1. Morphological Image Processing
Department of Computer Engineering, CMU
Morphological Image Processing

2. More on Hit-and-Miss Transform

3. Hit-and-Miss Transform
hit-and-miss: selects corner points, isolated points, border points
hit-and-miss: performs template matching, thinning, thickening, centering
hit-and-miss: intersection of erosions
J,K kernels satisfy
hit-and-miss of set A by (J,K)
hit-and-miss: to find upper right-hand corner

4. Hit-and-Miss Transform (cont’)

6. Hit-and-Miss Transform (cont’)
J locates all pixels with south, west neighbors part of A
K locates all pixels of Ac with south, west neighbors in Ac
J and K displaced from one another
Hit-and-miss: locate particular spatial patterns

7. Hit-and-Miss Transform (cont’)
hit-and-miss: to compute genus of a binary image

8. Hit-and-Miss Transform (cont’)

9. 5.2.3 Hit-and-Miss Transform (cont’)
hit-and-miss: thickening and thinning
hit-and-miss: counting
hit-and-miss: template matching
DC & CV Lab.
CSIE NTU

10. 5.2.3 Hit-and-Miss Transform (cont’)
hit-and-miss: thickening and thinning
hit-and-miss: counting
hit-and-miss: template matching
DC & CV Lab.
CSIE NTU

11. 5.7 Bounding Second Derivatives
opening or closing a gray scale image simplifies the image complexity

12. 5.8 Distance Transform and Recursive Morphology

13. 5.9 Generalized Distance Transform

14. Distance Transform and Recursive Morphology

15. Distance Applies to binary images For each pixel in a region
distance = minimum path to outside 1 1 2

16. Distance Transform and Recursive Morphology (cont’)
Fig 5.39 (b) fire burns from outside but burns only downward and right-ward

17. Distance Transform and Recursive Morphology

18. Generalized Distance Transform

19. Distance Transform and Recursive Morphology (cont’)
Fig 5.39 (b) fire burns from outside but burns only downward and right-ward

20. Medial Axis

21. Medial Axis
medial axis transform medial axis with distance function

22. Processing grey scale images
Same methods can be applied to greyscale images
Slight redefinition

23. Computation Use erosion Use relationship operator
Label removed pixel with iteration number
Use relationship operator
f(i,j) are neighbours of f(x,y)

24. Skeleton Reduces regions of a binary image to lines one pixel thick
Preserves
Shape
Continuity
How? Uses?

25. Algorithms Thinning Distance Transform Repeatedly thin image
Retain end points and connections
Distance Transform
Skeleton lies along discontinuities
Sort of local maxima or ridges

26. Applications Shape representation, maintaining topology
Character recognition

27. Medial Axis and Morphological Skeleton
morphological skeleton of a set A by kernel K ,where

28. Medial Axis and Morphological Skeleton (cont’)
DC & CV Lab.
CSIE NTU

29. Medial Axis and Morphological Skeleton (cont’)
DC & CV Lab.
CSIE NTU

30. Medial Axis and Morphological Skeleton (cont’)

31. Morphological Sampling Theorem
Before sets are sampled for morphological processing, they must be morphologically simplified by an opening or a closing .
Such sampled sets can be reconstructed in two ways: by either a closing or a dilation.

32. Morphological Shape Feature Extraction
morphological pattern spectrum: shape-size histogram [Maragos 1987]

33. Fast Dilations and Erosions
decompose kernels to make dilations and erosions fast

34. Connectivity
morphology and connectivity: close relation

35. Separation Relation
S separation if and only if S symmetric, exclusive, hereditary, extensive

36. Morphological Noise Cleaning and Connectivity
images perturbed by noise can be morphologically filtered to remove some noise

37. Openings Holes and Connectivity
opening can create holes in a connected set that is being opened

38. Conditional Dilation
select connected components of image that have nonempty erosion conditional dilation J ,
defined iteratively J0 = J
J are points in the regions we want to select
conditional dilation J =Jm
where m is the smallest index Jm=Jm-1

39. DC & CV Lab.
CSIE NTU

40. Generalized Openings and Closings
generalized opening: any increasing, antiextensive, idempotent operation
generalized closing: any increasing. extensive, idempotent operation

41. Hit and Miss (cont’) hit-and-miss: thickening and thinning
hit-and-miss: template matching

42. Hit and Miss (cont’)
hit-and-miss: thickening

43. 450 convex hull
Hit and Miss (cont’)

