matlab中中影象PSNR和SSIM的計算

澍yeah發表於2018-09-07
Matlab

轉：https://blog.csdn.net/xiaohaijiejie/article/details/48053595

網上找了很多關於PSNR和SSIM的計算，很多結果算出來都不一樣，公式都是普遍的，如下：

現在總結下造成結果差異的原因。

 

PSNR的差異：

1.灰度影象：灰度影象比較好計算，只有一個灰度值。

 

2.彩色影象：

(a)可以將分別計算R,G,B三個通道總和，最後MSE直接在原公式上多除以3就行（opencv官方代碼是這麼做的，與matlab直接計算結果是一樣的）。

(b)將R,G,B格式轉換為YCbCr，只計算Y分量（亮度分量），結果會比直接計算要高几個dB。

 

貼程式碼，這裡是將圖片格式轉成YCbCr（只計算Y分量）：

function [PSNR, MSE] = psnr(X, Y)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 計算峰值訊雜比PSNR
% 將RGB轉成YCbCr格式進行計算
% 如果直接計算會比轉後計算值要小2dB左右（當然是個別測試）
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
 if size(X,3)~=1   %判斷影象時不是彩色圖，如果是，結果為3，否則為1
   org=rgb2ycbcr(X);
   test=rgb2ycbcr(Y);
   Y1=org(:,:,1);
   Y2=test(:,:,1);
   Y1=double(Y1);  %計算平方時候需要轉成double型別，否則uchar型別會丟失資料
   Y2=double(Y2);
 else              %灰度影象，不用轉換
     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);

控制檯輸入下面三條語句：


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

SSIM的差異：同上，如果直接不轉換成YCbCr格式，結果會偏高很多（matlab中，SSIM提出者【1】，程式碼）。opencv裡面是分別計算了R,G,B三個分量的SSIM值（官方程式碼）。最後我將3個值取了個平均（這個值比matlab裡面低很多）。

以下程式碼主要是參考原作者修改的，原始碼是直接沒有進行格式轉換，直接RGB格式，下面我是將他轉換成YCbCr計算圖片的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;
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))   % 影象大小過小，則沒有意義。
           ssim_index = -Inf;
           ssim_map = -Inf;
      return
   end
   window = fspecial('gaussian', 11, 1.5);        % 引數一個標準偏差1.5，11*11的高斯低通濾波。
   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   %判斷影象時不是彩色圖，如果是，結果為3，否則為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;    % 計算C1引數，給亮度L（x，y）用。    C1=6.502500
C2 = (K(2)*L)^2;    % 計算C2引數，給對比度C（x，y）用。  C2=58.522500 
window = window/sum(sum(window)); %濾波器歸一化操作。
 
 
mu1   = filter2(window, img1, 'valid');  % 對影象進行濾波因子加權  valid改成same結果會低一丟丟
mu2   = filter2(window, img2, 'valid');  % 對影象進行濾波因子加權
 
mu1_sq = mu1.*mu1;     % 計算出Ux平方值。
mu2_sq = mu2.*mu2;     % 計算出Uy平方值。
mu1_mu2 = mu1.*mu2;    % 計算Ux*Uy值。
 
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq;  % 計算sigmax （標準差）
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq;  % 計算sigmay （標準差）
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2;   % 計算sigmaxy（標準差）
 
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

控制檯輸入以下程式碼：


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

最後說一句，不管是結果如何，只要對比實驗用的同一種評價程式碼工具，無所謂結果和原論文一不一樣，問題是很多論文實驗都搞不出來滴

參考文獻

【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.

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