1. Digital Image Processing
Image Enhancement
Part II

2. Intensity Histogram

3. Intensity Histogram
Example
a 4x4, 4bits/pixel image 

4. From [Gonzalez & Woods]
Intensity Histogram
From [Gonzalez & Woods]

5. From [Gonzalez & Woods]
Intensity Histogram
From [Gonzalez & Woods]

6. Fixed Intensity Transformations

7. Basic Transformations
Negative:
Log:
Inverse Log:
Power-law: ……
From [Gonzalez & Woods]

8. Negative Transformation
From [Gonzalez & Woods]

9. From [Gonzalez & Woods]
Log Transformation
From [Gonzalez & Woods]

10. Power-law (Gamma) Transformation
From [Gonzalez & Woods]

11. Power-law (Gamma) Transformation
From [Gonzalez & Woods]

12. Power-law (Gamma) Transformation
From [Gonzalez & Woods]

13. From [Gonzalez & Woods]
Thresholding
m : threshold
From [Gonzalez & Woods]

14. Example: Fixed Intensity Transformation
A 4x4, 4bits/pixel image passes through
an intensity transformation
1  round(0.0667) = 0;
3  round(0.6) = 1;
6  round(2.4) = 2;
7  round(3.2667) = 3;
8  round(4.2667) = 4;
9  round(5.4) =5;
10  round(6.6667) = 7;
11  round(8.0667) = 8;
The resulting
image is:

15. Example: Histogram Change

16. Contrast Stretch

17. General Idea: Make Best Use of the Dynamic Range
From [Gonzalez & Woods]

18. Contrast Stretch General form:
Special case  Full-scale contrast stretch:
Typically used:

19. Example: Full-Scale Contrast Stretch
Full-scale contrast stretch of a 4x4, 4bits/pixel image
Find
4  round(0) = 0;
6  round(4.29) = 4;
7  round(6.43) = 6;
8  round(8.57) = 9;
9  round(10.71) = 11;
10  round(12.86) = 13;
11  round(15) = 15;
The resulting
image is:

20. Example: Histogram Change

21. Histogram Equalization

22. Histogram Equalization
From [Gonzalez & Woods]

23. Histogram Equalization
From [Gonzalez & Woods]

24. Example A 4x4, 4bits/pixel image
First try: full-scale contrast stretch
2  round(0) = 0;
3  round(1.67) = 2;
8  round(10.00) = 10;
9  round(11.67) = 12;
10  round(13.33) = 13;
11  round(15) = 15;
The resulting
image is:

25. Example: Histogram Change
full-scale contrast stretch
original 
big gap

26. Cumulative Histogram
H(k)
Q(k)

27. Intermediate Image
intermediate image
original 

28. Full-Scale Contrast Stretch of Intermediate Image
2  round(0) = 0;
6  round(4.29) = 4;
9  round(7.50) = 8;
12  round(10.71) = 11;
14  round(12.86) = 13;
16  round(15) = 15;
final result:
histogram equalized image

29. direct full-scale contrast stretch
Histogram Comparison
original
direct full-scale contrast stretch
histogram-equalized
more equalized

30. Summary of the Histogram Equalization Algorithm
original image
histogram H(k)
cumulative histogram Q(k)
intermediate image
full-scale contrast stretch
histogram-equalized image