Chapter 9. Morphological Image Processing

1. Chapter 9. Morphological Image Processing Introduction Morphology: a branch of biology that deals with the form and structure of animals and plants Morphological image processing is used to extract image components for representation and description of region shape, such as boundaries, skeletons, and the convex hull

2. Preliminaries (1) • Reflection • Translation

3. Example: Reflection and Translation

4. Preliminaries (2) • Structure elements (SE) Small sets or sub-images used to probe an image under study for properties of interest origin

5. Examples: Structuring Elements Accommodate the entire structuring elements when its origin is on the border of the original set A Origin of B visits every element of A At each location of the origin of B, if B is completely contained in A, then the location is a member of the new set, otherwise it is not a member of the new set.

6. Erosion

7. Example of Erosion (1)

8. Example of Erosion (2)

9. Dilation

10. Examples of Dilation (1)

11. Examples of Dilation (2)

12. Erosion and dilation are duals of each other with respect to set complementation and reflection Duality

13. Erosion and dilation are duals of each other with respect to set complementation and reflection Duality

14. Erosion and dilation are duals of each other with respect to set complementation and reflection Duality

15. Opening generally smoothes the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions Closing tends to smooth sections of contours but it generates fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour Opening and Closing

16. Opening and Closing

17. Opening

18. Example: Opening

19. Example: Closing

21. Opening and closing are duals of each other with respect to set complementation and reflection Duality of Opening and Closing

22. Properties of Opening Properties of Closing The Properties of Opening and Closing

24. The Hit-or-Miss Transformation

25. Boundary Extraction The boundary of a set A, can be obtained by first eroding A by B and then performing the set difference between A and its erosion. Some Basic Morphological Algorithms (1)

26. Example 1

27. Example 2

28. Gray-Scale Morphology

29. Gray-Scale Morphology: Erosion and Dilation by Flat Structuring

31. Gray-Scale Morphology: Erosion and Dilation by Nonflat Structuring

32. Duality: Erosion and Dilation

33. Opening and Closing

35. Properties of Gray-scale Opening

36. Properties of Gray-scale Closing

38. Opening suppresses bright details smaller than the specified SE, and closing suppresses dark details. Opening and closing are used often in combination as morphological filters for image smoothing and noise removal. Morphological Smoothing

39. Morphological Smoothing

40. Dilation and erosion can be used in combination with image subtraction to obtain the morphological gradient of an image, denoted by g, The edges are enhanced and the contribution of the homogeneous areas are suppressed, thus producing a “derivative-like” (gradient) effect. Morphological Gradient

41. Morphological Gradient