ssim.m

function [mssim, ssim_map] = ssim(img1, img2, K, window, L)

% ========================================================================
% SSIM Index with automatic downsampling, Version 1.0
% Copyright(c) 2009 Zhou Wang
% All Rights Reserved.
%
% ----------------------------------------------------------------------
% 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 
% appear on 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 and the website with suggested usage
%
% 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.
%
% http://www.ece.uwaterloo.ca/~z70wang/research/ssim/
%
% Note: This program is different from ssim_index.m, 
% where no automatic downsampling is performed.
% (downsampling was done in the above paper
% and was described as suggested usage in the above website.)
%
% 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
%            depends on the window size and the downsampling factor.
%
%----------------------------------------------------------------------
%Basic Usage:
% Given 2 test images img1 and img2, whose dynamic range is 0-255
% [mssim, ssim_map] = ssim(img1, img2);
%
%Advanced Usage:
% User defined parameters. For example
% K = [0.05 0.05];
% window = ones(8);
% L = 100;
% [mssim, ssim_map] = ssim(img1, img2, K, window, L);
%Visualize the results:
% mssim %Gives the mssim value
% imshow(max(0, ssim_map).^4) %Shows the SSIM index map
%========================================================================


%% 
% 
% if size(img1,3)==3  %把rgb图像转换为灰度图像
%     img1=rgb2gray(img1);
%     img2=rgb2gray(img2);
% end

%% 参数个数小于2个或者大于5个,则退出
if (nargin < 2 || nargin > 5) 
    mssim = -Inf;
    ssim_map = -Inf;
    return;
end


%% 对比的两幅图大小要一致，否则将原图img1裁剪

if size(img1,3)~=1   %判断图像时不是彩色图rgb，如果是，结果为3，否则为1  
    org=rgb2ycbcr(img1);  
    test=rgb2ycbcr(img2);  
    img1=double(org(:,:,1));    %只取亮度分量进行计算
    img2=double(test(:,:,1));   %计算平方时候需要转成double类型，否则uchar类型会丢失数据 
else              %灰度图像/只有亮度分量，不用转换  
    img1=double(img1);  
    img2=double(img2);  
end  

if any(size(img1)~=size(img2))
    s1 = (size(img1,1)-size(img2,1))/2;
    s2 = (size(img1,2)-size(img2,2))/2;
    img1 = img1(1+s1 : size(img1,1)-s1 , 1+s2 : size(img1,2)-s2);
end


[M, N] = size(img1); %将图1的大小赋值给M N

%% 2个参数
if (nargin == 2) 
    if ((M < 11) || (N < 11)) %图像长宽都不能小于11，否则退出
        mssim = -Inf;
        ssim_map = -Inf;
        return
    end
    window = fspecial('gaussian', 11, 1.5); %建立预定义的滤波算子。%类型为gaussian，11为窗口尺寸，1.5为标准差
    %为高斯低通滤波，有两个参数，hsize表示模板尺寸，默认值为[3 3]，sigma为滤波器的标准值，单位为像素，默认值为0.5.
    %K L参数设置为最佳默认值
    K(1) = 0.01;    % default settings
    K(2) = 0.03;    
    L = 255; %设置L的默认值
end

%% 3个参数
if (nargin == 3) %第3个参数为K
    if ((M < 11) || (N < 11)) %图像长宽都不能小于11，否则退出
        mssim = -Inf;
        ssim_map = -Inf;
        return
    end
    window = fspecial('gaussian', 11, 1.5); %获取滤波算子，类型为gaussian，11为窗口尺寸，1.5为标准差
    L = 255;
    if (length(K) == 2) %参数K需要满足：为2个元素的数组，且都大于0
        if (K(1) < 0 || K(2) < 0)
            mssim = -Inf;
            ssim_map = -Inf;
            return;
        end
    else
        mssim = -Inf;
        ssim_map = -Inf;
        return;
    end
end

%% 4个参数
if (nargin == 4) %参数3为K，参数4为窗口大小
    [H, W] = size(window); %window参数类似ones(8)
    if ((H*W) < 4 || (H > M) || (W > N)) %窗口大小要求大于4或者长宽不小于图像的长宽
        mssim = -Inf;
        ssim_map = -Inf;
        return
    end
    L = 255;
    if (length(K) == 2) %判断参数K
        if (K(1) < 0 || K(2) < 0)
            mssim = -Inf;
            ssim_map = -Inf;
            return;
        end
    else
        mssim = -Inf;
        ssim_map = -Inf;
        return;
    end
end

%% 5个参数
if (nargin == 5) %当后3个参数都设置时，其中L参数执行传入的参数
    [H, W] = size(window);
    if ((H*W) < 4 || (H > M) || (W > N)) %判断窗口大小
        mssim = -Inf;
        ssim_map = -Inf;
        return
    end
    if (length(K) == 2) %判断参数K
        if (K(1) < 0 || K(2) < 0)
            mssim = -Inf;
            ssim_map = -Inf;
            return;
        end
    else
        mssim = -Inf;
        ssim_map = -Inf;
        return;
    end
end

%%

% automatic downsampling
f = max(1,round(min(M,N)/256)); %先选择像素矩阵行列两者中的最小值取整，再选择1和最小值/256 中的较大值
%downsampling by f . use a simple low-pass filter 
if(f>1)
    lpf = ones(f,f); %初始化一个单位矩阵，用于归一化
    lpf = lpf/sum(lpf(:)); %归一化，除以单位矩阵的个数
    %使用线性空间滤波函数imfilter对img1进行处理，lpf是归一化的滤波模板，
    %g=imfilter(f, w, filtering_mode, boundary_options, size_options)
    %       f为输入图像，w为滤波掩模，g为滤波后图像。
    %       filtering_mode用于指定在滤波过程中是使用“相关”还是“卷积”。这里用默认的“相关”
    %       boundary_options用于处理边界充零问题，边界的大小由滤波器的大小确定。
    %       这里边界使用symmetric镜像反射填充边界
    %s      ize_options 默认值为‘same’	输出图像的大小与输入图像的大小相同。这可通过将滤波掩模的中心点的偏移限制到原图像中包含的点来实现。
    %                    ‘full’	输出图像的大小与被扩展图像的大小相同
    img1 = imfilter(img1,lpf,'symmetric','same');     
    img2 = imfilter(img2,lpf,'symmetric','same');
    %%% 均值滤波
    img1 = img1(1:f:end,1:f:end); %向下隔点取样
    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。 
C2 = (K(2)*L)^2;  % 计算C2参数，给对比度C（x，y）用。
window = window/sum(sum(window)); %滤波器归一化操作。

%{
%使用设定好的高斯低通滤波器window 对img1进行滤波，结果保存在mu1、mu2中
%mu1相当于图像img1的均值Ux，mu2相当于图像img2的均值Uy
%点乘模板相加，因为window归一化了，所以是均值
%}
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'); 
mu1_sq = mu1.*mu1; %矩阵运算，相当于img1均值的矩阵乘法平方
mu2_sq = mu2.*mu2;
mu1_mu2 = mu1.*mu2; %img1和img2均值的矩阵乘法平方
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq; %协方差期望公式：sigma_x=E（X^2）-（EX）^2
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq; %协方差期望公式：sigma_y=E（Y^2）-（EY）^2
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2; %协方差期望公式：sigma_xy=E(XY）-（EX）*（EY）

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