1. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

2. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

3. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

4. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

5. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

6. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

7. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

8. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

9. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

10. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

11. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

12. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

13. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

14. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

15. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

16. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

17. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

18. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

19. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods DFT in Matlab Compute DFT: >> f = imread(’center_bump.tif’); >> F = fft2(f); >> S = abs(F); >>imshow(S,[])

20. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Centering DFT >> Fc=fftshift(F); >> imshow(abs(Fc),[])

21. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Sharpening by Log Transform >> S2=log(1+abs(Fc)); >> imshow(S2,[])

22. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods From DFT back to signal >> F=ifftshift(Fc); >> f=ifft2(F); >> f=real(ifft2(F));

23. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Basic Frequency Filtering >> f=imread(’square_original.tif’); >> [M,N]=size(f); >> F=fft2(f); >> sig=10; >> H=lpfilter(’gaussian’,M,N,sig); >> G=H.*F; >> g=real(ifft2(G)); >> imshow(g,[])

24. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain (the need for padding) Chapter 4 Frequency Domain (the need for padding)

25. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain (the need for padding) Chapter 4 Frequency Domain (the need for padding)

26. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain (why padding) Chapter 4 Frequency Domain (why padding)

27. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

28. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

29. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

30. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain Processing Chapter 4 Frequency Domain Processing

31. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain Processing Chapter 4 Frequency Domain Processing

32. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain Processing Chapter 4 Frequency Domain Processing

33. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Frequency Domain Processing Chapter 4 Frequency Domain Processing

34. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Padding in Practice Assume images f(x,y) & h(x,y) of sizes A × B and C × D Form two padded functions of size P × Q by appending zeros to f and g. You can show that wraparound error is avoided by choosing P  A + C − 1 and Y  B + D − 1 For special case of f(x,y) & h(x,y) of the same size, M × N, we pad with P  2M − 1 and Q  2N − 1

35. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Padding in Practice >> PQ=paddedsize(size(f)); %Compute the FFT with padding. >> Fp=fft2(f,PQ(1),PQ(2)); >> Hp=lpfilter(’gaussian’,PQ(1),PQ( 2),2*sig); >> Gp=Hp.*Fp; >> gp=real(ifft2(Gp)); >> gpc=gp(1:size(f,1),1:size(f,2)); >> imshow(gp,[]) >> imshow(gpc,[])

36. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

37. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

38. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

39. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

40. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

41. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

42. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

43. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

44. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

45. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

46. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

47. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

48. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

49. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

50. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

51. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

52. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

53. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

54. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

55. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

56. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

57. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

58. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

59. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

60. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

61. Digital Image Processing, 2nd ed. www.imageprocessingbook.com © 2002 R. C. Gonzalez & R. E. Woods Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain