1. Lecture Six
Figures from Gonzalez and Woods, Digital Image Processing, Second Edition, Copyright 2002.

2. Histogram Function(1)
Dark Images- Histogram components are concentrated on dark side
Bright images- Components on light side
Low-contrast images- Components clustered
High contrast images- Spread out.

3. Histogram Function (2)
Normalize gray level to interval [0,1], r<- r/(L-1)
Thus

4. Histogram Function (3)
We need to compute

5. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

6. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

7. Histogram Matching
Histogram Equalization does not always yield good images with high contrast. Sometime it is better to ask that the gray values fix a specified distribution

8. Histogram Matching (2)
Computation of the function

9. Histogram Matching Algorithm
Obtain histogram of given image
Compute a table lookup function mapping s =T(r).
Repeated using a binary search algorithm, construct s=G(z) to get inverse of G.
For each pixel in the image, map r value to s value to z value using steps (2) and (3).

10. Table Lookup function

11. Table Lookup for inverse

12. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

13. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

14. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

15. Histogram Equalization
Results in washed out image
Does not necessarily increase detail
Better to specify gray value distribution that still yields a dark image

16. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

17. Histogram Matching on Moon
This just pushes the gray values to the right a bit. Distribution ends up quite similar.

18. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

19. Localized Histogram Equalization
Chose neighborhood of (x,y) and equalize histogram over that neighborhood
Brings out local phenomena

20. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

21. Histogram Statistics
Local mean and variance

22. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

23. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

24. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

25. Logical Operations NOT, AND, OR NOT – same as negative
AND – good for using white portion to select part of an image
OR– good for using black portion to select part of an image

26. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

27. Image Subtraction g(x,y) =f(x,y)-h(x,y)
Used to bring out details of f(x,y) or enhance differences.
In medical images where contrast medium is inserted, this value is subtracted out.

28. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

29. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

30. Image Averaging

31. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

32. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

33. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

34. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

35. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

36. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

37. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain