1. Digital Image Processing Chapter 9: Morphological Image Processing 5 September 2007 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. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. 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.

4. Translation and Reflection Operations A (A) z z = (z 1,z 2 ) TranslationReflection B

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

24. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Region Filling Original image Results of region filling where X 0 = seed pixel p

25. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Extraction of Connected Components where X 0 = seed pixel p

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, 2 nd Edition.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

51. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Gradient Original image Morphological Gradient

52. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Top-Hat Transformation Original image Results of top-hat transform

53. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Texture Segmentation Application Algorithm: 1. Perform closing on the image by using successively larger structuring elements until small blobs are vanished. 2. Perform opening to join large blobs together 3. Perform intensity thresholding Original imageSegmented result Small blob Large blob

54. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Example: Granulometry Objective: to count the number of particles of each size Method: 1. Perform opening using structuring elements of increasing size 2. Compute the difference between the original image and the result after each opening operation 3. The differenced image obtained in Step 2 are normalized and used to construct the size-distribution graph. Original image Size distribution graph

55. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

56. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

57. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

58. Surface of at edges look like mountain ridges. Original image Gradient Image

59. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

60. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

61. (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2 nd Edition. Morphological Watershads

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