1. CS489-02 & CS589-02 Multimedia Processing Lecture 2. Intensity Transformation and Spatial Filtering Spring 2009

2. Spatial Domain vs. Transform Domain  Spatial domain Image plane itself, directly process the intensity values of the image plane  Transform domain Process the transform coefficients, not directly process the intensity values of the image plane 4/27/20152

3. Spatial Domain Process 4/27/20153

4. Spatial Domain Process 4/27/20154

5. Spatial Domain Process 4/27/20155

6. Some Basic Intensity Transformation Functions 4/27/20156

7. Image Negatives 4/27/20157

8. Example: Image Negatives 4/27/20158 Small lesion

9. Log Transformations 4/27/20159

10. Example: Log Transformations 4/27/201510

11. Power-Law (Gamma) Transformations 4/27/201511

12. Example: Gamma Transformations 4/27/201512

13. Example: Gamma Transformations 4/27/201513

14. Piecewise-Linear Transformations  Contrast Stretching — Expands the range of intensity levels in an image ― spans the full intensity range of the recording medium  Intensity-level Slicing — Highlights a specific range of intensities in an image 4/27/201514

15. 4/27/201515

16. 4/27/201516 Highlight the major blood vessels and study the shape of the flow of the contrast medium (to detect blockages, etc.) Measuring the actual flow of the contrast medium as a function of time in a series of images

17. Bit-plane Slicing 4/27/201517

18. Example 4/27/201518

19. Example 4/27/201519

20. Histogram Processing  Histogram Equalization  Histogram Matching  Local Histogram Processing  Using Histogram Statistics for Image Enhancement 4/27/201520

21. Histogram Processing 4/27/201521

22. 4/27/201522

23. Histogram Equalization 4/27/201523

24. Histogram Equalization 4/27/201524

25. Histogram Equalization 4/27/201525

26. Histogram Equalization 4/27/201526

27. Example 4/27/201527

28. Example 4/27/201528

29. Histogram Equalization 4/27/201529

30. Example: Histogram Equalization 4/27/201530 Suppose that a 3-bit image (L=8) of size 64 × 64 pixels (MN = 4096) has the intensity distribution shown in following table. Get the histogram equalization transformation function and give the p s (s k ) for each s k.

31. Example: Histogram Equalization 4/27/201531

32. Example: Histogram Equalization 4/27/201532

33. 4/27/201533

34. 4/27/201534

35. Question Is histogram equalization always good? No 4/27/201535

36. Histogram Matching Histogram matching (histogram specification) —A processed image has a specified histogram 4/27/201536

37. Histogram Matching 4/27/201537

38. Histogram Matching: Procedure  Obtain p r (r) from the input image and then obtain the values of s  Use the specified PDF and obtain the transformation function G(z)  Mapping from s to z 4/27/201538

39. Histogram Matching: Example Assuming continuous intensity values, suppose that an image has the intensity PDF Find the transformation function that will produce an image whose intensity PDF is 4/27/201539

40. Histogram Matching: Example Find the histogram equalization transformation for the input image Find the histogram equalization transformation for the specified histogram The transformation function 4/27/201540

41. Histogram Matching: Discrete Cases  Obtain p r (r j ) from the input image and then obtain the values of s k, round the value to the integer range [0, L- 1].  Use the specified PDF and obtain the transformation function G(z q ), round the value to the integer range [0, L-1].  Mapping from s k to z q 4/27/201541

42. Example: Histogram Matching 4/27/201542 Suppose that a 3-bit image (L=8) of size 64 × 64 pixels (MN = 4096) has the intensity distribution shown in the following table (on the left). Get the histogram transformation function and make the output image with the specified histogram, listed in the table on the right.

