图像PSNR及其计算（OpenCV和matlab实现）

引言：在图像处理中，要对图像进行客观的评价，常常需要计算PSNR，本文将简单介绍PSNR的定义，并给出相关的源代码。

PSNR的概念

PSNR (Peak Signal to Noise Ratio)
峰值信噪比PSNR衡量图像失真或是噪声水平的客观标准。2个图像之间PSNR值越大，则越相似。普遍基准为30dB，30dB以下的图像劣化较为明显。定义为，

这里MAX表示图像颜色的最大数值，8bit图像取值为255。我们还要介绍MSE（均方差），即m×n单色图像 I 和 K（原图像与处理图像）之间均方误差，定义为：

PSNR编程实现

matlab实现

第一种实现方法：

• 在matlab 2016版本中是带有psnr的计算的，只需调用相关函数就好。官方详细说明链接

peaksnr = psnr(A,ref)
%peaksnr = psnr(A,ref) calculates the peak signal-to-noise ratio for the image A, with the image ref as the reference. A and ref must be of the same size and class.
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第二种直观方法

• 在matlab中新建m文件，下面这个实现简单明了

function [PSNR, MSE]=psnr(I,K)
[M,N,D] = size(I);
Diff = double(I)-double(K);
MSE = sum(Diff(:).^2)/numel(I);
PSNR=10*log10(255^2/MSE);
end
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第三种实现方法：

• 在matlab中新建m文件，复制进去保存就可以调用了。

function PSNR(A,B)

% PURPOSE: To find the PSNR (peak signal-to-noise ratio) between two
%          intensity images A and B, each having values in the interval
%          [0,1]. The answer is in decibels (dB).
%
%          There is also a provision, in EXAMPLE 3 below, for images 
%          stored in the interval [0,255], i.e. 256 gray levels. 
%
% SYNOPSIS: PSNR(A,B)
%
% DESCRIPTION: The following is quoted from "Fractal Image Compression",
%              by Yuval Fisher et al.,(Springer Verlag, 1995),
%              section 2.4, "Pixelized Data".
%
%              "...PSNR is used to measure the difference between two
%              images. It is defined as
%
%                           PSNR = 20 * log10(b/rms)
%
%              where b is the largest possible value of the signal
%              (typically 255 or 1), and rms is the root mean square
%              difference between two images. The PSNR is given in
%              decibel units (dB), which measure the ratio of the peak 
%              signal and the difference between two images. An increase
%              of 20 dB corresponds to a ten-fold decrease in the rms
%              difference between two images.
%              
%              There are many versions of signal-to-noise ratios, but
%              the PSNR is very common in image processing, probably
%              because it gives better-sounding numbers than other
%              measures."
%
% EXAMPLE 1: load clown
%            A = ind2gray(X,map); % Convert to an intensity image in [0,1].
%            B = 0.95 * A;        % Make B close to, but different from, A.
%            PSNR(A,B)            % ---> "PSNR = +33.49 dB"
%
% EXAMPLE 2: A = rand(256); % A is a random 256 X 256 matrix in [0,1].
%            B = 0.9 * A;   % Make B close to, but different from, A.
%            PSNR(A,B)      % ---> "PSNR = +24.76 dB (approx)"
%
% EXAMPLE 3: For images with 256 gray levels: this function PSNR was 
%            originally written for matrix-values between 0 and 1,
%            because of MATLAB's preference for that interval.
%
%            However, suppose the matrix has values in [0,255]. Taking
%            Example 1 above, we could change the image to 256 gray levels.
%         
%            load clown
%            A = ind2gray(X,map); % Convert to intensity image in [0,1]
%            AA = uint8(255*A);   % Change to integers in [0,255]
%            BB = 0.95*AA;        % Make BB close to AA.
%
%            Now we must alter the code for this new case. Comment out the
%            existing program (using %) and uncomment the alternative 
%            underneath it.
%
%            PSNR(AA,BB)          % ---> "PSNR = +33.56 dB"
%
%            Note the slightly different result from Example 1, because
%            decimal values were rounded into integers.

if A == B
   error('Images are identical: PSNR has infinite value')
end

max2_A = max(max(A));
max2_B = max(max(B));
min2_A = min(min(A));
min2_B = min(min(B));

if max2_A > 1 || max2_B > 1 || min2_A < 0 || min2_B < 0
   error('input matrices must have values in the interval [0,1]')
end

error_diff = A - B;
decibels = 20*log10(1/(sqrt(mean(mean(error_diff.^2)))));
disp(sprintf('PSNR = +%5.2f dB',decibels))

% if A == B
%    error('Images are identical: PSNR has infinite value')
% end

% max2_A = max(max(A));
% max2_B = max(max(B));
% min2_A = min(min(A));
% min2_B = min(min(B));
%
% if max2_A > 255 || max2_B > 255 || min2_A < 0 || min2_B < 0
%   error('input matrices must have values in the interval [0,255]')
% end

% error_diff = A - B;
% decibels = 20*log10(255/(sqrt(mean(mean(error_diff.^2)))));
% disp(sprintf('PSNR = +%5.2f dB',decibels))
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OpenCV实现

• 使用的是opencv 2.0版本，核心程序如下，很简单的程序，详细的注释可以帮助你理解getPSNR函数：

//输入格式是Mat类型，I1，I2代表是输入的两幅图像
double getPSNR(const Mat& I1, const Mat& I2)
{
    Mat s1;
    absdiff(I1, I2, s1);       // |I1 - I2|AbsDiff函数是 OpenCV 中计算两个数组差的绝对值的函数
    s1.convertTo(s1, CV_32F);  // 这里我们使用的CV_32F来计算，因为8位无符号char是不能进行平方计算
    s1 = s1.mul(s1);           // |I1 - I2|^2

    Scalar s = sum(s1);         //对每一个通道进行加和

    double sse = s.val[0] + s.val[1] + s.val[2]; // sum channels

    if( sse <= 1e-10) // 对于非常小的值我们将约等于0
        return 0;
    else
    {
        double  mse =sse /(double)(I1.channels() * I1.total());//计算MSE
        double psnr = 10.0*log10((255*255)/mse);
        return psnr;//返回PSNR
    }
}
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可能需要添加的头文件是：

#include         // Basic OpenCV structures (cv::Mat, Scalar)
#include   // OpenCV window I/O
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使用说明：

//先定义PSNR
double psnr;
//然后读取输入的两幅图像
Mat img1=imread('1.jpg');
Mat img2=imread('2.jpg');
//调用函数
psnr = getPSNR(img1,img2);  
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参考资料

[1]http://iyenn.com/index/link?url=http://www.opencv.org.cn/opencvdoc/2.3.2/html/doc/tutorials/highgui/video-input-psnr-ssim/video-input-psnr-ssim.html
[2]http://iyenn.com/index/link?url=http://www.mathworks.com/matlabcentral/fileexchange/135-psnr