%%%%suggestion of usage
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 (nargin < 2 || nargin > 5) %參數個數小於2個或者大於5個,則退出
mssim = -Inf;
ssim_map = -Inf;
return;
end
if (size(img1) ~= size(img2)) %對比的兩幅圖大小要一致，否則退出
mssim = -Inf;
ssim_map = -Inf;
return;
end
[M, N] = size(img1); %將圖1的大小賦值給M N
if (nargin == 2) %參數為2時
if ((M < 11) || (N < 11)) %圖像長寬都不能小於11，否則退出
mssim = -Inf;
ssim_map = -Inf;
return
end
window = fspecial('gaussian', 11, 1.5); %建立預定義的濾波算子。
%為高斯低通濾波，有兩個參數，hsize表示模板尺寸，默認值為[3 3]，sigma為濾波器的標准值，單位為像素，默認值為0.5.
K(1) = 0.01; % default settings
K(2) = 0.03; %K L參數設置為最佳默認值
L = 255; %設置L的默認值
end
if (nargin == 3) %參數為3個時，第3個參數為K
if ((M < 11) || (N < 11))
mssim = -Inf;
ssim_map = -Inf;
return
end
window = fspecial('gaussian', 11, 1.5); %獲取濾波算子，類型為gaussian，11為窗口尺寸，1.5為標准差
L = 255;
if (length(K) == 2) %參數K為2個元素的數組，且都大於0
if (K(1) < 0 || K(2) < 0)
mssim = -Inf;
ssim_map = -Inf;
return;
end
else
mssim = -Inf;
ssim_map = -Inf;
return;
end
end
if (nargin == 4) %參數3為K，參數4為窗口大小
[H, W] = size(window); %window參數類似ones(8)
if ((H*W) < 4 || (H > M) || (W > N)) %窗口大小要求大於4或者長寬不小於圖像的長寬
mssim = -Inf;
ssim_map = -Inf;
return
end
L = 255;
if (length(K) == 2) %判斷K數組的大小
if (K(1) < 0 || K(2) < 0)
mssim = -Inf;
ssim_map = -Inf;
return;
end
else
mssim = -Inf;
ssim_map = -Inf;
return;
end
end
if (nargin == 5) %當后3個參數都設置時，其中L參數執行傳入的參數
[H, W] = size(window);
if ((H*W) < 4 || (H > M) || (W > N))
mssim = -Inf;
ssim_map = -Inf;
return
end
if (length(K) == 2)
if (K(1) < 0 || K(2) < 0)
mssim = -Inf;
ssim_map = -Inf;
return;
end
else
mssim = -Inf;
ssim_map = -Inf;
return;
end
end
img1 = double(img1);
img2 = double(img2);
% automatic downsampling
f = max(1,round(min(M,N)/256)); %先選擇行列兩者中的最小值取整，再選擇其中的最大值
%downsampling by f
%use a simple low-pass filter
if(f>1)
lpf = ones(f,f); %初始化一個單位矩陣，用於歸一化
lpf = lpf/sum(lpf(:)); %歸一化，除以單位矩陣的個數
img1 = imfilter(img1,lpf,'symmetric','same'); %使用濾波函數對img1進行處理，lpf是歸一化的濾波模板，
%邊界使用symmetric鏡像反射填充邊界
img2 = imfilter(img2,lpf,'symmetric','same');
%%% 均值濾波
img1 = img1(1:f:end,1:f:end); %向下隔點取樣
img2 = img2(1:f:end,1:f:end);
end
C1 = (K(1)*L)^2; %求取論文中C1的值
C2 = (K(2)*L)^2; %求取論文中C2的值
window = window/sum(sum(window)); %濾波器歸一化操作。缺省的sum(x)就是豎向相加，求每列的和，結果是行向量
mu1 = filter2(window, img1, 'valid'); %使用設定好的高斯低通濾波器window對img1進行濾波，結果保存在mu1中
%mu1相當於論文中的Ux,即圖像img1的均值
mu2 = filter2(window, img2, 'valid'); %mu2相當於論文中的Uy，即圖像img2的均值，點乘模板相加，因為window歸一化了，所以是均值
mu1_sq = mu1.*mu1; %矩陣運算，相當於img1均值的矩陣乘法平方
mu2_sq = mu2.*mu2;
mu1_mu2 = mu1.*mu2; %img1和img2均值的矩陣乘法平方
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq; %協方差期望公式：sigma_x=E（X^2）-（EX）^2
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq; %協方差期望公式：sigma_y=E（Y^2）-（EY）^2
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2; %協方差期望公式：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
