1. Statistical Operations
Gray-level transformation
Histogram equalization
Multi-image operations
Image Processing

2. Histogram
If the number of pixels at each gray level in an image is counted (may use the following code fragment)
for (row=0; row<rowmax; roww++)
for (col=0; col=colmax; col++) {
count[image[row,col]]++; }
Image Processing

3. Histogram
The array “count” can be plotted to represent a “histogram” of the image as the number of pixels at particular gray level
The histogram can yield useful information about the nature of the image. An image may be too bright or too dark.
Image Processing

4. Histogram Illustration10 9 8 7 6 5 4 3 2 1 1 2 3 4 5
Image Processing

5. Global Attenuation in Brightness
To alter the brightness of an image by adding or subtracting all pixel values with a constant
for (row=0; row<rowmax; roww++)
for (col=0; col=colmax; col++) {
image[row,col] += constant; }
Image Processing

6. Image Processing

7. Image Processing

8. Image Processing

9. Image Processing

10. Thresholding Use: Operation:
To remove the gray level trends in an image
To make gray level more discrete
To segment or split an image into distinct parts
Operation:
setting all gray levels below a certain level to “zero”, and above a certain level to a maximum brightness
Image Processing

11. Code for Thresholding for (row=0; row<rowmax; roww++)
for (col=0; col=colmax; col++) {
if (image[row,col] > threshold)
image[row,col] = MAX;
else
image[row,col] = MIN; }
Image Processing

12. Image Processing

13. Thresholding Errors
Rarely is it possible to identify a perfect gray level break, what we want to be background pixels become foreground or vice versa
Type 1: not all pixels caught that should be included
Type 2: some pixels caught should not be included in the group
Image Processing

14. An image before and after thresholding
Image Processing

15. Bunching (Quantizing)
Use:
to reduce the number of different gray level in an image
to segment an image
to remove unwanted gray level degradation
Operation:
Close gray levels are combined, thus removing unwanted variations in data
Image Processing

16. Bunching (Quantizing)
Method 1: inspecting histogram and combining close group into single gray level
Method 2: identifying a set of gray levels allowed in the final image, then changing the gray level in every pixel to its nearest allowed value
Image Processing

17. Bunching Example 0 **** 0 ****** 1 ** 1 2 ***** 2 3 *********
0 ****
1 **
2 *****
3 *********
4 *****
5 *****
6 *****
7 *****
8 *********
9 ***
0 ****** 1 2
3 ******************* 4 5
6 *************** 7 8
9 ************
Image Processing

18. Bunching Code for (row=0; row<rowmax; row++)
for (col=0; col<colmax; col++) {
image[row,col] = bunchsize*((int)image[row,col]/bunchsize); }
bunchsize = number of levels to be grouped into one
Image Processing

19. Splittings Use: Operation:
to increase the different two groups of gray levels so that the contrast between segments compose of one group of the other is enhanced
Operation:
rounding the gray levels up if they are in the range and down if they are in another
Image Processing

20. Splitting Example
The characters on a car number-plate are at gray level 98
The background of the characters is at gray level 99
Pushing 98 down to 80 and pushing 99 up to 120 will give the picture a better contrast around the number plate
Question: How to find a good splitting level?
Image Processing

21. Automatic Selection of Splitting Level
Use:
to find the best gray level for splitting--usually for thresholding to black and white
Operation:
Let
Image Processing

22. Automatic Selection of Splitting Level
Let P=NxM = the number of pixels under consideration
Let m(g) = mean gray level for only those pixels containing gray level between zero and g, i.e.
If the maximum number of gray level is G (G=0,…,G-1) then evaluate the following equation (T = splitting threshold) A B
Image Processing

23. Example
Histogram f(g) t(g) g.f(g) Sg.f(g) m(g) A B A*B
0 ****
1 **
2 *****
3 *********
4 *****
5 *****
6 *****
7 *****
8 *********
9 *** INF-
T = max(A*B) - 1 = 4
Image Processing