44. Hit and Miss (cont’)
Octagonal skeleton
DC & CV Lab.
CSIE NTU

45. Hit and Miss (cont’)
hit-and-miss: thinning

46. Hit and Miss (cont’)
hit-and-miss: template matching

47. Openings Closings and Medians
median filter: most common nonlinear noise-smoothing filter
median filter: for each pixel, the new value is the median of a window
median filter: robust to outlier pixel values leaves, edges sharp
median root images: images remain unchanged after median filter

48. Hit-or-Miss Transformation

49. Hit-or-Miss Transformation

50. Morphological edge detection

51. Boundary Extraction = a form of edge detection
Structuring Element
Set A
Boundary of A
A eroded by B

52. Example of morphological edge detection

53. Region Filling

54. Region Filling

55. Region Filling Set A Initial point inside the boundary
Complement of set A
Set A SE
Initial point inside the boundary
Calculations of Xi
Union of X7 and A

56. Example of Region Filling

57. Extraction of Connected Components

58. Extraction of connected components

59. Example: extracting connected components

60. Convex Hull

61. Convex Hull
Convex hull follows outline of object, except for concavities.
Number and shape of regions between convex hull and object are characteristic of object shape.

62. Growth of Convex Hull

63. Convex hull

64. Growth of Convex Hull

65. Problems for students to solve
1. Write a program for thinning with your own set of rules, that transform a kernel (3 by 3 or larger) to a point
2. Write a program for thinning that replaces rectangle to rectangle according to one of sorted rules, about 10 rules.
3. Compare with Zhang and Suen algorithm on images from FAB building interiors

66. More Problems to solve
The slides describe the rules used for the ``binary thinning'' which is applied to the edge images (found using the SUSAN edge detector - see [9,8]) after non-maximum suppression has taken place. The rules are simple and quick to carry out, requiring only one pass through the image. Similar text originally appeared in Appendix B of [7].
Write LISP program with the code of this edge detector and check it on similar images.
For examples and reviews of work on ``skeletonization'' see [6,4,1,2,5]. Implement any of these programs in LISP. Parametrize it.

67. Conclusion
Much work has been done on the thinning of ``thick'' binary images, where attempts are made to reduce shape outlines which are many pixels thick to outlines which are only one pixel thick.
However, because of the non-maximum suppression which is applied before thinning in edge detectors such as SUSAN, this kind of approach is not necessary.

68. Literature
1 R.M. Haralick. Performance characterization in image analysis: Thinning, a case in point. Pattern Recognition Letters, 13:5--12, 1992.
2 P. Kumar, D. Bhatnagar, and P.S. Umapathi Rao. Pseudo one pass thinning algorithm. Pattern Recognition Letters, 12: , 1991.
3 O. Monga, R. Deriche, G. Malandain, and J.P. Cocquerez. Recursive filtering and edge tracking: Two primary tools for 3D edge detection. Image and Vision Computing, 9(4): , 1991.
4 J.A. Noble. Descriptions of Image Surfaces. D.Phil. thesis, Robotics Research Group, Department of Engineering Science, Oxford University, 1989.
5 M. Otte and H.-H. Nagel. Extraction of line drawings from gray value images by non-local analysis of edge element structures. In Proc. 2nd European Conf. on Computer Vision, pages Springer-Verlag, 1992.

69. Literature
6 S. Pal. Some Low Level Image Segmentation Methods, Algorithms and their Analysis. PhD thesis, Indian Institute of Technology, 1991.
7 S.M. Smith. Feature Based Image Sequence Understanding. D.Phil. thesis, Robotics Research Group, Department of Engineering Science, Oxford University, 1992.
8 S.M. Smith. SUSAN -- a new approach to low level image processing. Internal Technical Report TR95SMS1, Defence Research Agency, Chobham Lane, Chertsey, Surrey, UK, Available at for downloading.
9 S.M. Smith and J.M. Brady. SUSAN - a new approach to low level image processing. Int. Journal of Computer Vision, 23(1):45--78, May 1997.

70. Department of Computer Engineering, CMU
SOURCES
Wanasanan Thongsongkrit
Luis O. Jimenez-Rodriguez
傅楸善 & 王林農
指導教授: 傅楸善 博士