1. Image Restoration : Noise Reduction

2. Image degradation / restoration model

3. Gaussian Noise

4. Gaussian Noise : Matlab
t_gaus = imnoise (t, ‘gaussian’);
imshow(t_gaus);
TRY !!

5. Salt and Pepper Noise

6. Salt and Pepper Noise : MATLAB
t_sp = imnoise (t, ‘salt & pepper’);
imshow(t_sp);
TRY !!

7. Other Additive Noise Models
Rayleigh Noise
Gamma(Erlang) Noise
Exponential Noise
Uniform Noise
Impulse Noise

8. Other Additive Noises

9. Other Additive Noises

10. Periodic Noise Noise components
Periodic noise can be reduced in via frequency domain
Are generated due to electrical or electromechanical interference during image acquisition

11. Periodic Noise : MATLAB
tw = imread(filename); t = rgb2gray(tw); s = size(t); [x,y] = meshgrid(1:s(1), 1:s(2)); p = sin(x/3+y/5)+1; t_pn = (im2double(t)+p’/2)/2; imshow(t_pn);
TRY !!

12. Restoration by Spatial Filtering

13. Rank-Order Filter Sort intensity Sort the intensities within the mask.
Choose the intensity at ith position as output.
Min. filter 10 20 10 15 5 5 10 10 13 13 5 5 20 11 11 20 20 20 15 15 5
Median filter
Sort intensity 10 8 8 10 10 20 15 10
Max. filter

14. Rank-Order Filter

15. Rank-Order Filter Max filter = mengambil pixel dengan nilai tinggi
Min filter = mengambil pixel dengan nilai rendah

16. Rank-Order Filter : Max Filter
Output pixel is the maximum intensity of the pixels within the mask. (find brightest point)
BEFORE
AFTER
Image corrupted by pepper noise

17. Rank-Order Filter : Min Filter
Output pixel is the minimum intensity of the pixels within the mask. (find darkest point)
BEFORE
AFTER
Image corrupted by salt noise

18. Rank-Order Filter : Median Filter
-- Repeated passes of median filter tend to blur the image.
-- Keep the number of passes as low as possible.

19. Rank-Order Filter : Median Filter
Output pixel is the mid-intensity of the pixels within the mask (the median intensity).
Adaptive median filter memiliki tujuan ganda yaitu menghapus impuls noise pada gambar dan mengurangi distorsi pada gambar.

20. Rank-Order Filter : Median Filter
BEFORE
AFTER
3x3 Kernel

21. Rank-Order Filtering: MATLAB
Command: ordfilt2
Syntax: ordfilt2(image, order, domain); medfilt2(image);
image : input image
order : which order of the sorted intensity (minimum to maximum value) taken as output
domain : matrix indicating the neighborhood.
1 : pixels in the neighbor.
0 : pixels not in the neighbor
E.g. cmin = ordfilt2(image, 1, ones(3,3));
Try to restore Salt and Pepper Noise by Median Filter !!

22. Mean Filters Arithmetic & Geometric

23. Mean Filters Arithmetic & Geometric

24. Mean Filter Good Results of Geometric Mean Filter
BEFORE
AFTER
Image corrupted by Gaussian noise with variance = 300, mean = 0

25. Mean Filter : Bad Results of Geometric Mean Filter
BEFORE
AFTER
Image corrupted by pepper noise with probability = 0.4

26. Mean Filters Harmonic

27. Mean Filters Contraharmonic

28. Mean Filters Good Results of Contraharmonic Mean Filter
Pepper noise
Salt noise

29. Mean Filters Bad Results of Contraharmonic Mean Filter
Arithmetic mean filter and geometric mean filter are well suited for random noise such as Gaussian noise
Contraharmonic mean filter is well suited for impulse noise
Disadvantage: must know pepper noise or salt noise in advance

30. Order-statistic Filters

31. Order-statistic Filters Alpha-Trimmed Mean Filter
Output is the mean of the data after removing the first d/2 and the last d/2 ordered data.
d =2 10 20 10 15 5
Trim the data by 2.
(1 from the top.
1 from the bottom.) 5 10 13 5 5 8 20 11 20 20 15 5 10
Sort intensity
Output = average intensity of the remaining data.
= 9.5 11 10 8 10 13 10 20 15 10 15 20

32. Order-statistic Filters Effect of Alpha-Trimmed Mean Filter
BEFORE
AFTER
Image corrupted by salt-and-pepper noise with variance = 200, mean = 0
Trim size = 2, mask size =1

33. Median and alpha-trimmed filter performed better
High level of noise  large filter
Median and alpha-trimmed filter performed better
Alpha-trimmed did better than median filter

34. Periodic Noise Reduction Frequency Domain Filtering  Band Reject Filters (Selective Filter)
Ideal Band-Reject Filters
-D(u,v) =distance from the origin of the centered freq. rectangle
-W =width of the band
-D0=Radial center of the band.

35. Periodic Noise Reduction Frequency Domain Filtering  Band Reject Filters
Butterworth Band-Reject Filter of Order n
Gaussian and-Reject Filter

36. Periodic Noise Reduction Frequency Domain Filtering  Band Reject Filters

37. Periodic Noise Reduction Frequency Domain Filtering  Band Pass Filters
Opposite operation of a band-reject filter

38. Periodic Noise Reduction Frequency Domain Filtering  Notch Filters
Rejects (or passes) frequencies in predefined neighborhoods about a center frequency
Must appear in symmetric pairs about the origin.
Ideal
Butterworth
Gaussian

39. Periodic Noise Reduction Frequency Domain Filtering  Notch Filters
Ideal Notch Filters
Center frequency components
Shift with respect to the center

40. Notch pass filter
Horizontal lines of the noise pattern I can be seen

41. Tugas
Cari tahu bagaimana cara menghilangkan periodic noise menggunakan band-reject filter, band-pass filter atau notch filter pada MATLAB.
Simulasikan dan analisis hasilnya