一、SSIM基本定义
SSIM全称为“Structural Similarity Index”，中文意思即为结构相似性，是衡量图像质量的指标之一。给定两张图像x和y，其结构相似性可以定义为：
matlab中对SSIM的文档说明：
SSIM的范围为[0,1]，其值越大，表示图像的质量越好。当两张图像一模一样时，此时SSIM=1。计算SSIM有两种方法：
方法一：使用开源结构相似性函数
方法二：直接使用matlab的内置函数ssim()
matlab中对ssim()函数的文档说明：
二、matlab实现SSIM
1、方法二：SSIM.m
function [mssim, ssim_map] = SSIM(img1, img2, K, window, L)% ========================================================================% SSIM Index with automatic downsampling, Version 1.0% Copyright(c) 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. .%% 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@%%----------------------------------------------------------------------%%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)mssim = -Inf;ssim_map = -Inf;return;endif (size(img1) ~= size(img2))mssim = -Inf;ssim_map = -Inf;return;end[M N] = size(img1);if (nargin == 2)if ((M < 11) || (N < 11))mssim = -Inf;ssim_map = -Inf;returnendwindow = fspecial('gaussian', 11, 1.5);%K(1) = 0.01;% default settingsK(2) = 0.03;%L = 255; %endif (nargin == 3)if ((M < 11) || (N < 11))mssim = -Inf;ssim_map = -Inf;returnendwindow = fspecial('gaussian', 11, 1.5);L = 255;if (length(K) == 2)if (K(1) < 0 || K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;endelsemssim = -Inf;ssim_map = -Inf;return;endendif (nargin == 4)[H W] = size(window);if ((H*W) < 4 || (H > M) || (W > N))mssim = -Inf;ssim_map = -Inf;returnendL = 255;if (length(K) == 2)if (K(1) < 0 || K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;endelsemssim = -Inf;ssim_map = -Inf;return;endendif (nargin == 5)[H W] = size(window);if ((H*W) < 4 || (H > M) || (W > N))mssim = -Inf;ssim_map = -Inf;returnendif (length(K) == 2)if (K(1) < 0 || K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;endelsemssim = -Inf;ssim_map = -Inf;return;endendimg1 = double(img1);img2 = double(img2);% automatic downsamplingf = max(1,round(min(M,N)/256));%downsampling by f%use a simple low-pass filterif(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);endC1 = (K(1)*L)^2;C2 = (K(2)*L)^2;window = window/sum(sum(window));mu1 = filter2(window, img1, 'valid');mu2 = filter2(window, img2, 'valid');mu1_sq = mu1.*mu1;mu2_sq = mu2.*mu2;mu1_mu2 = mu1.*mu2;sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq;sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq;sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2;if (C1 > 0 && C2 > 0)ssim_map = ((2*mu1_mu2 + C1).*(2*sigma12 + C2))./((mu1_sq + mu2_sq + C1).*(sigma1_sq + sigma2_sq + C2));elsenumerator1 = 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);endmssim = mean2(ssim_map);return
2、主函数main.m
clc;clear;close all;rgbimage=imread('boy.jpg');attack_rgbimage=imnoise(rgbimage,'salt & pepper',0.1);figure(1),subplot(121),imshow(rgbimage);title('原始图像');subplot(122),imshow(attack_rgbimage);title('噪声攻击图像');ssimval1=SSIM(rgbimage,attack_rgbimage);% 方法一disp('SSIM函数的结构相似性：');disp(ssimval1);ssimval2=ssim(rgbimage,attack_rgbimage);% 方法二disp('matlab内置函数的结构相似性：');disp(ssimval2);
三、实现结果分析
1、输出结果
2、结果分析
1、注意每次运行主函数main.m文件，输出的SSIM值都会有细微差别，可以对比上下两张图。
2、可以发现开源函数计算的SSIM值总比matlab内置函数计算的SSIM值大，具体原因不可知。
3、仅以椒盐噪声的参数为讨论，我们将主函数main.m文件椒盐噪声的方差改为0.01，可以与上方得到方差为0.05的SSIM结果进行对比，可以看出得到的SSIM要大很多。
参考博客：图像质量评估指标：MSE，PSNR，SSIM
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