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Image Processing

Image HistogramLecture 8

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Image enhancement

The main objective of enhancement techniques is to process an image so the result is more suitable than original image for a specific application

(improve the appearance of an image)  

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•Spatial domain :- Direct manipulation of image pixels•Frequency domain :- Manipulation of Fourier ,wavelet, DCT , haar transforms of an image

Enhancement techniques

Spatial domain

Frequency domain

applications

Block diagram of image enhancement

Poor image I(r , c)

Enhance image E(r , c)

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As a block diagram of image enhancement we use it in :-

•Preprocessing :- to ease the next processing steps ( computer vision)

•Post processing :- to improve the visual perception of processed image( image compression)

•Image enhancement may be an end in itself

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image enhancement techniques

1. image histogram (in spatial domain)

2. image Sharpening 3. image smoothing (in

spatial & frequency domain )

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Image histogram The histogram of an image is a plot of the gray-level values versus the number of pixels at

that value(shows us the distribution of grey levels in the image).

A histogram appear as a graph with ‘brightness‘ on the horizontal axis from 0 to 255 (for an 8-bit

intensity scale) and ‘number of pixels’ on the vertical axis. To find the number of pixels having a

particular brightness within an image, we simply look up the brightness on the horizontal axis .s

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For each colored image three histogram are computed, one for

each component (RGB, HSL).The histogram gives us a convenient -

easy -to -read representation of the concentration of pixels versus

brightness of an image,

using this graph we able to see immediately:

1 Whether an image is basically dark or light and high or low

contrast.

2 Give us our first clues about what contrast enhancement would

be appropriately applied to make the image more subjectively

pleasing to an observer, or easier to interpret by succeeding image

analysis operations.

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So the shape of histogram provide us with information about nature of

the image or sub image if we considering an object within the image. For

example:

1 Very narrow histogram implies a low-contrast image.

2 Histogram skewed to word the high end implies a bright image.

3 Histogram with two major peaks , called bimodal, implies an object

that is in contrast with the background.

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Example:- find & draw the histogram for the sub image2

0 10

10

10

10

22

12

12

12

12

23

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14

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23

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14

14

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20

12

15

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No pixels

Gray level value

4 1o 5 12 5 13 5 14 1 15 2 20 1 22

2 23

23

22

21

20

19

18

17

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15

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12

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10

9

8

7

6

5

4

3

2

1

Gray levels

Nu

mb

er

of

pix

els

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The histogram can be modified or scaled by three methods

1.histogram stretching 2. histogram shrinking 3. histogram sliding

Image histogram modification -:

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The gray level histogram of an

image is the distribution of the

gray level in an image. The

histogram can be modified by

mapping functions, which will

stretch, shrink (compress), or

slide the histogram. Figure below

illustrates a graphical

representation of histogram

stretch, shrink and slide.s

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I(r , c)max is the largest gray-level value in the image I(r , c)

I(r , c)min is the smallest gray level value in the image I(r , c)

Max and min correspond to the maximum and minimum gray-level values

possible(for 8-bit image these are 255 and 0)

Histogram Stretching :

take an image and stretch the histogram across the entire gray-level

range, which has the effect of increasing the contrast of a low

contrast image . the histogram of an image can be stretched by the

following equation

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18Example:- apply histogram stretching for the following sub image values

7 12

8

20

9 6

10

15

1

80.52

147.63

93.94

255 107.36

67.10

120.78

187.89

0I(r, c)max =20 , I(r ,c)min =1 , max=255 , min= 0

I (Stretch)= [7-1/20-1] * [255-0]+0= 80.52 = [12-1/20-1] * [255-0]+0=147.63 = [8-1/20-1] * [255-0]+0=93.94 = [20-1/20-1] * [255-0]+0=255 =[9-1/20-1] * [255-0]+0=107.36 =[6-1/20-1] * [255-0]+0= 67.10 =[10-1/20-1] * [255-0]+0= 120.78 =[15-1/20-1] * [255-0]+0= 187.89 = [1-1/20-1] * [255-0]+0= 0

