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% 使用升余弦的快速双边滤波
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % inImg : 灰度图像 % sigma1 : 空间高斯核的宽度 % sigma2 : 范围高斯核的宽度 % [-w, w]^2 : 空间高斯核的领域 % tol : 截断误差 % % 作者: Kunal N. Chaudhury. % 日期: 2012年3月1日. % 修改: 2014年6月21日. % % 参考文献: % [1] K.N. Chaudhury, D. Sage, 和 M. Unser, “使用三角范围核的快速O(1)双边过滤,” IEEE Trans. Image Proc., % 卷. 20, 号. 11, 2011. % % [2] K.N. Chaudhury, “加速可移动的O(1)算法用于双边过滤和非局部均值,” IEEE Transactions on Image Proc., % 卷. 22, 号. 4, 2013. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 加载测试图像 clc, clear all, close all force; Img = double( imread(‘./images/ckb.jpg’) ); [m, n] = size(Img);
% 创建带噪声图像（加性高斯噪声） sigma = 20; inImg = Img + sigma * randn(m, n);
% 过滤参数 sigma1 = 4; sigma2 = 30; tol = 0.01;
% 设置空间高斯核的窗口 w = 6*sigma1; if (mod(w,2) == 0) w = w+1; end
% 调用双边滤波器 tic; [outImg, param] = shiftableBF(inImg, sigma1, sigma2, w, tol); toc;
% 绘制结果 T = param.T; N = param.N; M = param.M; gamma = 1 / (sqrt(N) * sigma2); twoN = 2^N;
warning(‘off’); %#ok
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( (2k - 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(‘高斯’,’升余弦’,’截断升余弦’,’FontSize’, 10); title(‘范围核的比较’, ‘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(‘原始’, ‘FontSize’, 10), axis(‘image’, ‘off’); subplot(1,3,2), imshow(uint8(inImg)), title([ ‘带噪声, ‘, num2str(PSNR0, ‘%.2f’), ‘dB’] , ‘FontSize’, 10), axis(‘image’, ‘off’); subplot(1,3,3), imshow(uint8(outImg)), title([ ‘滤波后, ‘, num2str(PSNR1, ‘%.2f’), ‘dB’] , ‘FontSize’, 10), axis(‘image’, ‘off’);
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