digital image processing-8

8/6/2019 Digital Image Processing-8

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TopicsSegmentationTexture Based SegmentationLevel Set Segmentation Watershed Segmentation

RepresentationIntroductionChain Codes

Polygonal ApproximationsSignaturesBoundary SegmentsSkeletons


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Introduction Image segmentation is the process of partitioning the

digital image into multiple regions that can be

associated with the properties of one or more objects


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TopicsSegmentationTexture Based SegmentationLevel Set Segmentation Watershed Segmentation

RepresentationIntroductionChain Codes



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TextureTexture provides measures of properties such assmoothness, coarseness, and regularity.


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Co-Occurance MatrixLet P be a position operator, and A a k x k matrix.aij shows the number of times that pixels with gray

level zi occur at position given by P relative to points with gray level z j.

Matrix A is called co-occurance matrix and can provide

statistical properties of the texture.


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Example Assume P is one pixel to the right and one pixel belowGray level values are : 0, 1, and 2

Image data:

Co-occurance matrix is:


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Statistical Moments of TextureLet Matrix C be formed by dividing every element of A by the numberof point pairs that satisfy P.The following moments are defined to compare textures:


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TopicsSegmentationTexture Based SegmentationLevel Set Segmentation

Watershed SegmentationRepresentation

IntroductionChain Codes



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Level Set SegmentationInstead of manipulating the contour directly, thecontour is embedded as the zero level set of a higherdimensional function called the level-set function y( X, t).The level-set function is evolved under the control of adifferential equation.

At any time, the evolving contour can be obtained by extracting the zero level-set G(( X), t) = {y(X, t) = 0}from the output


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Zero Set in a Level Set


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Example


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Watershed Segmentation Algorithm:

Convert the gray level image into a topographic image where the height of each point is proportional to its gray level intensity.Punch a hole at each region minimum at let the wholetopography be flooded from below.The points where the water from different regions joinare boundaries of the regions


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Watershed Segmentation


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Example


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Example


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RepresentationThe result of segmentation should be represented anddescribed in a form suitable for further computerprocessing.

A region can be represented in terms of its externalcharacteristics (boundary). A region can be represented in terms of its internalcharacteristics.


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Chain CodesChain codes are generated by following a boundary in aclockwise or counter-clockwise direction and assigning adirection to the segments connecting every pair of pixels.

Disadvantage: Can be unacceptably long.Solution: Re-sampling (down sample) the boundary

Disadvantage: Is starting point dependentSolution: Normalize the representation string to thesmallest integer.


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Chain Code Directions


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Sample Chain Code


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Polygonal Approximation A boundary can be represented with arbitrary accuracy by a polygon.The approximation is exact when the number of sidesis equal to the number of points in the boundary.Finding a polygonal representation can be very time-consuming.


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Splitting Techniques


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Signature A signature is a 1D representation of a boundary.e.g. Plotting distance to centroid as a function of angle

Invariant to translation

Disadvantages:Rotation and scaling dependant

Defined only for convex regions


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Signature Example


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Boundary SegmentsDecomposing a boundary into segments simplifiesrepresentation.Convex Hull can be used for decomposition.

A new segment can be started whenever a Convex Hulldeficiency is entered or exited.


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Boundary Segments Example


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SkeletonThe structural shape of a region can be represented by a graph.The structural graph is obtained by thinning theregion and finding the skeleton.


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Questions?

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