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# Enhancement in frequency domain

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### Enhancement in frequency domain

1. 1. Image Enhancement in theFrequency Domain
2. 2. Basic steps for filtering in thefrequency domain 2
3. 3. Basics of filtering in the frequency domain1. multiply the input image by (-1)x+y to center the transform to u = M/2 and v = N/2 (if M and N are even numbers, then the shifted coordinates will be integers)2. computer F(u,v), the DFT of the image from (1)3. multiply F(u,v) by a filter function H(u,v)4. compute the inverse DFT of the result in (3)5. obtain the real part of the result in (4)6. multiply the result in (5) by (-1)x+y to cancel the multiplication of the input image. 3
4. 4. Notch filter• this filter is to force the F(0,0)which is the average value of animage (dc component of thespectrum)• the output has prominent edges• in reality the average of thedisplayed image can’t be zero asit needs to have negative graylevels. the output image needs toscale the gray level 0 if (u, v) = (M/2, N/2 ) H (u , v) =  1 otherwise4
5. 5. Low pass filterhigh pass filter5
6. 6. Add the ½ of filter height toF(0,0) of the high pass filter 6
7. 7. Correspondence between filterin spatial and frequency domains 7
8. 8. Smoothing Frequency-domainfilters: Ideal Lowpass filter 8
9. 9. image power circles 9
10. 10. Result of ILPF 10
11. 11. Example 11
12. 12. Butterworth Lowpass Filter:BLPF 12
13. 13. Example 13
14. 14. Spatial representation of BLPFs 14
15. 15. Gaussian Lowpass Filter: GLPF 15
16. 16. Example 16
17. 17. Example 17
18. 18. Example 18
19. 19. Example 19
20. 20. Sharpening Frequency Domain Filter: Ideal highpass filter 0 if D(u, v) ≤ D 0H (u , v) =  1 if D(u, v) > D 0Butterworth highpass filter 1H (u , v) = 1 + [ D 0 D(u , v)] 2nGaussian highpass filter − D 2 ( u ,v ) / 2 D0 2 H (u , v) = 1 − e 20
21. 21. Spatial representation of Ideal,Butterworth and Gaussian highpassfilters 21
22. 22. Example: result of IHPF 22
23. 23. Example: result of BHPF 23
24. 24. Example: result of GHPF 24
25. 25. Laplacian in the Frequencydomain 25
26. 26. Example: Laplacian filteredimage 26
27. 27. Example: high-boost filter 27
28. 28. Examples 28
29. 29. Homomorphic Filter 29
30. 30. Result of Homomorphic filter 30
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