官方网站：https://ece.uwaterloo.ca/~z70wang/research/ssim/
1、SSIM
structural similarity index
一种衡量两幅图像相似度的新指标，其值越大越好，最大为1，
经常用到图像处理中，特别在图像去噪处理中在图像相似度评价上全面超越SNR（signal to noise ratio）和PSNR（peak signal to noise ratio）。
具体原理见
Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli. Image quality assessment: From error visibility to structural similarity. IEEE Transaction on Image Processing, 2004, 13(4):600–612
结构相似性理论认为，自然图像信号是高度结构化的，即像素间有很强的相关性，特别是空域中最接近的像素，这种相关性蕴含着视觉场景中物体结构的重要信息；HVS的主要功能是从视野中提取结构信息，可以用对结构信息的度量作为图像感知质量的近似。结构相似性理论是一种不同于以往模拟HVS低阶的组成结构的全新思想，与基于HVS特性的方法相比，最大的区别是自顶向下与自底向上的区别。这一新思想的关键是从对感知误差度量到对感知结构失真度量的转变。它没有试图通过累加与心理物理学简单认知模式有关的误差来估计图像质量，而是直接估计两个复杂结构信号的结构改变，从而在某种程度上绕开了自然图像内容复杂性及多通道去相关的问题。
作为结构相似性理论的实现，，结构相似度指数从图像组成的角度将结构信息定义为独立于亮度、对比度的，反映场景中物体结构的属性，并将失真建模为亮度、对比度和结构三个不同因素的组合。用均值作为亮度的估计，标准差作为对比度的估计，协方差作为结构相似程度的度量。
2.峰值信噪比（PSNR）
峰值信噪比（PSNR）是最普遍，最广泛使用的评鉴画质的客观量测法，PSNR的单位为dB。所以PSNR值越大，就代表失真越少PSNR=10*log10((2^n-1)^2/MSE)，MSE是原图像与处理图像之间均方误差。
源代码：
function s=csnr(A,B,row,col)%%峰值信噪比（PSNR）是最普遍，最广泛使用的评鉴画质的客观量测法，PSNR的单位为dB。所以PSNR值越大，就代表失真越少%%PSNR=10*log10((2^n-1)^2/MSE)，MSE是原图像与处理图像之间均方误差。%%row和col表示图像的边界像素数，A表示元图像，B表示处理后图像，返回值是性噪比[n,m,ch]=size(A);if ch==1%%二维灰度图像 e=A-B; e=e(row+1:n-row,col+1:m-col); me=mean(mean(e.^2));%%每个元素平方后，先求每列的均值，再求向量的均值，结果相当于求每个元素平方后的均值，即均方误差 s=10*log10(255^2/me);else%%表示二维彩色图像，具有三个通道，相当于有三层二维灰度图像，计算PSNR时每层分别进行计算 e=A-B; e=e(row+1:n-row,col+1:m-col,:); e1=e(:,:,1);e2=e(:,:,2);e3=e(:,:,3); me1=mean(mean(e1.^2)); %R me2=mean(mean(e2.^2)); %G me3=mean(mean(e3.^2)); %B s(1)=10*log10(255^2/me1); s(2)=10*log10(255^2/me2); s(3)=10*log10(255^2/me3);endreturn;
function ssim = cal_ssim( im1, im2, b_row, b_col )[h w] = size( im1 );ssim = ssim_index( im1( b_row+1:h-b_row, b_col+1:w-b_col ), im2( b_row+1:h-b_row, b_col+1:w-b_col ) );return;function [mssim, ssim_map] = ssim_index(img1, img2, K, window, L)%========================================================================%SSIM Index, Version 1.0%Copyright(c) 2003 Zhou Wang%All Rights Reserved.%%The author was with Howard Hughes Medical Institute, and Laboratory%for Computational Vision at Center for Neural Science and Courant%Institute of Mathematical Sciences, New York University, USA. He is%currently with Department of Electrical and Computer Engineering,%University of Waterloo, Canada.%%———————————————————————-%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.%———————————————————————-%是一个计算两幅图像结构相似性指数SSIM的算法%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 measurement to structural similarity"%IEEE Transactios on Image Processing, vol. 13, no. 4, 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) 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;return end window = fspecial('gaussian', 11, 1.5);% K(1) = 0.01;% default settings K(2) = 0.03;% L = 255;%endif (nargin == 3) if ((M < 11) | (N < 11))mssim = -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)mssim = -Inf;ssim_map = -Inf;return;end elsemssim = -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;return end L = 255; if (length(K) == 2)if (K(1) < 0 | K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;end elsemssim = -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;return end if (length(K) == 2)if (K(1) < 0 | K(2) < 0)mssim = -Inf;ssim_map = -Inf;return;end elsemssim = -Inf;ssim_map = -Inf;return; endendC1 = (K(1)*L)^2;C2 = (K(2)*L)^2;window = window/sum(sum(window));img1 = double(img1);img2 = double(img2);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));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);endmssim = mean2(ssim_map);return
在乎的应该是沿途的风景以及看风景的心情。
