Segmentation (continued)
Segmentation (continued)Segmentation (continued)
Segmentation (continued)Segmentation (continued)
Conclusion: Conclusion:
Segmentation via SVD transforms isolates objects Segmentation via SVD transforms isolates objects on the basis of their local texture structures.on the basis of their local texture structures.
Is not sensitive to changes in lighting, orientation, Is not sensitive to changes in lighting, orientation,
or similar distortions.or similar distortions.
Locating the Eyes
- =
SVD Transform
Edge detection
Edge detection with noise removal
RobustRobust
Analysis of SVDAnalysis of SVD
Understanding the meaning and implications of Understanding the meaning and implications of the SVD decompositionthe SVD decomposition
Substituting the diagonal part D from one image Substituting the diagonal part D from one image into another.into another.
Analysis of SVD (cont.)Analysis of SVD (cont.)
D woman in U,V LenaD woman in U,V Lena
ws=4ws=4
Analysis of SVD (cont.)Analysis of SVD (cont.)
ws=4ws=4
D Lena in U,V womanD Lena in U,V woman
Analysis of SVD (cont.)Analysis of SVD (cont.)
ws=32ws=32
D Lena in U,V womanD Lena in U,V woman
Analysis of SVDAnalysis of SVD
ws=4ws=4
D Lena in U,V randomD Lena in U,V random
Analysis of SVD (cont.)Analysis of SVD (cont.)
ws=32ws=32
D random in U,V LenaD random in U,V Lena
ConclusionConclusion
Diagonal SVD contains significant information.Diagonal SVD contains significant information.
Relative importance of D relative to U,V decreases as Relative importance of D relative to U,V decreases as window size increases.window size increases.
U, V contain information about correlational structure of U, V contain information about correlational structure of image.image.
For small window sizes U and V behave like high frequencies.For small window sizes U and V behave like high frequencies.
Other ResearchOther Research
1. Eye/Iris Printing1. Eye/Iris Printing
2. Shape Matching2. Shape Matching
3. Robotic Motion3. Robotic Motion
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