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Image Restoration : Noise Reduction

Image Restoration : Noise Reduction. Image degradation / restoration model. Gaussian Noise. Gaussian Noise : Matlab. t_gaus = imnoise (t, ‘ gaussian ’); imshow ( t_gaus );. TRY !!. Salt and Pepper Noise. Salt and Pepper Noise : MATLAB. t_sp = imnoise (t, ‘salt & pepper’);

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Image Restoration : Noise Reduction

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  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. Min. filter Median filter Max. filter Rank-Order Filter • Sort the intensities within the mask. • Choose the intensity at ith position as output. 10 20 10 15 5 5 10 13 13 5 0 10 5 20 11 20 15 5 11 20 20 15 Sort intensity 8 0 0 10 8 0 0 10 10 20 15 0 10

  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) AFTER BEFORE 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) AFTER BEFORE 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 menghapusimpuls noise pada gambar dan mengurangi distorsi pada gambar.

  20. Rank-Order Filter : Median Filter AFTER BEFORE 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 FiltersArithmetic & Geometric

  23. Mean FiltersArithmetic & Geometric

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

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

  26. Mean FiltersHarmonic

  27. Mean FiltersContraharmonic

  28. Mean FiltersGood Results of Contraharmonic Mean Filter Pepper noise Salt noise

  29. Mean FiltersBad 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 FiltersAlpha-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 0 10 20 10 15 5 0 Trim the data by 2. (1 from the top. 1 from the bottom.) 5 13 5 0 10 5 8 10 20 20 5 11 20 15 Sort intensity Output = average intensity of the remaining data. = 9.5 11 8 0 0 10 10 13 10 20 15 0 10 15 20

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

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

  34. Periodic Noise ReductionFrequency 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 ReductionFrequency Domain Filtering  Band Reject Filters • Butterworth Band-Reject Filter of Order n • Gaussian and-Reject Filter

  36. Periodic Noise ReductionFrequency Domain Filtering  Band Reject Filters

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

  38. Periodic Noise ReductionFrequency 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. Center frequency components Shift with respect to the center Periodic Noise ReductionFrequency Domain Filtering  Notch Filters • Ideal Notch Filters

  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

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