Enhancement in frequency domain
Download as PPT, PDF12 likes13,053 views
This document discusses various frequency domain image filtering techniques. It outlines the basic steps for filtering in the frequency domain which includes centering the Fourier transform, computing the discrete Fourier transform, multiplying by a filter function, computing the inverse transform and canceling centering operations. Specific filters are then described including low pass, high pass, ideal filters and Butterworth filters. Examples of applying these filters to images are provided to demonstrate the effects. Homomorphic filtering is also introduced as a technique for illumination correction.
![Sharpening Frequency Domain
Filter:
Ideal highpass filter
0 if D(u, v) ≤ D 0
H (u , v) =
1 if D(u, v) > D 0
Butterworth highpass filter
1
H (u , v) =
1 + [ D 0 D(u , v)]
2n
Gaussian highpass filter
− D 2 ( u ,v ) / 2 D0
2
H (u , v) = 1 − e
20](https://image.slidesharecdn.com/enhancementinfrequencydomain-121206041015-phpapp02/85/Enhancement-in-frequency-domain-20-320.jpg)
Enhancement in frequency domain
- 1. Image Enhancement in the Frequency Domain
- 2. Basic steps for filtering in the frequency domain 2
- 3. Basics of filtering in the frequency domain 1. 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 an image (dc component of the spectrum) • the output has prominent edges • in reality the average of the displayed image can’t be zero as it needs to have negative gray levels. the output image needs to scale the gray level 0 if (u, v) = (M/2, N/2 ) H (u , v) = 1 otherwise4
- 5. Low pass filter high pass filter 5
- 6. Add the ½ of filter height to F(0,0) of the high pass filter 6
- 7. Correspondence between filter in spatial and frequency domains 7
- 8. Smoothing Frequency-domain filters: Ideal Lowpass filter 8
- 9. image power circles 9
- 10. Result of ILPF 10
- 11. Example 11
- 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 0 H (u , v) = 1 if D(u, v) > D 0 Butterworth highpass filter 1 H (u , v) = 1 + [ D 0 D(u , v)] 2n Gaussian highpass filter − D 2 ( u ,v ) / 2 D0 2 H (u , v) = 1 − e 20
- 21. Spatial representation of Ideal, Butterworth and Gaussian highpass filters 21
- 22. Example: result of IHPF 22
- 23. Example: result of BHPF 23
- 24. Example: result of GHPF 24
- 25. Laplacian in the Frequency domain 25
- 27. Example: high-boost filter 27
- 28. Examples 28
- 29. Homomorphic Filter 29
- 30. Result of Homomorphic filter 30
- 31. 31
- 32. 32
- 33. 33
- 34. 34
- 35. 35
- 36. 36
- 37. 37
- 38. 38
- 39. 39
- 40. 40
- 41. 41
- 42. 42