图像质量的客观评估指标PSNR与SSIM

怼烎@ 2022-07-28 05:09 666阅读 0赞

*  **PSNR**
 *  **SSIM**
 *  **代码**
 *  **参考文献**

--------------------

## 1：PSNR ##

PSNR是最为常用的图像质量评估指标：  
![这里写图片描述][20160330213107500]

其中K为图像对应二进制位数，一般为8。MSE为均方误差，计算公式为：  
![这里写图片描述][20160330213140422]

## 2：SSIM ##

SSIM\[1\]主要用来衡量图像结构完整性，是另一种比较常用的客观评估指标。实际应用中，一般用滑动窗口对图像进行分块，这里的滑动窗口一般为高斯窗口，并用高斯加权计算每个窗口的均值、方差和协方差。这样每块的SSIM计算如下：  
![这里写图片描述][20160330213341579]  
其中：  
![这里写图片描述][20160330213412345]  
文献\[1\]给出公式中默认参数：窗口w为11\*11的高斯窗口；其中K1=0.01，K2=0.02，L=255,C1=(K1\*L)^2,C2=(K2\*L)^2

## 3:代码 ##

问题在于给定了一副彩色图片，彩色图片有RGB三通道，如何计算其PSNR或者SSIM值，方法有以下三种(以PSNR为例)：  
(1)计算彩色图像RGB三通道每一通道的PSNR值，然后求均值  
(2)计算彩色图像RGB三通道每一通道的MSE值，求平均，然后再代入求PSNR  
(3)求图像YUV空间中的Y分量，仅仅计算Y分量的PSNR值(YUV空间中Y表示亮度信息，UV分别为浓度偏移分量，在视频编解码中比较常用)

其中方法(2)和(3)比较常用，下面给出方法(2)和(3)的c++代码：

#include <iostream>
    #include <vector>
    #include <opencv2\highgui\highgui.hpp>
    #include <opencv2\imgproc\imgproc.hpp>
    #include <opencv2\core\core.hpp>
    using namespace std;
    using namespace cv;
    
    
    double getPSNR(const Mat& I1, const Mat& I2){
        Mat s1;
        absdiff(I1, I2, s1);
        s1.convertTo(s1, CV_32F);
        s1 = s1.mul(s1);
        Scalar s = sum(s1);
        double sse = s.val[0] + s.val[1] + s.val[2];
        if(sse <= 1e-10)
            return 0;
        else{
            double mse = sse/(double)(I1.channels()*I1.total());
            double psnr = 10.0*log10(255*255/mse);
            return psnr;
        }
    
    }
    
    Scalar getMSSIM(const Mat& i1, const Mat& i2){
        const double C1=6.5025, C2 = 58.5225;
        int d = CV_32F;
    
        Mat I1, I2;
        i1.convertTo(I1, d);
        i2.convertTo(I2, d);
        Mat I2_2 = I2.mul(I2);     // I2^2
        Mat I1_2 = I1.mul(I1);      //I1^2
        Mat I1_I2 = I1.mul(I2);     // I1*I2
    
        Mat mu1, mu2;
        GaussianBlur(I1, mu1, Size(11, 11), 1.5);
        GaussianBlur(I2, mu2 ,Size(11, 11), 1.5);
    
        Mat mu1_2 = mu1.mul(mu1);
        Mat mu2_2 = mu2.mul(mu2);
        Mat mu1_mu2 = mu1.mul(mu2);
    
        Mat sigma1_2, sigma2_2, sigma12;
    
        GaussianBlur(I1_2, sigma1_2, Size(11, 11), 1.5);
        sigma1_2 -= mu1_2;
    
        GaussianBlur(I2_2, sigma2_2, Size(11,11), 1.5);
        sigma2_2 -= mu2_2;
    
        GaussianBlur(I1_I2, sigma12, Size(11,11), 1.5);
        sigma12 -= mu1_mu2;
    
        Mat t1, t2, t3;
        t1 = 2*mu1_mu2 + C1;
        t2 = 2*sigma12 + C2;
        t3 = t1.mul(t2);
    
        t1 = mu1_2 + mu2_2 + C1;
        t2 = sigma1_2 + sigma2_2 + C2;
        t1 = t1.mul(t2);
    
        Mat ssim_map;
        divide(t3, t1, ssim_map);
        Scalar mssim = mean(ssim_map);
        return mssim;
    }
    
    
    int main(){
        Mat i1 = imread("E:\\leetcode\\calcEvaluation\\1.jpg");
        Mat i2 = imread("E:\\leetcode\\calcEvaluation\\2.jpg");
        if(!i1.data || !i2.data){
            cout << "图片路径有误!" << endl;
            return -1;
        }
    
        cout << "PSNR: " << getPSNR(i1, i2) << endl;
        Scalar result = getMSSIM(i1, i2);
        if(i2.channels() == 3)
            cout<< "SSIM: " << (result.val[0]+ result.val[1]+result.val[2])/3 << endl;
        else cout << "SSIM: " << result.val[0] << endl;
    
        Mat i11, i22;
        cvtColor(i1, i11, COLOR_BGR2YUV);
        cvtColor(i2, i22, COLOR_BGR2YUV);
        vector<Mat> mv1, mv2;
        split(i11, mv1);
        split(i22, mv2);
        cout << "Y 分量PSNR: " << getPSNR(mv1[0], mv2[0]) << endl;
        cout << "Y 分量SSIM: " << getMSSIM(mv1[0], mv2[0]).val[0] << endl;
        return 0;
    }

最后参考网友\[2\]给出的一份matlab代码,仅针对方法(3)中的Y分量。  
psnr.m:

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);

ssim.m

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;
    end
    
    if (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;                                  %
    end
    
    if (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
    end
    
    if (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
    end
    
    if (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
    end
    
    if 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);
    % end
    
    C1 = (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

--------------------

## 参考文献 ##

\[1\] Image Quality Assessment: From Error Visibility to Structural Similarity  
\[2\][http://download.csdn.net/download/xiaohaijiejie/9058653][http_download.csdn.net_download_xiaohaijiejie_9058653]  
\[3\][http://blog.csdn.net/xiaxiazls/article/details/47952611][http_blog.csdn.net_xiaxiazls_article_details_47952611]

[20160330213107500]: /images/20220727/6a5c0adeb81d40e7b1064b630cf350dc.png
[20160330213140422]: /images/20220727/25439732206345d8984e5e3d01459c6a.png
[20160330213341579]: /images/20220727/54e4b5745aa24e539c8015ab1602fcc2.png
[20160330213412345]: /images/20220727/95b5a77b6df4401cbc73f157356545a3.png
[http_download.csdn.net_download_xiaohaijiejie_9058653]: http://download.csdn.net/download/xiaohaijiejie/9058653
[http_blog.csdn.net_xiaxiazls_article_details_47952611]: http://blog.csdn.net/xiaxiazls/article/details/47952611