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; endMSE = 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 [e-mail]%%----------------------------------------------------------------------%%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;   endendif (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;   endendif (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;   endendif 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); endimg1 = 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=6.502500C2 = (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);endmssim = 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.