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Statistical Operations - PowerPoint PPT Presentation


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Statistical Operations. Gray-level transformation Histogram equalization Multi-image operations. 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++) {

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statistical operations
Statistical Operations
  • Gray-level transformation
  • Histogram equalization
  • Multi-image operations

240-373 Image Processing

histogram
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]]++;

}

240-373 Image Processing

histogram1
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.

240-373 Image Processing

histogram illustration
Histogram Illustration

Histogram

10

9

1 2 3 2 3 2

0 0 1 2 1 4

4 4 2 1 2 1

1 2 1 2 1 2

5 4 2 1 4 0

8

7

6

5

4

3

2

1

0

0

1

2

3

4

5

240-373 Image Processing

global attenuation in brightness
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;

}

240-373 Image Processing

thresholding
Thresholding
  • Use:
    • 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

240-373 Image Processing

code for thresholding
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;

}

240-373 Image Processing

thresholding errors
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

240-373 Image Processing

bunching quantizing
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

240-373 Image Processing

bunching quantizing1
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

240-373 Image Processing

bunching example
Bunching Example

0 ****

1 **

2 *****

3 *********

4 *****

5 *****

6 *****

7 *****

8 *********

9 ***

0 ******

1

2

3 *******************

4

5

6 ***************

7

8

9 ************

240-373 Image Processing

bunching code
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

240-373 Image Processing

splittings
Splittings
  • Use:
    • 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

240-373 Image Processing

splitting example
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?

240-373 Image Processing

automatic selection of splitting level
Automatic Selection of Splitting Level
  • Use:
    • to find the best gray level for splitting--usually for thresholding to black and white
  • Operation:
    • Let

240-373 Image Processing

automatic selection of splitting level1
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

240-373 Image Processing

example
Example

Histogram f(g) t(g) g.f(g) Sg.f(g) m(g) A B A*B

0 **** 4 4 0 0 0 0.08 23.04 0.18

1 ** 2 6 2 2 0.3 0.13 20.25 2.83

2 ***** 5 11 10 12 1.1 0.27 13.69 3.70

3 ********* 9 20 27 39 2 0.63 7.84 4.94

4 ***** 5 25 20 59 2.4 0.93 5.76 5.36

5 ***** 5 30 25 84 2.8 1.36 4.00 5.44

6 ***** 5 35 30 114 3.3 2.06 2.25 4.64

7 ***** 5 40 35 149 3.7 3.33 1.21 4.03

8 ********* 9 49 72 221 4.5 16.33 0.09 1.47

9 *** 3 52 27 248 4.8 -INF-

T = max(A*B) - 1 = 4

240-373 Image Processing