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Morphological Operations
Dr. Praveen Sankaran
Department of ECE
NIT Calicut
February 28, 2013
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 1 / 22
Outline
1 Basic Operations
2 Morphological Algorithms
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 2 / 22
Basic Operations
Change in outcome
Till now our discussion dealt with methods that took in an
image and processed it, which produced an output image.
Our focus now move to a set of algorithms that take in an
image as an input, but the outputs are information contained and
extracted from within the image.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 3 / 22
Basic Operations
Morphology
Morphology: is the identi�cation, analysis and description of thestructure of [· · · ].Image: extract image components.
region shape
boundaries etc.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 4 / 22
Basic Operations
Sets
Sets: represents objects in an image.
Binary image: Sets ∈ 2D integer space Z 2.
[x ,y ] coordinates with either 0 or 1.
Gray scale: Sets ∈ Z 3
[x ,y ] coordinates,intensity value.
C = {w |w =−d , d ∈ D}⇒ set C is the set of elements, w , formedby multiplying each of the elements of set D by −1.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 5 / 22
Basic Operations
Background and Foreground
Lets deal with binary images for now.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 6 / 22
Basic Operations
Re�ection and Translation
Re�ection:B̂ = {w |w =−b, b ∈ B} (1)
[−x ,−y ]
Translation:Bz = {c |c = b+ z , b ∈ B} (2)
[x+ z1,y + z2]
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 7 / 22
Basic Operations
Structuring Elements (SE) - Example
Small sets or sub-images used to probe an image.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 8 / 22
Basic Operations
Structuring Elements (SE) - Processing
Create a new set:
Run B over A - origin of B overlaps each point of A.
At each location, if B is completely contained in A, mark location as
member of new set.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 9 / 22
Erosion
The gradual destruction or diminution of something.
AB = {z |Bz ⊆ A}= {z |Bz ∩Ac = Ø} (3)
Basic Operations
Erosion - Image Example - Variation with SE Size
Figure: 486×486 binary image eroded with square SE of sizes 11×11, 15×15
and 45×45. Elements of SEs = 1.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 11 / 22
Basic Operations
Dilation
The act of expanding or the state of being expanded.
A⊕B ={z |B̂z ∩A 6= Ø
}={z |[B̂z ∩A
]⊆ A
}(4)
Set of all displacements z , such that B̂ and A overlap by at-least oneelement.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 12 / 22
Basic Operations
Dilation Example
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 13 / 22
Basic Operations
Opening and Closing
Opening: erosion, followed by dilation.
A◦B = (AB)⊕B (5)
Smoothen the contour of an object,
breaks narrow isthmuses,
eliminates thin protrusions.
Closing:dilation, followed by erosion.
A•B = (A⊕B)B (6)
Smoothen contour,
fuses narrow breaks and long thin gulfs,
eliminates small holes,
�lls gaps in the contour.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 14 / 22
Basic Operations
Opening - Geometrical Interpretation
A◦B = ∪{Bz |Bz ⊆ A} (7)
Union of all translates of B that �ts into A.
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 15 / 22
Basic Operations
Closing - Geometrical Interpretation
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 16 / 22
Basic Operations
Combined Process - Noise Removal
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 17 / 22
Hit-or-Miss Transform
Morphological Algorithms
Boundary Extraction
β (A) = A− (AB) (8)
-
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 19 / 22
Hole Filling
Hole: a background region surrounded by a connected border of foregroundpixels.
Morphological Algorithms
Questions
5,6,7,8
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 21 / 22
Morphological Algorithms
Reference
http://en.wikipedia.org/wiki/Morphology_%28linguistics%29
Dr. Praveen Sankaran (Department of ECE NIT Calicut )DIP Winter 2013 February 28, 2013 22 / 22