Morphological Image Processing

Anoop M. Namboodiri

anoop@iiit.ac.in

DIP: Monsoon 2003

Morphological OperationsMorphological Operations

• Neighbourhood operations carried out in spatial domain

• Based on mathematical morphology

• set theoretical framework

• originally for binary images

• extended for grey scale images

• Applications:

• extract info about forms and structures

• shaping and filtering of forms and structures

DIP: Monsoon 2003

Morphological ProcessingMorphological Processing

• Consists essentially of two steps:

• Probe a given object in x[m,n] with a structuring element (se)

• Find how the se fits with the object

• Information about fit is used to

• extract info about the form of object; OR

• change pixel values and shape objects

• Different size & shape of se yields different kinds of info about the object; shapes the regions in different ways

DIP: Monsoon 2003

Set Theory BasicsSet Theory Basics

• Union, Intersection

• Complement, Difference

• Subset, Superset, Disjoint Sets

• Reflection:

• Translation:

},|{ˆ BbforbwwB ∈−==

},|{)( AaforzaccA z ∈+==

DIP: Monsoon 2003

ExamplesExamples

(A)z | z = (3,5)

A

(0,0)

-A

(0,0)

B

A - B

(3,5)

DIP: Monsoon 2003

Morphological Operations/AlgorithmsMorphological Operations/Algorithms

• Basic Morphological Operations

• Dilation

• Erosion

• Opening

• Closing

• Hit-or-Miss Transformation

• Morphological Algorithms

• Extensions to Grayscale

DIP: Monsoon 2003

DilationDilation

• Dilation of A by B: A⊕B

})ˆ(|{ Φ≠∩=⊕ ABzBA z }])ˆ[(|{ AABzBA z ⊆∩=⊕

x

x

A

B

B̂

A⊕B

x

x

x x

x

DIP: Monsoon 2003

Dilation: ExampleDilation: Example

DIP: Monsoon 2003

Dilation: ExampleDilation: Example010

111

010

DIP: Monsoon 2003

ErosionErosion

• Erosion of A by B: A B

A B = {z | (B)z ⊆ A}.

x

A

B

A⊕B

x

x

DIP: Monsoon 2003

Erosion: ExampleErosion: Example

DIP: Monsoon 2003

Erosion + DilationErosion + Dilation

DIP: Monsoon 2003

Opening and ClosingOpening and Closing

• Opening: Erosion followed by Dilation

• Opening A by B: A ○ B = (A B) ⊕ B

• Smoothes Contours, Breaks narrow bridges,

Eliminates thin protrusions

• Closing: Dilation followed by Erosion

• Closing A by B: A ● B = (A ⊕ B) B

• Smoothing, Closes small holes and channels

DIP: Monsoon 2003

Opening: Physical InterpretationOpening: Physical Interpretation

DIP: Monsoon 2003

Closing: Physical InterpretationClosing: Physical Interpretation

DIP: Monsoon 2003

Opening: ExampleOpening: Example

.

B

Erosion Dilation

DIP: Monsoon 2003

Closing: ExampleClosing: Example

.

B

ErosionDilation

DIP: Monsoon 2003

ExampleExample111

111

111

⊕⊕⊕⊕

⊕⊕⊕⊕

DIP: Monsoon 2003

Interesting PointsInteresting Points

• A ○B is a subset of A.

• If C ⊆ D; then C ○B ⊆ D ○B.

• (A ○B) ○B = A ○B.

• A is a subset of A ●B.

• If C ⊆ D; then C ●B ⊆ D ●B.

• (A ●B) ●B = A ●B.

DIP: Monsoon 2003

Hit-or-Miss Transform (HMT)Hit-or-Miss Transform (HMT)

• To detect an object in an image:

• Basic Idea:

• Use the object as se for erosion of A and

detect possible fits.

• Use the neighborhood of the object as

se for erosion of Ac and find over fits.

• Combine the two to detect exact fits.

DIP: Monsoon 2003

HMT: ExampleHMT: Example

DIP: Monsoon 2003

Morphological AlgorithmsMorphological Algorithms

• Boundary Extraction

• Region Filling

• Connected Components

• Convex Hull

• Thinning

• Thickening

• Skeletonization

• Pruning

DIP: Monsoon 2003

Boundary ExtractionBoundary Extraction

• Boundary of A is computed as:

β(A) = A - (A B)

B

DIP: Monsoon 2003

Boundary Extraction: ExampleBoundary Extraction: Example

DIP: Monsoon 2003

Region FillingRegion Filling

• Fills a regions, whose boundary is given as

8-connected neighbours:

Xk = (Xk-1 ⊕ B) ∩ Ac, k = 1, 2, 3,…

…