1. 1 © 2010 Cengage Learning Engineering. All Rights Reserved. 1 Introduction to Digital Image Processing with MATLAB ® Asia Edition McAndrew ‧ Wang ‧ Tseng Chapter 5: Neighborhood Processing

2. 2 © 2010 Cengage Learning Engineering. All Rights Reserved. 5.1 Introduction Move a mask A rectangle (usually with sides of odd length) or other shape over the given image Ch5-p.87

3. 3 5.1 Introduction © 2010 Cengage Learning Engineering. All Rights Reserved. Mask values Ch5-p.88

4. 4 5.1 Introduction © 2010 Cengage Learning Engineering. All Rights Reserved. Corresponding pixel values Ch5-p.88

5. 5 FIGURE 5.2 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.89

6. 6 5.1 Introduction © 2010 Cengage Learning Engineering. All Rights Reserved. Allied to spatial filtering is spatial convolution The filter must be rotated by 180° before multiplying and adding Ch5-p.89

7. 7 5.1 Introduction © 2010 Cengage Learning Engineering. All Rights Reserved. EXAMPLE One important linear filter is to use a 3×3 mask and take the average of all nine values within the mask Ch5-p.90

8. 8 5.1 Introduction © 2010 Cengage Learning Engineering. All Rights Reserved. The result of filtering x with 3×3 averaging filter Ch5-p.90

9. 9 5.2 Notation © 2010 Cengage Learning Engineering. All Rights Reserved. It is convenient to describe a linear filter simply in terms of the coefficients of all the gray values of pixels within the mask The averaging filter Ch5-p.91-92

10. 10 5.2 Notation © 2010 Cengage Learning Engineering. All Rights Reserved. EXAMPLE The filter would operate on gray values as Ch5-p.92

11. 11 5.2.1 Edges of the Image © 2010 Cengage Learning Engineering. All Rights Reserved. What happens at the edge of the image, where the mask partly falls outside the image? There are a number of different approaches to dealing with this problem Ch5-p.92

12. 12 5.2.1 Edges of the Image © 2010 Cengage Learning Engineering. All Rights Reserved. Ignore the edges Pad with zeros 000 0 0000000000 0 0 0 0 0 0 0 0 0 000000000000 0 0 000 Ch5-p.92

13. 13 5.2.1 Edges of the Image © 2010 Cengage Learning Engineering. All Rights Reserved. Mirroring 2 2 3 4 5 4 3 2 1 2 3 4 4 3456734567 3456734567 6 5 4 3 2 1 2 3 4 5 7 7 6 5 4 3 2 1 2 3 4 5 5 3456534565 34563456 Ch5-p.93

14. 14 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. filter2 function shape is optional; it describes the method for dealing with the edges ‘same’- pad with zeros ‘valid’- ignore the edges the result is a matrix of data type double!! Ch5-p.93

15. 15 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.93

16. 16 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.94

17. 17 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. The result of ’same’ may also be obtained by padding with zeros and using ’valid’: Ch5-p.94

18. 18 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. filter2(filter,image,’full’) returns a result larger than the original It does this by padding with zero and applying the filter at all places on and around the image where the mask intersects the image matrix Ch5-p.94

19. 19 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.94

20. 20 5.3 Filtering in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. filter2 provides no mirroring option The mirroring approach can be realized by placing the following codes before filter2 (filter,image,’valid’) Ch5-p.95

21. 21 © 2010 Cengage Learning Engineering. All Rights Reserved. 5.3 Filtering in M ATLAB Where matrix x is extended to m_x, wr/wc is defined as one half total column/row number of the mask (chopping the decimal) Ch5-p.95

22. 22 © 2010 Cengage Learning Engineering. All Rights Reserved. 5.3 Filtering in M ATLAB fspecial function h = fspecial(type, parameters) >>imshow(uint8(cf1)) >>imshow(cf1/255) or Ch5-p.95

23. 23 FIGURE 5.4 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.97

24. 24 5.4 Frequencies: Low- and High-Pass Filters © 2010 Cengage Learning Engineering. All Rights Reserved. Frequencies of an image are a measure of the amount by which gray values change with distance high-pass filter low-pass filter Ch5-p.98

25. 25 5.4 Frequencies: Low- and High-Pass Filters © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.99

26. 26 FIGURE 5.5 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.100

27. 27 5.4 Frequencies: Low- and High-Pass Filters © 2010 Cengage Learning Engineering. All Rights Reserved. VALUES OUTSIDE THE RANGE 0–255 Make negative values positive Clip values Ch5-p.100

28. 28 5.4 Frequencies: Low- and High-Pass Filters © 2010 Cengage Learning Engineering. All Rights Reserved. 0-255 Scaling transformation (uint8) Ch5-p.101

29. 29 © 2010 Cengage Learning Engineering. All Rights Reserved. 5.4 Frequencies: Low- and High-Pass Filters 0-1 Scaling transformation (double) Ch5-p.101-102

30. 30 © 2010 Cengage Learning Engineering. All Rights Reserved. FIGURE 5.6 Ch5-p.102

31. 31 5.5 Gaussian Filters © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.103

32. 32 FIGURE 5.8 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.104

33. 33 5.5 Gaussian Filters © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.104

34. 34 FIGURE 5.9 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.105

35. 35 5.6 Edge Sharpening © 2010 Cengage Learning Engineering. All Rights Reserved. 5.6.1 Unsharp Masking Ch5-p.106

36. 36 FIGURE 5.11 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.107

37. 37 FIGURE 5.12 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.107

38. 38 5.6.1 Unsharp Masking © 2010 Cengage Learning Engineering. All Rights Reserved. The unsharp option of fspecial produces such filters α = 0.5 Ch5-p.108

39. 39 FIGURE 5.13 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.109

40. 40 5.6.2 High-Boost Filtering © 2010 Cengage Learning Engineering. All Rights Reserved. Allied to unsharp masking filters are the high- boost filters where A is an amplification factor If A = 1, then the high-boost filter becomes an ordinary high-pass filter Ch5-p.109

41. 41 5.6.2 High-Boost Filtering © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.111

42. 42 FIGURE 5.14 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.111 >> x1=filter2(hb1, x); >> imshow(x1/255) >> x2=filter2(hb2, x); >> imshow(x2/255)

43. 43 5.7 Nonlinear Filters © 2010 Cengage Learning Engineering. All Rights Reserved. Maximum filter Minimum filter Ch5-p.112

44. 44 FIGURE 5.15 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.113

45. 45 5.8 Region of Interest Processing © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.115

46. 46 5.8.1 Regions of Interest in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.115-116

47. 47 5.8.1 Regions of Interest in M ATLAB © 2010 Cengage Learning Engineering. All Rights Reserved. This will bring up the iguana image (if it isn’t shown already). Vertices of the ROI can be selected with the mouse Ch5-p.116

48. 48 5.8.2 Region of Interest Filtering © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.116

49. 49 FIGURE 5.18 © 2010 Cengage Learning Engineering. All Rights Reserved. Ch5-p.117