SSIM的全稱為structural similarity index，即為結(jié)構(gòu)相似性，是一種衡量兩幅圖像相似度的指標(biāo)。該指標(biāo)首先由德州大學(xué)奧斯丁分校的圖像和視頻工程實(shí)驗(yàn)室(Laboratory for Image and Video Engineering)提出。而如果兩幅圖像是壓縮前和壓縮后的圖像，那么SSIM算法就可以用來評估壓縮后的圖像質(zhì)量。

在實(shí)際應(yīng)用中，一般采用高斯函數(shù)計算圖像的均值、方差以及協(xié)方差，而不是采用遍歷像素點(diǎn)的方式，以換來更高的效率。

具體步驟：

更正下協(xié)方差計算

python 代碼：

def keras_SSIM_cs(y_true, y_pred):axis=Nonegaussian = make_kernel(1.5)x = tf.nn.conv2d(y_true, gaussian, strides=[1, 1, 1, 1], padding='SAME')y = tf.nn.conv2d(y_pred, gaussian, strides=[1, 1, 1, 1], padding='SAME')u_x=K.mean(x, axis=axis)u_y=K.mean(y, axis=axis)var_x=K.var(x, axis=axis)var_y=K.var(y, axis=axis)cov_xy=cov_keras(x, y, axis)K1=0.01K2=0.03L=1 # depth of image (255 in case the image has a differnt scale)C1=(K1*L)**2C2=(K2*L)**2C3=C2/2l = ((2*u_x*u_y)+C1) / (K.pow(u_x,2) + K.pow(u_x,2) + C1)c = ((2*K.sqrt(var_x)*K.sqrt(var_y))+C2) / (var_x + var_y + C2)s = (cov_xy+C3) / (K.sqrt(var_x)*K.sqrt(var_y) + C3)return [c,s,l]def keras_MS_SSIM(y_true, y_pred):iterations = 5x=y_truey=y_predweight = [0.0448, 0.2856, 0.3001, 0.2363, 0.1333]c=[]s=[]for i in range(iterations):cs=keras_SSIM_cs(x, y)c.append(cs[0])s.append(cs[1])l=cs[2]if(i!=4):x=tf.image.resize_images(x, (x.get_shape().as_list()[1]//(2**(i+1)), x.get_shape().as_list()[2]//(2**(i+1))))y=tf.image.resize_images(y, (y.get_shape().as_list()[1]//(2**(i+1)), y.get_shape().as_list()[2]//(2**(i+1))))c = tf.stack(c)s = tf.stack(s)cs = c*s#Normalize: suggestion from https://github.com/jorge-pessoa/pytorch-msssim/issues/2 last comment to avoid NaN valuesl=(l+1)/2cs=(cs+1)/2cs=cs**weightcs = tf.reduce_prod(cs)l=l**weight[-1]ms_ssim = l*csms_ssim = tf.where(tf.is_nan(ms_ssim), K.zeros_like(ms_ssim), ms_ssim)return K.mean(ms_ssim)

MATLAB代碼：

function [mssim, ssim_map] = ssim(img1, img2, K, window, L)% ======================================================================== % Edited code by Adam Turcotte and Nicolas Robidoux % Laurentian University % Sudbury, ON, Canada % Last Modified: 2011-01-22 % ---------------------------------------------------------------------- % This code implements a refactored computation of SSIM that requires % one fewer blur (4 instead of 5), the same number of pixel-by-pixel % binary operations (10), and two fewer unary operations (6 instead of 8). % % In addition, this version reduces memory usage with in-place functions. % As a result, it supports larger input images. %========================================================================% ======================================================================== % 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; 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;end endif (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;end endif (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;end endimg1 = 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 = (1./(f*f))*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)); ssim_map = filter2(window, img1, 'valid'); % gx w1 = filter2(window, img2, 'valid'); % gy w2 = ssim_map.*w1; % gx*gy w2 = 2*w2+C1; % 2*(gx*gy)+C1 = num1 w1 = (w1-ssim_map).^2+w2; % (gy-gx)^2+num1 = den1 ssim_map = filter2(window, img1.*img2, 'valid'); % g(x*y) ssim_map = (2*ssim_map+(C1+C2))-w2; % 2*g(x*y)+(C1+C2)-num1 = num2 ssim_map = ssim_map.*w2; % num img1 = img1.^2; % x^2 img2 = img2.^2; % y^2 img1 = img1+img2; % x^2+y^2if (C1 > 0 && C2 > 0)w2 = filter2(window, img1, 'valid'); % g(x^2+y^2)w2 = w2-w1+(C1+C2); % den2w2 = w2.*w1; % denssim_map = ssim_map./w2; % num/den = ssim elsew3 = filter2(window, img1, 'valid'); % g(x^2+y^2)w3 = w3-w1+(C1+C2); % den2w4 = ones(size(w1));index = (w1.*w3 > 0);w4(index) = (ssim_map(index))./(w1(index).*w3(index));index = (w1 ~= 0) & (w3 == 0);w4(index) = w2(index)./w1(index);ssim_map = w4; endmssim = mean2(ssim_map);return

