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Chapter 3

Chapter 3. Image Enhancement in the Spatial Domain. Outline. Background Basic Gray-level transformation Histogram Processing Arithmetic-Logic Operation Basics of Spatial Filtering Smoothing Spatial Filters Sharpening Spatial Filters Combining Spatial Enhancement Methods

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Chapter 3

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  1. Chapter 3 Image Enhancement in the Spatial Domain

  2. Outline • Background • Basic Gray-level transformation • Histogram Processing • Arithmetic-Logic Operation • Basics of Spatial Filtering • Smoothing Spatial Filters • Sharpening Spatial Filters • Combining Spatial Enhancement Methods • Fuzzy techniques*

  3. Background • Image enhancement approaches fall into two broad categories: spatial domain methods and frequency domain methods. • The term spatial domain refers to the image plane itself. • g(x,y)= T[f(x,y)] , T is an operator on f, defined over some neighborhood of f(x,y)

  4. Size of Neighborhood • Point processing • Larger neighborhood: mask (kernel, template, window) processing

  5. Gray-level Transformation thresholding Contrast stretching

  6. Basic Gray Level Transformation • Image negatives: s =L-1-r • Log transformation: s =clog(1+r) • Power-law transformation: s=crg

  7. Image Negatives

  8. Log Transformation

  9. Gamma Correction (I) • Cathode ray tube (CRT) devices have an intensity-to-voltage response that is a power function, with exponents varying from 1.8 to 2.5.

  10. Gamma Correction (II)

  11. Power-Law Transformation (I)

  12. Power-Law Transformation (II)

  13. Piece-wise Linear Transformation • Contrast stretching • Gray-level slicing(Figure 3.11,12) • Bit-plane slicing(Figures 3.13-15)

  14. Gray-level Slicing

  15. Bit-plane Slicing

  16. Bit-plane Slicing (Example 1)

  17. Bit-plane Slicing (Example 2)

  18. Histogram Processing • The histogram of a digital image with gray-levels in the range [0,L-1] is a discrete function h(rk)=nk where rk is the kth gray level and nk is the number of pixels in the image having gray level rk • Normalized histogram: p(rk)=nk/MN. • Easy to compute, good for real-time image processing.

  19. Four Basic Image Types

  20. Histogram Transformation • T(r) is a monotonically increasing function

  21. Histogram Equalization • What if we take the transformation T to be: • It can be shown that ps(s)=1/(L-1) • Example 3.4 (p.125)

  22. Histogram Equalization: Discrete Case • Example 3.5 (p.126)

  23. Histogram Equalization: Examples

  24. Histogram Matching

  25. Local Histogram Processing

  26. Histogram Statistics • N-th moment of r about its mean:

  27. Logic Operations

  28. Arithmetic Operations • Image Subtraction • Image Averaging

  29. Basics of Spatial Filtering • Mask, convolution kernels • Odd sizes

  30. Spatial Correlation and Convolution Correlation Convolution

  31. Smoothing Spatial Filters • Smoothing linear filters: averaging filters, low-pass filters • Box filter • Weighted average • Order-statistics filters: • Median-filter: removing salt-and-pepper noise • Max filter • Min filter

  32. Smoothing Filters (I)

  33. Smoothing Filters (II)

  34. Sharpening Spatial Filters • Foundation:

  35. The Laplacian • Development of the method:

  36. Image Enhancement

  37. The Gradient Simplification

  38. Combining Spatial Enhancement Methods (a) original (b) Laplacian, (c) a+b, (d) Sobel of (a) (a) (b) (c) (d)

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