43. Example: Histogram Matching 4/27/201543 Obtain the scaled histogram-equalized values, Compute all the values of the transformation function G,

44. Example: Histogram Matching 4/27/201544

45. Example: Histogram Matching 4/27/201545 Obtain the scaled histogram-equalized values, Compute all the values of the transformation function G, s0s0 s2s2 s3s3 s5s5 s6s6 s7s7 s1s1 s4s4

46. Example: Histogram Matching 4/27/201546

47. Example: Histogram Matching 4/27/201547

48. Example: Histogram Matching 4/27/201548

49. Example: Histogram Matching 4/27/201549

50. 4/27/201550

51. Local Histogram Processing 4/27/201551 Define a neighborhood and move its center from pixel to pixel At each location, the histogram of the points in the neighborhood is computed. Either histogram equalization or histogram specification transformation function is obtained Map the intensity of the pixel centered in the neighborhood Move to the next location and repeat the procedure

52. Local Histogram Processing: Example 4/27/201552

53. Using Histogram Statistics for Image Enhancement 4/27/201553 Average Intensity Variance

54. Using Histogram Statistics for Image Enhancement 4/27/201554

55. Using Histogram Statistics for Image Enhancement: Example 4/27/201555

56. Spatial Filtering 4/27/201556 A spatial filter consists of (a) a neighborhood, and (b) a predefined operation Linear spatial filtering of an image of size MxN with a filter of size mxn is given by the expression

57. Spatial Filtering 4/27/201557

58. Spatial Correlation 4/27/201558

59. Spatial Convolution 4/27/201559

60. 4/27/201560

61. Smoothing Spatial Filters 4/27/201561 Smoothing filters are used for blurring and for noise reduction Blurring is used in removal of small details and bridging of small gaps in lines or curves Smoothing spatial filters include linear filters and nonlinear filters.

62. Spatial Smoothing Linear Filters 4/27/201562

63. Two Smoothing Averaging Filter Masks 4/27/201563

64. 4/27/201564

65. Example: Gross Representation of Objects 4/27/201565

66. Order-statistic (Nonlinear) Filters 4/27/201566 — Nonlinear — Based on ordering (ranking) the pixels contained in the filter mask — Replacing the value of the center pixel with the value determined by the ranking result E.g., median filter, max filter, min filter

67. Example: Use of Median Filtering for Noise Reduction 4/27/201567

68. Sharpening Spatial Filters 4/27/201568 ► Foundation ► Laplacian Operator ► Unsharp Masking and Highboost Filtering ► Using First-Order Derivatives for Nonlinear Image Sharpening

69. Sharpening Spatial Filters: Foundation 4/27/201569 ► The first-order derivative of a one-dimensional function f(x) is the difference ► The second-order derivative of f(x) as the difference

70. 4/27/201570

71. Sharpening Spatial Filters: Laplace Operator 4/27/201571 The second-order isotropic derivative operator is the Laplacian for a function (image) f(x,y)

72. Sharpening Spatial Filters: Laplace Operator 4/27/201572

73. Sharpening Spatial Filters: Laplace Operator 4/27/201573 Image sharpening in the way of using the Laplacian:

74. 4/27/201574

75. Unsharp Masking and Highboost Filtering 4/27/201575 ► Unsharp masking Sharpen images consists of subtracting an unsharp (smoothed) version of an image from the original image e.g., printing and publishing industry ► Steps 1. Blur the original image 2. Subtract the blurred image from the original 3. Add the mask to the original

76. Unsharp Masking and Highboost Filtering 4/27/201576

77. Unsharp Masking: Demo 4/27/201577

78. Unsharp Masking and Highboost Filtering: Example 4/27/201578

79. Image Sharpening based on First-Order Derivatives 4/27/201579 Gradient Image

80. Image Sharpening based on First-Order Derivatives z1z1z1z1 z2z2z2z2 z3z3z3z3 z4z4z4z4 z5z5z5z5 z6z6z6z6 z7z7z7z7 z8z8z8z8 z9z9z9z9 4/27/201580

81. Image Sharpening based on First-Order Derivatives z1z1z1z1 z2z2z2z2 z3z3z3z3 z4z4z4z4 z5z5z5z5 z6z6z6z6 z7z7z7z7 z8z8z8z8 z9z9z9z9 4/27/201581

82. Image Sharpening based on First-Order Derivatives 4/27/201582

83. Example 4/27/201583

84. 4/27/201584 Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail

85. 4/27/201585 Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail