Digital Image Processing- morphological processing ppt
- 1. Morphological Image Processing (2) Digital Image Processing
- 2. Topics Morphological Operations Connected Component Extraction Convex Hull Thinning Thickening Skeleton Pruning Extension to gray level images Matlab Examples
- 3. Dilation and Erosion Dilation and Erosion are two basic operations in morphological processing. Dilation of a setA in Z2 by a set B in Z2 is denoted by A B and given by
- 4. Dilation The dilation ofA by B is the set of all displacements such that A and overlap with at least one point B is called structuring element
- 5. Dilation
- 6. Erosion Erosion of a set A in Z2 by a set B in Z2 is denoted by and given by: Erosion ofA by B is the set of all points z such that B translated by z is contained inA
- 7. Erosion
- 8. Opening Opening smoothes the outer contours, breaks narrow connections, and eliminates small protrusions. Opening is defined as :
- 9. Closing Closing smoothes the object contour, fuses narrow connections, eliminates small holes and gaps.
- 10. Extraction of Connected Components Begin with a point P inside the connected component, iterate: Until Xk = Xk-1 Initially X0 = P
- 12. Convex Hull A set is said convex if the straight line connecting any two points of the set lies entirely withinA. Convex Hull of set S is the smallest convex setA that contains S The set differenceA-S is called the convex deficiency of S
- 13. Computing Convex Hull Let Bi for i=1,2,3,4 represent the structuring elements shown below
- 14. Convex Hull Repeat the following equation until converge with is the Hit-or-Miss operator Assuming Convex Hull is 4 1 ) ( i i D A C
- 16. Improving Convex Hull Algorithm The algorithm can be improved by limiting the growth of the algorithm beyond the maximum dimensions of the original set.
- 17. Thinning and Thickening Thinning is an image-processing operation in which binary valued image regions are reduced to lines The purpose of thinning is to reduce the image components to their essential information for further analysis and recognition Thickening is changing a pixel from 1 to 0 if any neighbors of the pixel are 1. Thickening followed by thinning can be used for filling undesirable holes. Thinning followed by thickening is used for determining isolated components and clusters.
- 18. Thinning Thinning is defined in terms of hit or miss as where B is a sequence of structuring elements like {B} = {B1, B2, B3, …, Bn} and the operation can be given as
- 19. Thinning Sample set of structuring elements
- 20. Thinning Example
- 21. Thickening Thickening is the morphological dual of thinning and defined as or
- 23. Skeleton The informal definition of a skeleton is a line representation of an object that is: one-pixel thick, through the "middle" of the object, and, preserves the topology of the object.
- 24. Skeleton Skeleton is defined by where k is the last iterative step beforeA erodes to an empty set
- 25. Skeleton Example
- 26. Pruning Thinning and skeletonizing algorithms need a clean-up post- processing The following steps are used for pruning: Thinning Find the end points Dilate end points Find the union of X1 and X3
- 27. Pruning Example Original image and structuring elements
- 28. Pruning Example Result of thinning and end points detected
- 29. Pruning Example Dilation of end points and the pruned image
- 30. Extension to Gray Level Dilation is expressed in 1D as Erosion is given by
- 31. Extension to Gray Level (2D Case) Dilation Erosion
- 32. Morphological Operations in MATLAB To create structuring element use strel(.) SE = strel(shape, parameters) Examples: SE = strel('arbitrary', NHOOD) SE = strel('diamond', R) SE = strel('disk', R, N) SE = strel('line', LEN, DEG) SE = strel('octagon', R) SE = strel('pair', OFFSET) SE = strel('periodicline', P,V) SE = strel('rectangle', MN) SE = strel('square',W)
- 33. Morphological Operations in MATLAB SE=strel(NHOOD) is also a valid call for the function Use imerode(Im,SE) and imdialte(Im,SE) for erosion and dilation respectively Use imopen(Im,SE) and imcolose(Im,SE) for openning and closing For hit-or-miss use bwhitmiss(.) BW2 = bwhitmiss(BW1,SE1,SE2) BW2 = bwhitmiss(BW1,INTERVAL)
- 34. Hit or Miss Example
- 35. Questions?