1. CHAPTER 4 Image Enhancement in Frequency Domain
Digital Image Processing

2. Spectrum of images

3. Spectrum of images

4. Spectrum of images

5. Spectrum of images

6. Spectrum of images

7. Basic steps for filtering in the frequency domain

8. Basics of filtering in the frequency domain
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)
computer F(u,v), the DFT of the image
multiply F(u,v) by a filter function H(u,v)
compute the inverse DFT of the result in (3)
obtain the real part of the result in (4)
multiply the result in (5) by (-1)x+y to cancel the multiplication of the input image.

9. 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

10. Low pass filter
high pass filter

11. Filtering examples - revisited

12. Transfer function 5x5 lowpass filter

13. Filtering Examples

14. Filtering Examples

15. Filtering Examples

16. Transfer function high-pass filter

17. Filtering Examples

18. Filtering in frequency domain

19. Add the ½ of filter height to F(0,0) of the high pass filter

20. Correspondence between filter in spatial and frequency domains

21. Lowpass filtering

22. Lowpass filtering
α= 92.0, 94.6, 96.4, 98, % total power

23. Lowpass filtering

24. Lowpass filtering

25. Lowpass filtering

26. Lowpass filtering

27. Lowpass filtering

28. Lowpass filtering

29. Lowpass filtering

30. Lowpass filtering

31. Lowpass filtering

32. Lowpass filtering

33. Lowpass filtering

34. Lowpass filtering

35. Highpass filtering

36. Highpass filtering

37. Highpass filtering

38. Highpass filtering

39. Highpass filtering

40. Highpass filtering

41. Highpass filtering

42. Highpass filtering

43. Highpass filtering

44. Homomorphic filtering

45. Homomorphic filtering

46. Homomorphic filtering
C controls the sharpness of the slope

47. Homomorphic filtering