Add refinement code for posterization effect

Author: Fujun Luan

examples/refine_posterization/refine_1.png

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+function imDst = boxfilter(imSrc, r)
+
+%   BOXFILTER   O(1) time box filtering using cumulative sum
+%
+%   - Definition imDst(x, y)=sum(sum(imSrc(x-r:x+r,y-r:y+r)));
+%   - Running time independent of r; 
+%   - Equivalent to the function: colfilt(imSrc, [2*r+1, 2*r+1], 'sliding', @sum);
+%   - But much faster.
+
+[hei, wid] = size(imSrc);
+imDst = zeros(size(imSrc));
+
+%cumulative sum over Y axis
+imCum = cumsum(imSrc, 1);
+%difference over Y axis
+imDst(1:r+1, :) = imCum(1+r:2*r+1, :);
+imDst(r+2:hei-r, :) = imCum(2*r+2:hei, :) - imCum(1:hei-2*r-1, :);
+imDst(hei-r+1:hei, :) = repmat(imCum(hei, :), [r, 1]) - imCum(hei-2*r:hei-r-1, :);
+
+%cumulative sum over X axis
+imCum = cumsum(imDst, 2);
+%difference over Y axis
+imDst(:, 1:r+1) = imCum(:, 1+r:2*r+1);
+imDst(:, r+2:wid-r) = imCum(:, 2*r+2:wid) - imCum(:, 1:wid-2*r-1);
+imDst(:, wid-r+1:wid) = repmat(imCum(:, wid), [1, r]) - imCum(:, wid-2*r:wid-r-1);
+end
+

examples/refine_posterization/refine_11.png

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+function q = guidedfilter(I, p, r, eps)
+%   GUIDEDFILTER   O(1) time implementation of guided filter.
+%
+%   - guidance image: I (should be a gray-scale/single channel image)
+%   - filtering input image: p (should be a gray-scale/single channel image)
+%   - local window radius: r
+%   - regularization parameter: eps
+
+[hei, wid] = size(I);
+N = boxfilter(ones(hei, wid), r); % the size of each local patch; N=(2r+1)^2 except for boundary pixels.
+
+mean_I = boxfilter(I, r) ./ N;
+mean_p = boxfilter(p, r) ./ N;
+mean_Ip = boxfilter(I.*p, r) ./ N;
+cov_Ip = mean_Ip - mean_I .* mean_p; % this is the covariance of (I, p) in each local patch.
+
+mean_II = boxfilter(I.*I, r) ./ N;
+var_I = mean_II - mean_I .* mean_I;
+
+a = cov_Ip ./ (var_I + eps); % Eqn. (5) in the paper;
+b = mean_p - a .* mean_I; % Eqn. (6) in the paper;
+
+mean_a = boxfilter(a, r) ./ N;
+mean_b = boxfilter(b, r) ./ N;
+
+q = mean_a .* I + mean_b; % Eqn. (8) in the paper;
+end

