计算机视觉 matlab 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

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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