1. Chapter 9 Morphological Image Processing

2. Preview Morphology: denotes a branch of biology that deals with the form and structure of animals and planets. Mathematical morphology: tool for extracting image components that are useful in the representation and description of region shapes. Filtering, thinning, pruning.

3. Scope Will focus on binary images. Applicable to other situations. (Higher- dimensional space)

4. Set Theory Empty set Subset Union Intersection Disjoint sets Complement Difference Reflection of set B: Translation of set A by point z=(z 1,z 2 ):

5. Logic Operations AND OR NOT

6. Dilation With A and B as sets in Z 2, the dilation of A by B is defined as: Or, equivalently, B is commonly known as the structuring element.

7. Illustration

8. Example

9. Erosion With A and B as sets in Z 2, the erosion of A by B is defined as: Dilation and erosion are duals:

10. Illustration

11. Example: Removing image components

12. Opening and Closing Opening of set A by structuring element B: Erosion followed by dilation Closing of set A by structuring element B: Dilation followed by erosion

13. Opening Opening generally smoothes the contour of an object, breaks narrow isthmuses, eliminate thin protrusions.

14. Closing Closing tends to smooth contours, fuse narrow breaks and long thin gulfs, eliminate small holes, fill gaps in the contour.

15. Illustration

16. Example

17. Hit-or-Miss Transform Shape detection tool

18. Boundary Extraction Definition:

19. Region Filling Beginning with a point p inside the boundary, repeat: with X 0 =p Until X k =X k-1 Conditional dilation

20. Example

21. Extraction of Connected Component Beginning with a point p of the connected component, repeat: with X 0 =p Until X k =X k-1 The connected component Y=X k

22. Illustration

23. Example

24. Convex Hull A set A is said to be convex if the straight line segment joining any two points in A lies entirely within A. The convex hull H of an arbitrary set S is the smallest convex set containing S. H-S is called the convex deficiency of S. C(A): convex hull of a set A.

25. Algorithm Four structuring elements: B i, i=1,2,3,4 Repeat with X 0 i =A until X k i =X k-1 i to obtain D i The convex hull of A is:

26. Illustration

27. Thinning The thinning of a set A by a structuring element B is defined as:

28. Illustration

29. Thickening

30. Skeleton

31. Skeleton: Definition

32. Illustration

33. Pruning

34. Extension to Gray-Scale Images Dilation  Max Erosion  Min

35. Illustration

36. Opening and Closing

37. Smoothing and Gradient