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Segmentation and Representation
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
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
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Texture Texture provides measures of properties such as
smoothness, coarseness, and regularity.
Texture Based Segmentation
Co-Occurance Matrix Let 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 zj.
Matrix A is called co-occurance matrix and can provide statistical properties of the texture.
Example Assume P is one pixel to the right and one pixel below
Gray level values are : 0, 1, and 2
Image data:
Co-occurance matrix is:
Statistical Moments of Texture Let Matrix C be formed by dividing every element of A by the number
of point pairs that satisfy P.
The following moments are defined to compare textures:
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Level Set Segmentation Instead of manipulating the contour directly, the
contour is embedded as the zero level set of a higher dimensional function called the level-set function y(X, t).
The level-set function is evolved under the control of a differential 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
Zero Set in a Level Set
Example
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
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 whole topography be flooded from below.
The points where the water from different regions join are boundaries of the regions
Watershed Segmentation
Example
Example
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Representation The result of segmentation should be represented and
described in a form suitable for further computer processing.
A region can be represented in terms of its external characteristics (boundary).
A region can be represented in terms of its internal characteristics.
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Chain Codes Chain codes are generated by following a boundary in a
clockwise or counter-clockwise direction and assigning a direction to the segments connecting every pair of pixels.
Disadvantage: Can be unacceptably long.
Solution: Re-sampling (down sample) the boundary
Disadvantage: Is starting point dependent
Solution: Normalize the representation string to the smallest integer.
Chain Code Directions
Sample Chain Code
Down Sampling
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Polygonal Approximation A boundary can be represented with arbitrary accuracy
by a polygon.
The approximation is exact when the number of sides is equal to the number of points in the boundary.
Finding a polygonal representation can be very time-consuming.
Minimum Perimeter Polygons
Splitting Techniques
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
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
Signature Example
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Boundary Segments Decomposing a boundary into segments simplifies
representation.
Convex Hull can be used for decomposition.
A new segment can be started whenever a Convex Hull deficiency is entered or exited.
Boundary Segments Example
Topics Segmentation
Texture Based Segmentation
Level Set Segmentation
Watershed Segmentation
Representation Introduction
Chain Codes
Polygonal Approximations
Signatures
Boundary Segments
Skeletons
Skeleton The structural shape of a region can be represented by
a graph.
The structural graph is obtained by thinning the region and finding the skeleton.
Questions?
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