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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