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 MATLAB/Image Processing Toolbox MATLAB Fourier transforms >> f=imread(‘Figure_Rectangle.jpg’); % load in spatial rectangle >> F=fft2(f); % do 2D FFT >> S=abs(F); % determine magnitude for display >> imshow(S, [ ]) % shows in four corners of display >> Fc=fftshift(F); % shift FFT to center >> imshow(abs(Fc), [ ]); % show magnitude of FFT in center % much tougher to do display transform >> g=im2unit8(mat2gray(log(1+double(f)))); >> imshow(g) % double converts the image to double precision floating point % mat2gray brings the values to the range [0,1] % im2unit8 brings the values back to the range [0,255] % general log transform >> g=im2unit8(mat2gray(c*log(1+double(f)))); SEE GWE, Section 4.2 Computing and Visualizing the 2-D DFT in MATLAB GWE, Section 3.2.2 Logarithmic and Contrast Stretching Transformations

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 Chapter 4 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

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 Image Enhancement in the Frequency Domain Chapter 4 Image Enhancement in the Frequency Domain

31. 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

32. 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

33. 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

34. 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

35. 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

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