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

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

2. Spectrum of Images
2
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

3. Spectrum of Images
3
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

4. Spectrum of Images
4
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

5. Spectrum of Images
5
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

6. Spectrum of Images
6
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

7. Basic Steps for Filtering in the Frequency
Domain
7
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

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

9. Notch Filter
î
í
ì =
=
otherwise
1
N/2
(M/2,
v)
(u,
if
0
)
,
(
)
v
u
H
• This filter is to force the F(0,0)=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
9
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

10. Low pass filter
High pass filter
10
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020
Frequency Domain Filters

11. Filtering Examples
11
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

12. Transfer Function 5x5 LP Filter
12
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

13. Filtering Examples
13
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

14. Filtering Examples
14
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

15. Filtering Examples
15
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

16. Transfer Function High-Pass Filter
16
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

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

18. Filtering in Frequency Domain
18
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

19. Add Half of the Filter Height to F(0,0)
of the High Pass Filter
19
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

20. Correspondence Between Filters in
Spatial and Frequency Domains
20
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

21. Low-Pass Filtering
21
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

22. Low-Pass Filtering
22
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

23. Low-Pass Filtering
23
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

24. Low-Pass Filtering
24
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

25. Low-Pass Filtering
25
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

26. Low-Pass Filtering
26
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

27. Low-Pass Filtering
27
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

28. Low-Pass Filtering
28
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

29. Low-Pass Filtering
29
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

30. Low-Pass Filtering
30
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

31. Low-Pass Filtering
31
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

32. Low-Pass Filtering
32
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

33. Low-Pass Filtering
33
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

34. Low-Pass Filtering
34
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

35. High-Pass Filtering
35
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

36. High-Pass Filtering
36
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

37. High-Pass Filtering
37
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

38. High-Pass Filtering
38
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

39. High-Pass Filtering
39
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

40. High-Pass Filtering
40
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

41. High-Pass Filtering
41
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

42. High-Pass Filtering
42
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

43. High-Pass Filtering (1 minus Laplacian)
43
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

44. Homomorphic Filtering
44
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

45. Homomorphic Filtering
45
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

46. Homomorphic Filtering
2 2
0
( ( . )/ )
( , ) ( ) 1 c D u v D
H L L
h u v e
g g g
-
é ù
= - - +
ë û
C controls sharpness of the slope
46
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020

47. Homomorphic Filtering
47
Shiraz University, Comp. Sc.&Eng. Dpt,
Prof. Z. Azimifar, 2020