- PSNR
- SSIM
- 代碼
- 參考文獻
1:PSNR
PSNR是最爲常用的圖像質量評估指標:
其中K爲圖像對應二進制位數,一般爲8。MSE爲均方誤差,計算公式爲:
2:SSIM
SSIM[1]主要用來衡量圖像結構完整性,是另一種比較常用的客觀評估指標。實際應用中,一般用滑動窗口對圖像進行分塊,這裏的滑動窗口一般爲高斯窗口,並用高斯加權計算每個窗口的均值、方差和協方差。這樣每塊的SSIM計算如下:
其中:
文獻[1]給出公式中默認參數:窗口w爲11*11的高斯窗口;其中K1=0.01,K2=0.02,L=255,C1=(K1*L)^2,C2=(K2*L)^2
3:代碼
問題在於給定了一副彩色圖片,彩色圖片有RGB三通道,如何計算其PSNR或者SSIM值,方法有以下三種(以PSNR爲例):
(1)計算彩色圖像RGB三通道每一通道的PSNR值,然後求均值
(2)計算彩色圖像RGB三通道每一通道的MSE值,求平均,然後再代入求PSNR
(3)求圖像YUV空間中的Y分量,僅僅計算Y分量的PSNR值(YUV空間中Y表示亮度信息,UV分別爲濃度偏移分量,在視頻編解碼中比較常用)
其中方法(2)和(3)比較常用,下面給出方法(2)和(3)的c++代碼:
#include <iostream>
#include <vector>
#include <opencv2\highgui\highgui.hpp>
#include <opencv2\imgproc\imgproc.hpp>
#include <opencv2\core\core.hpp>
using namespace std;
using namespace cv;
double getPSNR(const Mat& I1, const Mat& I2){
Mat s1;
absdiff(I1, I2, s1);
s1.convertTo(s1, CV_32F);
s1 = s1.mul(s1);
Scalar s = sum(s1);
double sse = s.val[0] + s.val[1] + s.val[2];
if(sse <= 1e-10)
return 0;
else{
double mse = sse/(double)(I1.channels()*I1.total());
double psnr = 10.0*log10(255*255/mse);
return psnr;
}
}
Scalar getMSSIM(const Mat& i1, const Mat& i2){
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); // I2^2
Mat I1_2 = I1.mul(I1); //I1^2
Mat I1_I2 = I1.mul(I2); // I1*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;
}
int main(){
Mat i1 = imread("E:\\leetcode\\calcEvaluation\\1.jpg");
Mat i2 = imread("E:\\leetcode\\calcEvaluation\\2.jpg");
if(!i1.data || !i2.data){
cout << "圖片路徑有誤!" << endl;
return -1;
}
cout << "PSNR: " << getPSNR(i1, i2) << endl;
Scalar result = getMSSIM(i1, i2);
if(i2.channels() == 3)
cout<< "SSIM: " << (result.val[0]+ result.val[1]+result.val[2])/3 << endl;
else cout << "SSIM: " << result.val[0] << endl;
Mat i11, i22;
cvtColor(i1, i11, COLOR_BGR2YUV);
cvtColor(i2, i22, COLOR_BGR2YUV);
vector<Mat> mv1, mv2;
split(i11, mv1);
split(i22, mv2);
cout << "Y 分量PSNR: " << getPSNR(mv1[0], mv2[0]) << endl;
cout << "Y 分量SSIM: " << getMSSIM(mv1[0], mv2[0]).val[0] << endl;
return 0;
}
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最後參考網友[2]給出的一份matlab代碼,僅針對方法(3)中的Y分量。
psnr.m:
function [PSNR, MSE] = psnr(X, Y)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 計算峯值信噪比PSNR
% 將RGB轉成YCbCr格式進行計算
% 如果直接計算會比轉後計算值要小2dB左右(當然是個別測試)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
if size(X,3)~=1 %判斷圖像時不是彩色圖,如果是,結果爲3,否則爲1
org=rgb2ycbcr(X);
test=rgb2ycbcr(Y);
Y1=org(:,:,1);
Y2=test(:,:,1);
Y1=double(Y1); %計算平方時候需要轉成double類型,否則uchar類型會丟失數據
Y2=double(Y2);
else %灰度圖像,不用轉換
Y1=double(X);
Y2=double(Y);
end
if nargin<2
D = Y1;
else
if any(size(Y1)~=size(Y2))
error('The input size is not equal to each other!');
end
D = Y1 - Y2;
end
MSE = sum(D(:).*D(:)) / numel(Y1);
PSNR = 10*log10(255^2 / MSE);
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ssim.m
function [mssim, ssim_map] = ssim(img1, img2, K, window, L)
%========================================================================
%SSIM Index, Version 1.0
%Copyright(c) 2003 Zhou Wang
%All Rights Reserved.
