Slides of image processing lesson of Professor Zohreh Azimifar taught at Shiraz University.

1. 1
Digital Image Processing
Image Enhancement in the
Frequency Domain,
Part III
Dr Z. Azimifar
Computer Science and Engineering Department
Shiraz University
Winter 2020
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

2. Fourier Transform and Convolution
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 2
Convolution in spatial domain ⇔ Multiplication in frequency domain

3. Fourier Transform and Convolution
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 3

4. 4
Important Transform Pairs
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

5. 5
Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

6. 6
Example 1
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

7. 7
Example 2
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

8. 8
Spatial Frequency
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

9. 9
Spatial Frequency
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

10. 10
Spatial Frequency
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

11. 11
Spatial Frequency
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

12. 12
Spatial Frequency
n F(u,v): weighting factor measuring the relative
contribution of the elementary pattern
n (u,v): frequency domain
n F(u,v): frequency component of the transform
n |F(u,v)|: frequency spectrum of the transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

13. 13
Example 1:
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

14. 14
Example: 2-D Box Function
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

15. 15
Example 2:
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

16. 16
Example 3:
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

17. Smoothing
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 17

18. Smoothing
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 18

19. Example
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 19

20. Low and High Pass filtering
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 20

21. Properties of Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 21

22. Fourier Pairs
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 22

23. Smoothing Pairs
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 23

24. Sampling Pairs
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020 24

25. 25
Properties of Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

26. 26
Properties of Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

27. 27
Properties of Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

28. 28
Properties of Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

29. 29
Properties of Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

30. 30
Sampling Theorem
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

31. 31
Sampling Theorem
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

32. 32
Sampling Theorem
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

33. 33
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

34. 34
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

35. 35
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

36. 36
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

37. 37
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

38. 38
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

39. 39
Discrete Fourier Transform
n Separability
q Since Fourier transform involves orthogonal basis, DFT
is separable so that it can be written as a separable
transform in n and m respectively.
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

40. 40
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

41. 41
Example 1: Separability of 2D FT
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

42. 42
Rotation
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

43. 43
Rotation: Example of Rotation
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

44. 44
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

45. 45
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

46. 46
Discrete Fourier Transform
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

47. 47
Shifting low freq. compo. into the center
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020

48. 48
Fourier Transform Types
Shiraz University, Comp. Sc. & Eng Dpt,
Prof. Z. Azimifar, 2020