examples/refine_posterization/refine_13.png

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+function q = guidedfilter_color(I, p, r, eps)
+%   GUIDEDFILTER_COLOR   O(1) time implementation of guided filter using a color image as the guidance.
+%
+%   - guidance image: I (should be a color (RGB) image)
+%   - filtering input image: p (should be a gray-scale/single channel image)
+%   - local window radius: r
+%   - regularization parameter: eps
+
+[hei, wid] = size(p);
+N = boxfilter(ones(hei, wid), r); % the size of each local patch; N=(2r+1)^2 except for boundary pixels.
+
+mean_I_r = boxfilter(I(:, :, 1), r) ./ N;
+mean_I_g = boxfilter(I(:, :, 2), r) ./ N;
+mean_I_b = boxfilter(I(:, :, 3), r) ./ N;
+
+mean_p = boxfilter(p, r) ./ N;
+
+mean_Ip_r = boxfilter(I(:, :, 1).*p, r) ./ N;
+mean_Ip_g = boxfilter(I(:, :, 2).*p, r) ./ N;
+mean_Ip_b = boxfilter(I(:, :, 3).*p, r) ./ N;
+
+% covariance of (I, p) in each local patch.
+cov_Ip_r = mean_Ip_r - mean_I_r .* mean_p;
+cov_Ip_g = mean_Ip_g - mean_I_g .* mean_p;
+cov_Ip_b = mean_Ip_b - mean_I_b .* mean_p;
+
+% variance of I in each local patch: the matrix Sigma in Eqn (14).
+% Note the variance in each local patch is a 3x3 symmetric matrix:
+%           rr, rg, rb
+%   Sigma = rg, gg, gb
+%           rb, gb, bb
+var_I_rr = boxfilter(I(:, :, 1).*I(:, :, 1), r) ./ N - mean_I_r .*  mean_I_r; 
+var_I_rg = boxfilter(I(:, :, 1).*I(:, :, 2), r) ./ N - mean_I_r .*  mean_I_g; 
+var_I_rb = boxfilter(I(:, :, 1).*I(:, :, 3), r) ./ N - mean_I_r .*  mean_I_b; 
+var_I_gg = boxfilter(I(:, :, 2).*I(:, :, 2), r) ./ N - mean_I_g .*  mean_I_g; 
+var_I_gb = boxfilter(I(:, :, 2).*I(:, :, 3), r) ./ N - mean_I_g .*  mean_I_b; 
+var_I_bb = boxfilter(I(:, :, 3).*I(:, :, 3), r) ./ N - mean_I_b .*  mean_I_b; 
+
+a = zeros(hei, wid, 3);
+for y=1:hei
+    for x=1:wid        
+        Sigma = [var_I_rr(y, x), var_I_rg(y, x), var_I_rb(y, x);
+            var_I_rg(y, x), var_I_gg(y, x), var_I_gb(y, x);
+            var_I_rb(y, x), var_I_gb(y, x), var_I_bb(y, x)];
+        %Sigma = Sigma + eps * eye(3);
+        
+        cov_Ip = [cov_Ip_r(y, x), cov_Ip_g(y, x), cov_Ip_b(y, x)];        
+        
+        a(y, x, :) = cov_Ip * inv(Sigma + eps * eye(3)); % Eqn. (14) in the paper;
+    end
+end
+
+b = mean_p - a(:, :, 1) .* mean_I_r - a(:, :, 2) .* mean_I_g - a(:, :, 3) .* mean_I_b; % Eqn. (15) in the paper;
+
+q = (boxfilter(a(:, :, 1), r).* I(:, :, 1)...
++ boxfilter(a(:, :, 2), r).* I(:, :, 2)...
++ boxfilter(a(:, :, 3), r).* I(:, :, 3)...
++ boxfilter(b, r)) ./ N;  % Eqn. (16) in the paper;
+end

examples/refine_posterization/refine_16.png

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+
+***************************************************************************************
+***************************************************************************************
+
+Matlab demo code for "Guided Image Filtering" (ECCV 2010)
+
+by Kaiming He ([email protected])
+
+If you use/adapt our code in your work (either as a stand-alone tool or as a component 
+of any algorithm), you need to appropriately cite our ECCV 2010 paper.
+
+This code is for academic purpose only. Not for commercial/industrial activities.
+
+
+The running time reported in the paper is from C++ implementation. This matlab code is
+a reference for those who would like to reimplement our method.
+
+***************************************************************************************
+***************************************************************************************
+
+Usage:
+
+guidedfilter.m - guided filter implementation (Eqn(5), (6), (8) in the paper)
+guidedfilter_color.m - guided filter for color guidance (Eqn(14), (15), (16) in the paper)
+
+Run the four examples to see the results shown in the paper.

examples/refine_posterization/refine_2.png

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+function K = refine_posterization(I, J)
+    addpath guided_filter/
+    r = 8;
+    eps = 0.1^2;
+    I_f = I;
+    for c = 1 : 3
+        I_f(:,:,c) = guidedfilter_color(I, I_f(:,:,c), r, eps);       
+    end 
+    K = J + I - I_f;
+end