%
%The author is with Howard Hughes Medical Institute, and Laboratory
%for Computational Vision at Center for Neural Science and Courant
%Institute of Mathematical Sciences, New York University.
%
%----------------------------------------------------------------------
%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 ap pearon 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:
%
%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.
%
%Kindly report any suggestions or corrections to [email protected]
%
%----------------------------------------------------------------------
%
%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)
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
if (size(img1) ~= size(img2))
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
[M N] = size(img1);
if (nargin == 2)
if ((M < 11) | (N < 11)) % 圖像大小過小,則沒有意義。
ssim_index = -Inf;
ssim_map = -Inf;
return
end
window = fspecial('gaussian', 11, 1.5); % 參數一個標準偏差1.5,11*11的高斯低通濾波。
K(1) = 0.01; % default settings
K(2) = 0.03; %
L = 255; %
end
if (nargin == 3)
if ((M < 11) | (N < 11))
ssim_index = -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)
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
else
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
end
if (nargin == 4)
[H W] = size(window);
if ((H*W) < 4 | (H > M) | (W > N))
ssim_index = -Inf;
ssim_map = -Inf;
return
end
L = 255;
if (length(K) == 2)
if (K(1) < 0 | K(2) < 0)
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
else
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
end
if (nargin == 5)
[H W] = size(window);
if ((H*W) < 4 | (H > M) | (W > N))
ssim_index = -Inf;
ssim_map = -Inf;
return
end
if (length(K) == 2)
if (K(1) < 0 | K(2) < 0)
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
else
ssim_index = -Inf;
ssim_map = -Inf;
return;
end
end
if size(img1,3)~=1 %判斷圖像時不是彩色圖,如果是,結果爲3,否則爲1
org=rgb2ycbcr(img1);
test=rgb2ycbcr(img2);
y1=org(:,:,1);
y2=test(:,:,1);
y1=double(y1);
y2=double(y2);
else
y1=double(img1);
y2=double(img2);
end
img1 = double(y1);
img2 = double(y2);
% 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; % 計算C1參數,給亮度L(x,y)用。 C1=6.502500
C2 = (K(2)*L)^2; % 計算C2參數,給對比度C(x,y)用。 C2=58.522500
window = window/sum(sum(window)); %濾波器歸一化操作。
mu1 = filter2(window, img1, 'valid'); % 對圖像進行濾波因子加權 valid改成same結果會低一丟丟
mu2 = filter2(window, img2, 'valid'); % 對圖像進行濾波因子加權
mu1_sq = mu1.*mu1; % 計算出Ux平方值。
mu2_sq = mu2.*mu2; % 計算出Uy平方值。
mu1_mu2 = mu1.*mu2; % 計算Ux*Uy值。
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq; % 計算sigmax (標準差)
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq; % 計算sigmay (標準差)
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2; % 計算sigmaxy(標準差)
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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參考文獻
[1] Image Quality Assessment: From Error Visibility to Structural Similarity
[2]http://download.csdn.net/download/xiaohaijiejie/9058653
[3]http://blog.csdn.net/xiaxiazls/article/details/47952611