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% Fast Bilateral Filter Using Raised Cosines
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % inImg : grayscale image % sigma1 : width of spatial Gaussian % sigma2 : width of range Gaussian % [-w, w]^2 : domain of spatial Gaussian % tol : truncation error % % Author: Kunal N. Chaudhury. % Date: March 1, 2012. % Modified: June 21, 2014. % % References: % [1] K.N. Chaudhury, D. Sage, and M. Unser, “Fast O(1) bilateral % filtering using trigonometric range kernels,” IEEE Trans. Image Proc., % vol. 20, no. 11, 2011. % % [2] K.N. Chaudhury, “Acceleration of the shiftable O(1) algorithm for % bilateral filtering and non-local means,” IEEE Transactions on Image Proc., % vol. 22, no. 4, 2013. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load test image clc, clear all, close all force; Img = double( imread(‘./images/ckb.jpg’) ); [m, n] = size(Img);
% create noisy image (additive Gaussian noise) sigma = 20; inImg = Img sigma * randn(m, n);
% filter parameters sigma1 = 4; sigma2 = 30; tol = 0.01;
% Set window for spatial Gaussian w = 6*sigma1; if (mod(w,2) == 0) w = w 1; end
% call bilateral filter tic; [outImg, param] = shiftableBF(inImg, sigma1, sigma2, w, tol); toc;
% plot results T = param.T; N = param.N; M = param.M; gamma = 1 / (sqrt(N) * sigma2); twoN = 2^N;
warning(‘off’); %#ok<WNOFF>
s = linspace(-T, T, 200); g = exp( -s.^2 / (2 * sigma2 *sigma2) ); gApprox = cos(gamma * s).^N; if M == 0 gTrunc = gApprox; else gTrunc = zeros( 1, length(s) ); for k = M : N – M gTrunc = gTrunc (nchoosek(N, k) / twoN) * … cos( (2*k – N) * gamma * s ); end end
figure(‘Units’,’normalized’,’Position’,[0 0.5 1 0.5]); plot(s, g, ‘b’); hold on, plot(s, gApprox, ‘m’), hold on, plot(s, gTrunc, ‘r’); axis(‘tight’), grid(‘on’), legend(‘Gassian’,’Raised cosine’,’Truncated raised cosine’,’FontSize’, 10); title(‘Comparison of the range kernels’, ‘FontSize’, 10),
peak = 255; PSNR0 = 10 * log10(m * n * peak^2 / sum(sum( (inImg – Img).^2)) ); PSNR1 = 10 * log10(m * n * peak^2 / sum(sum((outImg – Img).^2)) );
figure(‘Units’,’normalized’,’Position’,[0 0.5 1 0.5]); colormap gray, subplot(1,3,1), imshow(uint8(Img)), title(‘Original’, ‘FontSize’, 10), axis(‘image’, ‘off’); subplot(1,3,2), imshow(uint8(inImg)), title([ ‘Noisy, ‘, num2str(PSNR0, ‘%.2f’), ‘dB’] , ‘FontSize’, 10), axis(‘image’, ‘off’); subplot(1,3,3), imshow(uint8(outImg)), title([ ‘Filtered, ‘, num2str(PSNR1, ‘%.2f’), ‘dB’] , ‘FontSize’, 10), axis(‘image’, ‘off’);
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