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’); imshow(t_sp); TRY !!

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

Other Additive Noises

Other Additive Noises

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

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 !!

Restoration by Spatial Filtering

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

Rank-Order Filter

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

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

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

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

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.

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

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 !!

Mean Filters Arithmetic & Geometric

Mean Filters Arithmetic & Geometric

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

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

Mean Filters Harmonic

Mean Filters Contraharmonic

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

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

Order-statistic Filters

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

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

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

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.

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

Periodic Noise Reduction Frequency Domain Filtering  Band Reject Filters

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

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

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

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

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