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⛄ 内容介绍
近几年，徐立提出的 L0 梯度最小化模型在图像平滑领域得到了广泛的应用和发展[11]. 和以往的局部滤波模型不同的是该模型可以全局的估计图像的像素值，因此，L0 梯度最小化模型在处理图像的同时能够很好的保护图像的边缘.
⛄ 部分代码
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 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 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:
%
%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 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)
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))
ssim_index = -Inf;
ssim_map = -Inf;
return
end
window = fspecial('gaussian', 11, 1.5); %
K(1) = 0.01; % default settings
K(2) = 0.03; %
L = max(img2(:))-min(img2(:));%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 = max(img2(:))-min(img2(:));%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 = max(img2(:))-min(img2(:));%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
C1 = (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);
end
mssim = mean2(ssim_map);
return
⛄ 运行结果
⛄ 参考文献
[1]Wen Yunlei, 温云磊, Wang Yuanquan,等. 基于核回归和L0梯度最小化的图像去噪方法[C]// 中国图象图形学学会. 中国图象图形学学会, 2014.
