Enhancement in frequency domain
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  • 1. Image Enhancement in theFrequency Domain
  • 2. Basic steps for filtering in thefrequency domain 2
  • 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. 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. Low pass filterhigh pass filter5
  • 6. Add the ½ of filter height toF(0,0) of the high pass filter 6
  • 7. Correspondence between filterin spatial and frequency domains 7
  • 8. Smoothing Frequency-domainfilters: Ideal Lowpass filter 8
  • 9. image power circles 9
  • 10. Result of ILPF 10
  • 11. Example 11
  • 12. Butterworth Lowpass Filter:BLPF 12
  • 13. Example 13
  • 14. Spatial representation of BLPFs 14
  • 15. Gaussian Lowpass Filter: GLPF 15
  • 16. Example 16
  • 17. Example 17
  • 18. Example 18
  • 19. Example 19
  • 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. Spatial representation of Ideal,Butterworth and Gaussian highpassfilters 21
  • 22. Example: result of IHPF 22
  • 23. Example: result of BHPF 23
  • 24. Example: result of GHPF 24
  • 25. Laplacian in the Frequencydomain 25
  • 26. Example: Laplacian filteredimage 26
  • 27. Example: high-boost filter 27
  • 28. Examples 28
  • 29. Homomorphic Filter 29
  • 30. Result of Homomorphic filter 30
  • 31. 31
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