1. Digital Image Processing Week III
Thurdsak LEAUHATONG

2. Histogram Matching
Problem of Histogram Equalization
Histogram equalization may not always produce desirable results, particularly if the given histogram is very narrow.
It can produce false edges and regions.
It can also increase image “graininess” and “patchiness.”

3. Histogram Matching Transfer to a pre-specified histogram
In this case, transformation that yields an output image with a pre-specified histogram may produce the preferable result.
This technique is called histogram matching.

4. Histogram Matching Algorithm
Perform the histogram equalization of the input image.
Let be the pre-specified PDF of the output image.
Compute the CDF of
HM is the inverse of G(s).
T( )
G-1( ) r s t

5. Histogram Matching Example Intensity ( s ) # pixels 20 1 5 2 25 3 10 4
Histogram of
Input Image
Pre-specified
Histogram
Intensity
( s )
# pixels 20 1 5 2 25 3 10 4 15 6 7
Total
100
Intensity ( t )
# pixels 5 1 10 2 15 3 20 4 6 7
Total
100

6. Histogram Matching Example (cont.) 1. Histogram Equalization of both r
(nj)
SPr s 20
0.2 1 5
0.25 2 25
0.5 3 10
0.6 4 15
0.75
0.8 6
0.9 7
1.0 t
(nj)
SPt v 5
0.05 1 10
0.15 2 15
0.3 3 20
0.5 4
0.7
0.85 6
0.95 7
1.0

7. Histogram Matching Example (cont.) r s 1 2 3 4 5 6 7 v t 1 2 4 3 5 6 7
Actual Output
Histogram r s 1 2 3 4 5 6 7 v t 1 2 4 3 5 6 7 r t 1 2 3 4 5 6 7 t
# Pixels 1 20 2 30 3 10 4 15 5 6 7

8. Histogram Matching Example (cont.) Desired histogram Transfer function
Actual histogram

9. Histogram Matching Example (cont.) Original image After histogram
equalization
After histogram
matching

10. Local Histogram Processing
Global vs Local Histogram Processing
Global Histogram Processing
The intensity of a pixel depends on the PDF of intensities of an entire image.
Local Histogram Processing
The intensity at a position (x,y) depends on the PDF of intensities in a small window whose center locates at (x,y).

11. Local Histogram Processing
Global and Local Statistics
Global Mean and nth Moment
Local Mean and nth moment
Global Mean
Local Mean
Global nth Moment
Local nth Moment

12. Local Histogram Processing
Global and Local Statistics
Global Mean and nth Moment
Local Mean and nth moment
Global Mean
measures the intensity’s average of the entire image.
Global 2nd Moment or called Variance
measures how the intensity of the entire spread about the mean.
It is useful to measure the global contrast of the image.
Local Mean
measures the average of the local intensity.
Local 2nd Moment or called Variance
measures how the local intensity spread about the local mean.
It is useful to measure the local contrast, edge, and texture of the image.

13. Local Histogram Processing
Local Statistics Examples
Original image
Mean 3x3
Mean 5x5

14. Local Histogram Processing
Local Statistics Examples
Standard deviation 3x3
Standard deviation 5x5

15. Local Statistics Processing
Vision Feature
Vision feature
a piece of information which is relevant for solving the computational task related to a certain application.
Intensity : Simple vision feature
Dark Objects
Dark Background
For example
Want to enhance the dark objects.
How to separate the dark objects from the dark background.

16. Local Statistics Processing
Using intensity to detect the dark objects
Assumption:
The dark objects are the areas whose intensity is .
Result:
Cannot separate the dark objects from the dark area.
Intensity is not a good feature to detect the dark objects.

17. Local Statistics Processing
Using local mean to detect the dark objects
Assumption:
The dark objects are the areas whose local mean is .
Result:
Cannot separate the dark objects from the dark area.
Local mean is not a good feature to detect the dark objects.

18. Local Statistics Processing
Using local variance to detect the dark objects
Assumption:
The dark objects are the areas whose local variance is .
Result:
The local variance does not detect the dark backgrounds, but detects both of the bright and dark objects.
Local variance is not a good feature to separate the bright objects from the dark objects.

19. Local Statistics Processing
Using the combination of the local mean and local variance.
Assumption:
The dark objects are the areas whose local mean and local variance are .
Result:
Can well detect the dark objects.
window size 3x3
window size 5x5
window size 7x7

20. Local Statistics Processing
Using the local statistics to enhance the dark objects.
Original Image
window size 3x3