推荐|图像质量的客观评估指标PSNR与SSIM

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

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

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
其中：

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 
#include 
#include 
#include 
#include 
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 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 [email protected]
%
%----------------------------------------------------------------------
%
%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
[3]http://iyenn.com/rec/1702894.html

1：PSNR

2：SSIM

3:代码

参考文献

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