Digital Camera and Computer Vision Laboratory

1. Computer and Robot Vision I Chapter 6 Neighborhood Operators Presented by: 林德垣 林德垣 R00944051@.csie.ntu.edu.tw 指導教授: 傅楸善 博士 Digital Camera and Computer Vision Laboratory Department of Computer Science and Information Engineering National Taiwan University, Taipei, Taiwan, R.O.C.

2. 6.1 Introduction neighborhood operator: workhorse of low- level vision neighborhood operator: performs conditioning, labeling, grouping DC & CV Lab. CSIE NTU

3. 6.1 Introduction The output of a neighborhood operator at a given pixel position is a function of the position, of the input pixel value at the position, of the values of the input pixels in some neighborhood around the given input position, and possibly of some values of previously generated output pixels DC & CV Lab. CSIE NTU

4. 6.1 Introduction numeric domain: arithmetic operations, +, -, min, max symbolic domain: Boolean operations, AND, OR, NOT, table-look-up nonrecursive neighborhood operators: output is function of input recursive neighborhood operators: output depends partly on previous output DC & CV Lab. CSIE NTU

5. 6.1 Introduction neighborhood might be small and asymmetric or large DC & CV Lab. CSIE NTU

6. 6.1 Introduction : set of neighboring pixel positions around position general nonrecursive neighborhood operator : input , output  DC & CV Lab. CSIE NTU

7. 6.1 Introduction linear operator: one common nonrecursive neighborhood operator output: possibly position-dependent linear combination of inputs DC & CV Lab. CSIE NTU

8. 6.1 Introduction shift-invariant: position invariant: action same regardless of position composition of shift-invariant operators: shift- invariant [e.g.] N satisfies a Shift invariance: (r’, c’) ∈ N(r,c) (r’- u, c’-v) ∈ N(r-u, c-v) , for all (u,v) DC & CV Lab. CSIE NTU

9. 6.1 Introduction cross-correlation of with : weight function: kernel or mask of weights : domain of   DC & CV Lab. CSIE NTU

10. 6.1 Introduction common masks for noise cleaning, (a) box filter DC & CV Lab. CSIE NTU

11. 6.1 Introduction common masked for noise cleaning DC & CV Lab. CSIE NTU

12. 6.1 Introduction Different N x N filter effects comparison Original Image 3 x 3 5 x 5 9 x 9 15 x 15 35 x 35 DC & CV Lab. CSIE NTU

13. 6.1 Introduction application of mask with weights to image 7.69 DC & CV Lab. CSIE NTU

14. 6.1 Introduction convolution of with convolution: close relative to cross-correlation convolution: linear shift-invariant if mask symmetric, convolution, and correlation the same DC & CV Lab. CSIE NTU

15. 6.2 Symbolic Neighborhood Operators indexing of neighborhoods DC & CV Lab. CSIE NTU

16. 6.2.1 Region-Growing Operator : projection, outputs first or second argument  : background background pixel labeled first nonbackground label  DC & CV Lab. CSIE NTU

17. 6.2.1 Region-Growing Operator 4-connected: output: DC & CV Lab. CSIE NTU

18. 6.2.1 Region-Growing Operator 8-connected: output: DC & CV Lab. CSIE NTU

19. 6.2.1 Region-Growing Operator a7 a2 a6 a3 a0 a1 a8 a4 a5 DC & CV Lab. CSIE NTU

20. 6.2.1 Region-Growing Operator DC & CV Lab. CSIE NTU

21. 6.2.1 Region-Growing Operator DC & CV Lab. CSIE NTU

22. 6.2.1 Region-Growing Operator DC & CV Lab. CSIE NTU

23. 6.2.1 Region-Growing Operator DC & CV Lab. CSIE NTU

24. 6.2.2 Nearest Neighbor Sets and Influence Zones influence zones: nearest neighbor sets influence zones: iteratively region-growing DC & CV Lab. CSIE NTU

25. 6.2.2 Nearest Neighbor Sets and Influence Zones  4-neighborhood for city-block distance e.g. ( i , j ), ( k , l ) : | ( k – i ) | + | ( l – j ) |  8-neighborhood for max distance (of horizontal and vertical distances) e.g. ( i , j ), ( k , l ) : max( | k – i | , | l – j | )  alternate 4, 8-neighborhood for Euclidean distance DC & CV Lab. CSIE NTU

26. Take a Break DC & CV Lab. CSIE NTU

27. 6.2.3 Region-Shrinking Operator region-shrinking: changes all border pixels to background region-shrinking: can change connectivity region-shrinking: can entirely delete region if repeatedly applied DC & CV Lab. CSIE NTU

28. 6.2.3 Region-Shrinking Operator  : whether or not arguments identical  : background border: has different neighbor and becomes background DC & CV Lab. CSIE NTU

29. 6.2.3 Region-Shrinking Operator 4-connected: output: DC & CV Lab. CSIE NTU

30. 6.2.3 Region-Shrinking Operator 8-connected: output: DC & CV Lab. CSIE NTU

31. 6.2.3 Region-Shrinking Operator region shrinking: related to binary erosion except on labeled region DC & CV Lab. CSIE NTU

32. 6.2.3 Region-Shrinking Operator DC & CV Lab. CSIE NTU

33. 6.2.3 Region-Shrinking Operator DC & CV Lab. CSIE NTU

34. 6.2.3 Region-Shrinking Operator DC & CV Lab. CSIE NTU

35. 6.2.3 Region-Shrinking Operator DC & CV Lab. CSIE NTU

36. 6.2.4 Mark-Interior/Border-Pixel Operator mark-interior/border-pixel operator marks all interior pixels with the label and all border pixels with the label DC & CV Lab. CSIE NTU

37. 6.2.4 Mark-Interior/Border-Pixel Operator : whether or not arguments identical  : recognizes whether or not its argument is symbol  DC & CV Lab. CSIE NTU

38. 6.2.4 Mark-Interior/Border-Pixel Operator 4-connected: output: DC & CV Lab. CSIE NTU

39. 6.2.4 Mark-Interior/Border-Pixel Operator 8-connected: output: DC & CV Lab. CSIE NTU

40. 6.2.5 Connectivity Number Operator connectivity number: nonrecursive and symbolic data domain connectivity number: classify the way pixel connected to neighbors six values of connectivity: five for border, one for interior border: isolated, edge, connected, branching, crossing DC & CV Lab. CSIE NTU

41. 6.2.5 Connectivity Number Operator 4-connectivity DC & CV Lab. CSIE NTU

42. 6.2.5 Connectivity Number Operator corner neighborhood DC & CV Lab. CSIE NTU

43. 6.2.5 Connectivity Number Operator DC & CV Lab. CSIE NTU

44. Yokoi Connectivity Number 4-connectivity  : corner transition  : corner all , no transition  : center , neighbor , nothing will happen DC & CV Lab. CSIE NTU

45. Yokoi Connectivity Number 5: no transition all 8 neighbors 1, thus interior  : 1 transition generates one connected component if center removed DC & CV Lab. CSIE NTU

46. Yokoi Connectivity Number 4- Connectivity number DC & CV Lab. CSIE NTU

47. Yokoi Connectivity Number e b d c e b d c DC & CV Lab. CSIE NTU

48. Yokoi Connectivity Number e b d c e b d c DC & CV Lab. CSIE NTU

49. Yokoi Connectivity Number lena.64*64 DC & CV Lab. CSIE NTU

50. Yokoi Connectivity Number lena.yokoi DC & CV Lab. CSIE NTU