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Histogram Sliding :- Method can be used to make an image either darker or lighter but retain the relationship between gray-level values. this can be accomplished by simply adding or subtracting a fixed number from all the gray level values as follow

Where the offset value is the amount to slide the histogram ,a positive offset Value will increase the overall brightness where as negative offset will create a darker image

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20

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17 22 18

30 19 16

20 25 11

Example:- apply histogram slide for the following sub image 7 1

28

20

9 6

10

15

1Slide(I(r , c)) = 7+10 = 17 =12+10 = 22 = 8+10 = 18 = 20+10 = 130 =9+10 = 19 =6+10 = 16 = 10+10 = 20 = 15+10 = 25 = 1+10 = 11

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22histogram shrinking :- which will decrease image contrast by compressing the gray Levels. the histogram of an image can be shrink by the following equation

Where:- I(r , c)max is the largest gray-level value in the image I(r , c) I(r , c)min is the smallest gray level value in the image I(r , c)Shrink( Max) , shrink(min) correspond to the maximum and minimum desired in the compressed histogram.

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8.15 10.78 8.6815 9.21 7.639.73 12.36 5

7 12

8

20

9 6

10

15

1Shrink(max)= 15 , shrink(min)= 5I shrink = [15-5/20-1] * [7-1] +5 =8.15 = [15-5/20-1] * [ 12-1]+5=10.78 = [15-5/20-1] * [8-1]+5 =8.68 = [15-5/20-1] * [20-1]+5 =15 = [15-5/20-1] * [9-1]+5 =9.21 = [15-5/20-1] * [6-1]+5 =7.63 = [15-5/20-1] * [10-1]+5 =9.73 = [15-5/20-1] * [15-1]+5 =12.36 = [15-5/20-1] * [1-1]+5 = 5

Example:- apply histogram shrink for the following sub image

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25Image histogram equalization

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Histogram equalization is a technique where the histogram of the

resultant image is as flat as possible (with histogram stretching

the overall shape of the histogram remains the same)

The results in a histogram with a mountain grouped closely

together to "spreading or flatting histogram makes the dark

pixels appear darker and the light pixels appear lighter (the key

word is "appear" the dark pixels in a photograph can not by any

darker. If, however, the pixels that are only slightly lighter

become much lighter, then the dark pixels will appear darker).

 

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The histogram equalization process consists of four

steps

1. Find the running sum of the histogram values

2. Normalize the values from step1 by dividing by total number of

pixels.

3. Multiply the values from step2 by the maximum gray level

value and round.

4. Map the gray-level values to the results from step 3, using a

one-to- one correspondence.

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Example: apply histogram equalization for the following gray- level valuesGray-level values:- 0 1 2 3 4 5 6Histogram values:- 10 8 9 2 14 1 5

0 1 2 3 4 5 6 7

2 4

6 8

10

12 14

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0 1 2 3 4 5 6 7

1

2

3 4

5

6

7

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Step 1: Great a running sum of histogram values. This means that the

first values is 10, the second is 10+8=18, next is 10+8+9=27, and

soon. Here we get 10,18,29,43,44,49,51.

Step 2: Normalize by dividing by total number of pixels. The total

number of pixels is 10+8+9+2+14+1+5+0=51.

 

Step 3: Multiply these values by the maximum gray – level values in

this case 7 , and then round the result to the closet integer. After this is

done we obtain 1,2,4,4,6,6,7,7.

 

Step 4: Map the original values to the results from step3 by a one –to-

one correspondence.

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4 Histogram of the color image:There is one histogram per color band R, G, & B. Luminosity histogram is from 1 band = (R+G+B)/3 There is one histogram per color band R, G, & B. Luminosity histogram is from 1 band = (R+G+B)/3

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14-2-2012Histogram Equalization for the color image: