matlab中中图像PSNR和SSIM的计算 matlab

【matlab中中图像PSNR和SSIM的计算】网上找了很多关于PSNR和SSIM的计算，很多结果算出来都不一样，公式都是普遍的，如下：

现在总结下造成结果差异的原因。

PSNR的差异：
1.灰度图像：灰度图像比较好计算，只有一个灰度值。

2.彩色图像：
(a)可以将分别计算R,G,B三个通道总和，最后MSE直接在原公式上多除以3就行（opencv官方代码是这么做的，与matlab直接计算结果是一样的）。
(b)将R,G,B格式转换为YCbCr，只计算Y分量（亮度分量），结果会比直接计算要高几个dB。

贴代码，这里是将图片格式转成YCbCr（只计算Y分量）：

function [PSNR, MSE] = psnr(X, Y) %%%%%%%%%%%%%%%%%%%%%%%%%%% % % 计算峰值信噪比PSNR % 将RGB转成YCbCr格式进行计算 % 如果直接计算会比转后计算值要小2dB左右（当然是个别测试） % %%%%%%%%%%%%%%%%%%%%%%%%%%% if size(X,3)~=1%判断图像时不是彩色图，如果是，结果为3，否则为1 org=rgb2ycbcr(X); test=rgb2ycbcr(Y); Y1=org(:,:,1); Y2=test(:,:,1); Y1=double(Y1); %计算平方时候需要转成double类型，否则uchar类型会丢失数据 Y2=double(Y2); else%灰度图像，不用转换 Y1=double(X); Y2=double(Y); end if nargin<2 D = Y1; else if any(size(Y1)~=size(Y2)) error('The input size is not equal to each other!'); end D = Y1 - Y2; end MSE = sum(D(:).*D(:)) / numel(Y1); PSNR = 10*log10(255^2 / MSE);

控制台输入下面三条语句：

>> X= imread('C:\Users\Administrator\Desktop\noise_image.jpg'); >> Y= imread('C:\Users\Administrator\Desktop\actruel_image.jpg'); >> psnr(X, Y)

SSIM的差异：同上，如果直接不转换成YCbCr格式，结果会偏高很多（ matlab中，SSIM提出者【1】，代码）。opencv里面是分别计算了R,G,B三个分量的SSIM值（官方代码）。最后我将3个值取了个平均（这个值比matlab里面低很多）。