C++代碼

#include <opencv2/imgproc/imgproc.hpp> #include <opencv2/core/core.hpp> #include <opencv2/highgui/highgui.hpp> #include <iostream>using namespace std; using namespace cv;Scalar getMSSIM(Mat inputimage1, Mat inputimage2); int main() {Mat BlurImage1;Mat BlurImage2;Mat SrcImage = imread("1.jpg");blur(SrcImage, BlurImage1, Size(5, 5));blur(SrcImage,BlurImage2,Size(10,10));Scalar SSIM1 = getMSSIM(SrcImage, BlurImage1);Scalar SSIM2 = getMSSIM(SrcImage, BlurImage2);printf("模糊5*5通道1：%f\n", SSIM1.val[0] * 100);printf("模糊5*5通道2：%f\n", SSIM1.val[1] * 100);printf("模糊5*5通道3：%f\n", SSIM1.val[2] * 100);printf("模糊5*5：%f\n", (SSIM1.val[2] + SSIM1.val[1] + SSIM1.val[0])/3 * 100);printf("模糊10*10通道1：%f\n", SSIM2.val[0] * 100);printf("模糊10*10通道2：%f\n", SSIM2.val[1] * 100);printf("模糊10*10通道3：%f\n", SSIM2.val[2] * 100);printf("模糊10*10：%f\n", (SSIM2.val[2] + SSIM2.val[1] + SSIM2.val[0]) / 3 * 100);imshow("原圖",SrcImage);imshow("模糊5*5",BlurImage1);imshow("模糊10*10", BlurImage2);waitKey(0);return 0; } Scalar getMSSIM(Mat inputimage1, Mat inputimage2) {Mat i1 = inputimage1;Mat i2 = inputimage2;const double C1 = 6.5025, C2 = 58.5225;int d = CV_32F;Mat I1, I2;i1.convertTo(I1, d);i2.convertTo(I2, d);Mat I2_2 = I2.mul(I2);Mat I1_2 = I1.mul(I1);Mat I1_I2 = I1.mul(I2);Mat mu1, mu2;GaussianBlur(I1, mu1, Size(11, 11), 1.5);GaussianBlur(I2, mu2, Size(11, 11), 1.5);Mat mu1_2 = mu1.mul(mu1);Mat mu2_2 = mu2.mul(mu2);Mat mu1_mu2 = mu1.mul(mu2);Mat sigma1_2, sigma2_2, sigma12;GaussianBlur(I1_2, sigma1_2, Size(11, 11), 1.5);sigma1_2 -= mu1_2;GaussianBlur(I2_2, sigma2_2, Size(11, 11), 1.5);sigma2_2 -= mu2_2;GaussianBlur(I1_I2, sigma12, Size(11, 11), 1.5);sigma12 -= mu1_mu2;Mat t1, t2, t3;t1 = 2 * mu1_mu2 + C1;t2 = 2 * sigma12 + C2;t3 = t1.mul(t2);t1 = mu1_2 + mu2_2 + C1;t2 = sigma1_2 + sigma2_2 + C2;t1 = t1.mul(t2);Mat ssim_map;divide(t3, t1, ssim_map);Scalar mssim = mean(ssim_map);return mssim; }

這里附一個Python的工具箱，有各種評價函數(shù)：

The following metrics are included:

• Mean-Squared-Error (MSE).

• Peak-Signal-to-Noise-Ratio (PSNR).

• Structural Similarity Index (SSIM).

• Normalized Mutual Information (NMI).

• Image Complexity.

• Resolution analysis through Edge-Profile-Fitting (EPF).

• Resolution analysis through Fourier Ring Correlation (FRC).

The following routines to construct simulated datasets are included:

• Create a Shepp-Logan phantom.

• Create generic phantoms with analytical X-ray transform.

• Rescale image.

• Downsample sinogram.

• Add Gaussian or Poisson noise.

• Add Gaussian blurring.

? ?https://github.com/arcaduf/image_quality_assessment

【1】https://ieeexplore.ieee.org/abstract/document/1292216

?【2】Image?quality assessment: From error visibility to structural similarity,

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