Image Enhancement and Histogram Equalization in Digital Image Processing.ppt
- 1. 1 Digital Image Processing Histogram Equalization
- 2. 2 Image Enhancement Defined as it is usually used when an image having a distortion and noise present into it which can tend to make a loss of Information in the image to recover that key Information, Enhancement mainly use for removal of noise , sharpening and brightening of an image. Some Mathematical and Logical Operations are used to overcome the noise and to enhance the Image
- 3. 3 Histogram Equalization It is used to enhance the Contrast Contrast is the difference in color that makes an object distinguishable from other objects within the same field of view
- 4. 4 Cumulative Histogram (Exp) 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 Now, Let us take a grayscale image in matrix form. Let each element be a pixel of an image and values of the elements represent intensities of the pixels. We can see that the intensity of the pixels vary between 1-10. Suppose that we want to perform histogram equalization on this image & scale the intensity to 1-20. 4*4 image matrix
- 5. 5 First step is to count the total number of pixels associated with each pixel intensity. Cumulative Histogram (Exp) 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 4*4 image matrix Pixel Intensities (rk) No. of pixel (nk) 1 1 2 3 3 3 4 2 5 2 6 1 7 3 8 1 9 0 10 0 Total 16
- 6. 6 Second step is to calculate probability of each pixel intensity in the image matrix. Total number of element is 16! Probability is no. of pixel divided by total no. of pixels(16). Cumulative Histogram (Exp) Pixel Intensities (rk) No. of pixel (nk) Probability (PDF) 1 1 1/16=0.0625 2 3 3/16=0.1875 3 3 3/16=0.1875 4 2 2/16=0.125 5 2 2/16=0.125 6 1 1/16=0.0625 7 3 3/16=0.1875 8 1 1/16=0.0625 9 0 0/16=0 10 0 0/16=0 Total 16 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 4*4 image matrix
- 7. 7 The next step is to calculate cumulative probability. Cumulative probability (CDF) is equal to previous (PDF) plus current (PDF). 0.0625+0.1875=0.25 & so on.... Pixel Intensities (rk) No. of pixel (nk) Probability (PDF) Cumulative probability(CDF) 1 1 0.0625 0.0625 2 3 0.1875 0.25 3 3 0.1875 0.4375 4 2 0.125 0.5625 5 2 0.125 0.6825 6 1 0.0625 0.75 7 3 0.1875 0.9375 8 1 0.0625 1 9 0 0 1 10 0 0 1 Total 16 Total 1 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 4*4 image matrix Cumulative Histogram (Exp)
- 8. 8 Since we want to change the intensity range to 1-20, we shall multiply cumulative probability by 20. Cumulative probability (CDF) multiply by 20. 0.0625*20=1.25 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 4*4 image matrix Pixel Intensities (rk) No. of pixel (nk) Probability (PDF) Cumulative probability(CDF) Cumulative probability*20 1 1 0.0625 0.0625 1.25 2 3 0.1875 0.25 5 3 3 0.1875 0.4375 8.75 4 2 0.125 0.5625 11.25 5 2 0.125 0.6825 13.75 6 1 0.0625 0.75 15 7 3 0.1875 0.9375 18.75 8 1 0.0625 1 20 9 0 0 1 20 10 0 0 1 20 Total 16 Cumulative Histogram (Exp)
- 9. 9 Finally, we round the decimal values obtained to the lower integer values (also known as floor rounding). Like 13.75 to 13. Cumulative Histogram (Exp) 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 4*4 image matrix Pixel Intensities (rk) No. of pixel (nk) Probability (PDF) C.P(CDF) C.P*20 Floor Rounding 1 1 0.0625 0.0625 1.25 1 2 3 0.1875 0.25 5 5 3 3 0.1875 0.4375 8.75 8 4 2 0.125 0.5625 11.25 11 5 2 0.125 0.6825 13.75 13 6 1 0.0625 0.75 15 15 7 3 0.1875 0.9375 18.75 18 8 1 0.0625 1 20 20 9 0 0 1 20 20 10 0 0 1 20 20 Total 16
- 10. 10 So the original image has been transformed to the equalized image with different intensity on each pixel. 3 2 4 5 7 7 8 2 3 1 2 3 5 4 6 7 4*4 Original image matrix 8 5 11 13 18 18 20 5 8 1 5 8 13 11 15 18 4*4 Transformed image matrix Cumulative Histogram (Exp)
- 11. 11 Cumulative Histogram (Exp) We can see that the intensity range of the pixel have been increased and hence the histogram of the image will look more spread. This in turn is called Histogram Equalization.
- 12. 12 Example1:Perform Histogram Equalization of the Image
- 14. 14 Solution
- 15. 15 Solution
- 16. 16 Arithmetic Operation Between Images There are Array Operations which are carried out between corresponding pixels pairs. The four arithmetic operations are denoted as A(x,y) = f(x,y)+g(x,y) S(x,y) = f(x,y)-g(x,y) p(x,y) = f(x,y)*g(x,y) D(x,y) = f(x,y)/g(x,y) These all arithmetic operations are performed between corresponding pixels pairs.
- 17. 17 Important Points If the result is a floating point number, round off its value If the result is above the pixel range, select the max range value If the result is below the pixel range, select the min range value If the result is infinity, write it as zero
- 18. 18 Addition Uses: • Changing Image Background • Watermark Images
- 19. 19 Subtraction
- 21. 21 Division