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**Neighborhood Processing**

Digital Image Processing

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**Introduction Mask moving (or convolution)**

A rectangle (usually with sides of odd length) or other shape over the given image

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**Mask & Overlapping Pixel Values**

a 3X5 mask corresponding pixel values

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**Spatial Filtering Position mask over current pixel**

Form all products of filter elements with the corresponding elements of the neighborhood Add all the product Repeat for every pixel in image

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**Spatial Convolution Similar to spatial filtering, except ..**

The filter must be rotated by 180° before multiplying and adding Or, equivalently, The rationale of “convolution” will become apparent in view of Fourier Transform

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Mean Filter Example Given a 3×3 mask, take the average of all nine values within the mask The result of filtering x with 3×3 averaging filter

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Mask Notation It is convenient to describe a linear filter simply in terms of the coefficients of all the gray values of pixels within the mask The averaging filter The other filter example Ch5-p.91-92

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Mask on the Edge What happens at the edge of the image, where the mask partly falls outside the image? There are a number of different approaches to dealing with this problem Ignore the edges (like the example shown previously) Pad with zeros Mirroring

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**Filtering in MATLAB imfilter(image,filter,options..)**

filter2(filter, image, shape) The result is a matrix of data type “double” shape is optional; it describes the method for dealing with the edges ‘same’ – pad with zeros ‘valid’ – ignore the edges ‘full’ – pad with zeros and applying the filter at all places on and around the image where the mask intersects the image matrix imfilter(image,filter,options..) More advanced image filtering function

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**Filtering Examples in MATLAB (1/2)**

>> x = uint8(10*magic(5)) >> a = ones(3,3)/9 >> filter2(a,x,'same') >> filter2(a,x,'valid')

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**Filtering Examples in MATLAB (2/2)**

>> filter2(a,x,'full') filter2 provides no mirroring option Mirroring can be realized by >> D = floor(size(a)/2) >> wr=D(1);wc=D(2); % get half of the mask size >> m_x=[x(wr:-1:1,:);x;x(end:-1:end-(wr-1),:)] % additional mirrored-rows >> m_x=[m_x(:,wc:-1:1),m_x,m_x(:,end:-1:end-(wc-1))]; % additional mirrored columns >> filter2(a,m_x,'valid')

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**Pre-cooked Filtering in MATLAB: fspecial()**

I = imread('cameraman.tif'); subplot(2,2,1);imshow(I);title('Original Image'); H = fspecial('motion',20,45); MotionBlur = imfilter(I,H,'replicate'); subplot(2,2,2);imshow(MotionBlur);title('Motion Blurred Image'); H = fspecial('disk',10); blurred = imfilter(I,H,'replicate'); subplot(2,2,3);imshow(blurred);title('Blurred Image'); H = fspecial('unsharp'); sharpened = imfilter(I,H,'replicate'); subplot(2,2,4);imshow(sharpened);title('Sharpened Image');

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**Low- and High-Pass Filters (1/2)**

Frequencies of an image are a measure of the amount by which gray values change with distance High-pass filter (left) Low-pass filter (right) >> f = fspecial('laplacian') >> cf = imfilter(c,f); >> f1 = fspecial('log') % Laplacian of Gaussian >> cf1 = imfilter(c,f1); Ch5-p.98

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**Low- and High-Pass Filters (2/2)**

Values outside [0,255] range Make negative value positive Clip values 0-255 scaling transformation >> f2 = [1 -2 1; ; ]; >> cf2 = filter2(f2,c); >> figure, imshow(mat2gray(cf2)); >> % scaling transformation >> maxcf2 = max(cf2(:)); >> mincf2 = min(cf2(:)); >> cf2g = (cf2-mincf2)/(maxcf2-mincf2); >> figure, imshow(cf2/60);

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**Gaussian Filters (1/2) Ch5-p.103 >> a=50;s=3;**

>> g=fspecial('gaussian',[a a],s); >> surf(1:a,1:a,g) >> s = 9; >> g2 = fspecial('gaussian',[a a],s); >> figure, surf(1:a,1:a,g2) Ch5-p.103

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**Gaussian Filters (2/2) g3 g4 g1 g2**

>> c = imread('cameraman.tif'); >> g1 = fspecial('gaussian',[5 5]); >> g2 = fspecial('gaussian',[5 5],2); >> g3 = fspecial('gaussian',[11 11],1); >> g4 = fspecial('gaussian',[11 11],5); >> imshow(filter2(g1,c)/256); >> figure, imshow(filter2(g2,c)/256); >> figure, imshow(filter2(g3,c)/256); >> figure, imshow(filter2(g4,c)/256); g3 g4 g1 g2

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**Scheme for Sharpening Masking**

>> c = imread(‘cameraman.tif’); >> f = fspecial('average'); >> xf = filter2(f,c); >> xu = double(c)-xf/1.5; >> imshow(xu/70); Ch5-p.106

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**Unsharp Masking The unsharp option of fspecial produces such filters**

>> p = imread('pelicans.tif'); >> u = fspecial('unsharp',0.5); >> pu = filter2(u,p); >> imshow(p), figure, imshow(pu/255); α = 0.5 Ch5-p.108

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High-Boost Filtering Allied to unsharp masking filters are the high-boost filters where A is an amplification factor If A = 1, then the high-boost filter becomes an ordinary high-pass filter >> id = [0 0 0;0 1 0; 0 0 0]; >> f = fspecial('average'); >> hb1 = 3*id-2*f; >> hb2 = 1.25*id-0.25*f; >> x1 = filter2(hb1,p); >> x2 = filter2(hb2,p); >> figure, imshow(x1/255); >> figure, imshow(x2/255);

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**Nonlinear Filters Maximum filter Minimum filter**

>> cmax = nlfilter(c,[3 3],'max(x(:))'); >> cmin = nlfilter(c,[3 3],'min(x(:))'); >> figure, imshow(cmax); >> figure, imshow(cmin); Ch5-p.112

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**Region of Interest Processing**

>> ig = imread('iguana.tif'); >> roi = roipoly(ig,[ ],[ ]); >> figure, imshow(ig); >> figure, imshow(roi); >> roi_2 = roipoly(ig); % interactively select ROI Ch5-p.115

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**Region of Interest Filtering**

>> a = fspecial('average',[15 15]); >> iga = roifilt2(a,ig,roi); >> imshow(iga); >> u = fspecial('unsharp'); >> igu = roifilt2(u,ig,roi); >> figure, imshow(igu); >> L = fspecial('log'); >> igl = roifilt2(L,ig,roi); >> figure, imshow(igl); iga: average filtering igu: unsharp masking igl: Laplacian of Gaussian Ch5-p.116

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