图像处理之图像质量评价指标SSIM(结构相似性)

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) 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)
    mssim = -Inf;
    ssim_map = -Inf;
    return;
end

if (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;                                     %
end

if (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
    else
        mssim = -Inf;
        ssim_map = -Inf;
        return;
    end
end

if (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
    else
        mssim = -Inf;
        ssim_map = -Inf;
        return;
    end
end

if (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
    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));
%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;
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));
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
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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);
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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