1. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 9 Morphological Image Processing Chapter 9 Morphological Image Processing

2. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Concepts from Set Theory

3. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Concepts from Set Theory Translation Reflection

4. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Logic Operations Involving Binary Images

5. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Logic Operations Involving Binary Images AB

6. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Dilation and Erosion Dilation Dilation and Erosion Dilation With A and B as sets in Z 2, the dilation of A by B is defined as where : the reflection of B about its origin and shifting this reflection by z The dilation of A by B is the set of all displacements, z, such that and A overlap by at least one element. Thus, Set B is referred to as the structuring element in dilation.

7. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Dilation and Erosion Dilation Dilation and Erosion Dilation

8. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Dilation and Erosion Dilation Example Dilation and Erosion Dilation Example Structuring element

9. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Dilation and Erosion Erosion Dilation and Erosion Erosion For sets A and B in Z 2, the erosion of A by B is defined as where : the reflection of B about its origin and shifting this reflection by z The erosion of A by B is the set of all points z, such that B, translated by z is contained in A.

10. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Dilation and Erosion Erosion Dilation and Erosion Erosion

11. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Dilation and Erosion Erosion Example Dilation and Erosion Erosion Example

12. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing Opening: –smooth the contour of an object, break narrow isthmuses, and eliminate thin protrusions. –The opening A by B is the erosion of A by B, followed by a dilation of the result by B Closing: –smooth sections of contours but it generally fuses narrow breaks and long thing gulfs, eliminates small holes, and fills gaps in the contour.

13. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing Opening Opening and Closing Opening

14. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing Closing Opening and Closing Closing

15. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing Opening Example Opening and Closing Opening Example

16. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing Closing Example Opening and Closing Closing Example

17. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing The opening operation satisfies the following properties: – is a subset (subimage) of A. –If C is a subset of D, then is a subset of. – The closing operation satisfies the following properties: –A is a subset (subimage) of. –If C is a subset of D, then is a subset of. –

18. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Opening and Closing

19. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods The Hit-or-Miss Transformation ＊

20. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods The Hit-or-Miss Transformation ＊

21. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Boundary Extraction Some Basic Morphological Algorithms Boundary Extraction The boundary of a set A, where B is a suitable structuring element.

22. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Boundary Extraction Example Some Basic Morphological Algorithms Boundary Extraction Example

23. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Region Filling Some Basic Morphological Algorithms Region Filling The following procedure can fill the region: where X 0 = p, and B is the symmetric structuring element shown in Fig. 9.15. Note that p is the initial point we should assign.

24. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Region Filling Some Basic Morphological Algorithms Region Filling X 0 =p 0 1

25. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Region Filling Some Basic Morphological Algorithms Region Filling

26. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Extraction of Connected Components Some Basic Morphological Algorithms Extraction of Connected Components

27. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Extraction of Connected Components Some Basic Morphological Algorithms Extraction of Connected Components

28. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Thinning Some Basic Morphological Algorithms Thinning The thinning of a set A by a structuring element B can be defined in terms of the hit-or-miss transform: A more useful expression for thinning A symmetrically is based on a sequence of structuring elements: ＊ ＊

29. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Thinning Some Basic Morphological Algorithms Thinning

30. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Some Basic Morphological Algorithms Skeletons Some Basic Morphological Algorithms Skeletons

31. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Summary of Morphological Operations and Their Properties Summary of Morphological Operations and Their Properties

32. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Summary of Morphological Operations and Their Properties Summary of Morphological Operations and Their Properties

33. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Summary of Morphological Operations and Their Properties Summary of Morphological Operations and Their Properties

34. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Summary of Morphological Operations and Their Properties Summary of Morphological Operations and Their Properties

35. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Extensions to Gray-Scale Images

36. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Extensions to Gray-Scale Images

37. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Extensions to Gray-Scale Images