matlab中中图像PSNR和SSIM的计算

图像处理结果的度量 —— SNR、PSNR、SSIM

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）：

[cpp] view plaincopy

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);

控制台输入下面三条语句：

[cpp] view plaincopy

>> 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

[cpp] view plaincopy

function [mssim, ssim_map] = ssim(img1, img2, K, window, L)
%========================================================================
%SSIM Index, Version 1.0
%
%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

控制台输入以下代码：

[cpp] view plaincopy

>> 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.

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