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 timeconsuming.

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?