Digital Image Processing Chapter 9: Morphological Image Processing 5 September 2007

1. Digital Image Processing Chapter 9: Morphological Image Processing 5 September 2007

2. What are Morphological Operations? Morphological operations come from the word “morphing” in Biology which means “changing a shape”. Morphing Image morphological operations are used to manipulate object shapes such as thinning, thickening, and filling. Binary morphological operations are derived from set operations.

3. Basic Set Operations Concept of a set in binary image morphology: Each set may represent one object. Each pixel (x,y) has its status: belong to a set or not belong to a set. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

4. Translation and Reflection Operations Translation Reflection B A z = (z1,z2) (A)z

5. Logical Operations* *For binary images only (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

6. Dilation Operations = Empty set Dilate means “extend” A = Object to be dilated B = Structuring element (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

7. Dilation Operations (cont.) Reflection Structuring Element (B) Intersect pixel Center pixel Original image (A)

8. Dilation Operations (cont.) Result of Dilation Boundary of the “center pixels” where intersects A

9. Example: Application of Dilation “Repair” broken characters (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

10. Erosion Operation Erosion means “trim” A = Object to be eroded B = Structuring element (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

11. Erosion Operations (cont.) Structuring Element (B) Original image (A) Intersect pixel Center pixel

12. Erosion Operations (cont.) Result of Erosion Boundary of the “center pixels” where B is inside A

13. Example: Application of Dilation and Erosion Remove small objects such as noise (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

14. Duality Between Dilation and Erosion where c = complement Proof:

15. Opening Operation or = Combination of all parts of A that can completely contain B Opening eliminates narrow and small details and corners. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

16. Example of Opening (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

17. Closing Operation Closing fills narrow gaps and notches (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

18. Example of Closing (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

19. Duality Between Opening and Closing Properties Opening Properties Closing Idem potent property: can’t change any more

20. Example: Application of Morphological Operations Finger print enhancement (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

21. Hit-or-Miss Transformation * where X = shape to be detected W = window that can contain X (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

22. Hit-or-Miss Transformation (cont.) * (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

23. Boundary Extraction Original image Boundary (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

24. Region Filling where X0 = seed pixel p Results of region filling Original image (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

25. Extraction of Connected Components where X0 = seed pixel p (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

26. Example: Extraction of Connected Components X-ray image of bones Thresholded image Connected components (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

27. Convex Hull * Convex hull has no concave part. Convex hull Algorithm: where (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

28. Example: Convex Hull (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

29. Thinning * * (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

30. Example: Thinning Make an object thinner. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

31. Thickening * * . . . . . Make an object thicker (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

32. Skeletons Dot lines are skeletons of this structure (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

33. Skeletons (cont.) with where k times and

34. Skeletons (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

35. Pruning * = thinning = finding end points = dilation at end points = Pruned result (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

36. Example: Pruning Original image After Thinning 3 times End points Dilation of end points Pruned result

37. Summary of Binary Morphological Operations (Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

38. Summary of Binary Morphological Operations (cont.) (Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

39. Summary of Binary Morphological Operations (cont.) (Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

40. Summary of Binary Morphological Operations (cont.) (Tables from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

41. Basic Types of Structuring Elements x = don’t care (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

42. Gray-Scale Dilation 1-D Case 2-D Case (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

43. Gray-Scale Dilation (cont.) Original image Reflection of B Subimage + Max Moving window Structuring element B Note: B can be any shape and subimage must have the same shape as reflection of B. Output image

44. Gray-Scale Erosion 1-D Case 2-D Case (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

45. Gray-Scale Erosion (cont.) Original image Subimage B - Min Moving window Structuring element B Note: B can be any shape and subimage must have the same shape as B. Output image

46. Example: Gray-Scale Dilation and Erosion Original image After dilation Darker Brighter After erosion (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

47. Gray-Scale Opening Opening cuts peaks (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

48. Gray-Scale Closing Closing fills valleys (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

49. Example: Gray-Scale Opening and Closing Original image After opening After closing Reduce dark objects Reduce white objects (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

50. Gray-scale Morphological Smoothing Smoothing: Perform opening followed by closing Original image After smoothing (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.