2. Chapter 3 Image Enhancement in the Spatial Domain

3. 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

4. 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

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

6. Gray-level Transformation Contrast stretchingthresholding

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

8. Image Negatives

9. Log Transformation

10. 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.

11. Gamma Correction (II)

12. Piece-wise Linear Transformation Contrast stretching Gray-level slicing (Figure 3.11) Bit-plane slicing (Figures 3.13-14)

13. Gray-level Slicing

14. Bit-plane Slicing

15. 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 /n. Easy to compute, good for real-time image processing.

16. Four Basic Image Types

17. Histogram Equalization s= T(r) What if we take the transformation T to be: It can be shown that p s (s)=1 Discrete version:

18. Histogram Matching

19. Local Enhancements

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

21. Logic Operations

22. Arithmetic Operations Image Subtraction Image Averaging

23. Basics of Spatial Filtering Mask, convolution kernels Odd sizes

24. 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

25. Sharpening Spatial Filters Foundation:

26. The Laplacian Development of the method:

27. Image Enhancement

28. The Gradient Simplification

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