以下代码主要是参考原作者修改的，源代码是直接没有进行格式转换，直接RGB格式，下面我是将他转换成YCbCr计算图片的SSIM

function [mssim, ssim_map] = ssim(img1, img2, K, window, L)%======================================================================== %SSIM Index, Version 1.0 %Copyright(c) 2003 Zhou Wang %All Rights Reserved. % %The author is with Howard Hughes Medical Institute, and Laboratory %for Computational Vision at Center for Neural Science and Courant %Institute of Mathematical Sciences, New York University. % %---------------------------------------------------------------------- %Permission to use, copy, or modify this software and its documentation %for educational and research purposes only and without fee is hereby %granted, provided that this copyright notice and the original authors' %names ap pearon all copies and supporting documentation. This program %shall not be used, rewritten, or adapted as the basis of a commercial %software or hardware product without first obtaining permission of the %authors. The authors make no representations about the suitability of %this software for any purpose. It is provided "as is" without express %or implied warranty. %---------------------------------------------------------------------- % %This is an implementation of the algorithm for calculating the %Structural SIMilarity (SSIM) index between two images. Please refer %to the following paper: % %Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image %quality assessment: From error visibility to structural similarity" %IEEE Transactios on Image Processing, vol. 13, no. 4, pp.600-612, %Apr. 2004. % %Kindly report any suggestions or corrections to zhouwang@ieee.org % %---------------------------------------------------------------------- % %Input : (1) img1: the first image being compared %(2) img2: the second image being compared %(3) K: constants in the SSIM index formula (see the above %reference). defualt value: K = [0.01 0.03] %(4) window: local window for statistics (see the above %reference). default widnow is Gaussian given by %window = fspecial('gaussian', 11, 1.5); %(5) L: dynamic range of the images. default: L = 255 % %Output: (1) mssim: the mean SSIM index value between 2 images. %If one of the images being compared is regarded as %perfect quality, then mssim can be considered as the %quality measure of the other image. %If img1 = img2, then mssim = 1. %(2) ssim_map: the SSIM index map of the test image. The map %has a smaller size than the input images. The actual size: %size(img1) - size(window) + 1. % %Default Usage: %Given 2 test images img1 and img2, whose dynamic range is 0-255 % %[mssim ssim_map] = ssim_index(img1, img2); % %Advanced Usage: %User defined parameters. For example % %K = [0.05 0.05]; %window = ones(8); %L = 100; %[mssim ssim_map] = ssim_index(img1, img2, K, window, L); % %See the results: % %mssim%Gives the mssim value %imshow(max(0, ssim_map).^4)%Shows the SSIM index map % %========================================================================if (nargin < 2 | nargin > 5) ssim_index = -Inf; ssim_map = -Inf; return; endif (size(img1) ~= size(img2)) ssim_index = -Inf; ssim_map = -Inf; return; end[M N] = size(img1); if (nargin == 2) if ((M < 11) | (N < 11))% 图像大小过小，则没有意义。 ssim_index = -Inf; ssim_map = -Inf; return end window = fspecial('gaussian', 11, 1.5); % 参数一个标准偏差1.5，11*11的高斯低通滤波。 K(1) = 0.01; % default settings K(2) = 0.03; L = 255; endif (nargin == 3) if ((M < 11) | (N < 11)) ssim_index = -Inf; ssim_map = -Inf; return end window = fspecial('gaussian', 11, 1.5); L = 255; if (length(K) == 2) if (K(1) < 0 | K(2) < 0) ssim_index = -Inf; ssim_map = -Inf; return; end else ssim_index = -Inf; ssim_map = -Inf; return; end endif (nargin == 4) [H W] = size(window); if ((H*W) < 4 | (H > M) | (W > N)) ssim_index = -Inf; ssim_map = -Inf; return end L = 255; if (length(K) == 2) if (K(1) < 0 | K(2) < 0) ssim_index = -Inf; ssim_map = -Inf; return; end else ssim_index = -Inf; ssim_map = -Inf; return; end endif (nargin == 5) [H W] = size(window); if ((H*W) < 4 | (H > M) | (W > N)) ssim_index = -Inf; ssim_map = -Inf; return end if (length(K) == 2) if (K(1) < 0 | K(2) < 0) ssim_index = -Inf; ssim_map = -Inf; return; end else ssim_index = -Inf; ssim_map = -Inf; return; end endif size(img1,3)~=1%判断图像时不是彩色图，如果是，结果为3，否则为1 org=rgb2ycbcr(img1); test=rgb2ycbcr(img2); y1=org(:,:,1); y2=test(:,:,1); y1=double(y1); y2=double(y2); else y1=double(img1); y2=double(img2); end img1 = double(y1); img2 = double(y2); % automatic downsampling %f = max(1,round(min(M,N)/256)); %downsampling by f %use a simple low-pass filter % if(f>1) %lpf = ones(f,f); %lpf = lpf/sum(lpf(:)); %img1 = imfilter(img1,lpf,'symmetric','same'); %img2 = imfilter(img2,lpf,'symmetric','same'); %img1 = img1(1:f:end,1:f:end); %img2 = img2(1:f:end,1:f:end); % endC1 = (K(1)*L)^2; % 计算C1参数，给亮度L（x，y）用。C1=6.502500 C2 = (K(2)*L)^2; % 计算C2参数，给对比度C（x，y）用。C2=58.522500 window = window/sum(sum(window)); %滤波器归一化操作。mu1= filter2(window, img1, 'valid'); % 对图像进行滤波因子加权valid改成same结果会低一丢丢 mu2= filter2(window, img2, 'valid'); % 对图像进行滤波因子加权mu1_sq = mu1.*mu1; % 计算出Ux平方值。 mu2_sq = mu2.*mu2; % 计算出Uy平方值。 mu1_mu2 = mu1.*mu2; % 计算Ux*Uy值。sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq; % 计算sigmax （标准差） sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq; % 计算sigmay （标准差） sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2; % 计算sigmaxy（标准差）if (C1 > 0 & C2 > 0) ssim_map = ((2*mu1_mu2 + C1).*(2*sigma12 + C2))./((mu1_sq + mu2_sq + C1).*(sigma1_sq + sigma2_sq + C2)); else numerator1 = 2*mu1_mu2 + C1; numerator2 = 2*sigma12 + C2; denominator1 = mu1_sq + mu2_sq + C1; denominator2 = sigma1_sq + sigma2_sq + C2; ssim_map = ones(size(mu1)); index = (denominator1.*denominator2 > 0); ssim_map(index) = (numerator1(index).*numerator2(index))./(denominator1(index).*denominator2(index)); index = (denominator1 ~= 0) & (denominator2 == 0); ssim_map(index) = numerator1(index)./denominator1(index); end mssim = mean2(ssim_map); return

控制台输入以下代码：

>> img1= imread('C:\Users\Administrator\Desktop\noise_image.jpg'); >> img2= imread('C:\Users\Administrator\Desktop\actruel_image.jpg'); >> ssim(img1,img2)

最后说一句，不管是结果如何，只要对比实验用的同一种评价代码工具，无所谓结果和原论文一不一样，问题是很多论文实验都搞不出来滴

参考文献
【1】Wang Z, Bovik A C, Sheikh H R, et al. Image quality assessment: from error visibility to structural similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4):600-612.