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. 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) Background

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

5. Gray-level Transformation Contrast stretching thresholding

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

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(r k )=n k where r k is the kth gray level and n k is the number of pixels in the image having gray level r k Normalized histogram: p(r k )=n k /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 p s (s)=1/(L-1) Example 3.4 (p.125)

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

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)