1 简介
图像融合的方法很多,本文介绍的方法是基于主成分分析法(Principal Component Analysis)的可见光与红外图像的像素级融合.融合后的图像比原图具有更好的对比度.与直接重叠的融合方法相比,本文介绍的图像融合算法也具有更合适的对比度.因为本文所介绍的方法还利用了平滑滤波后的偏差信息,使图像的边缘更加清晰.
2 部分代码
% function Pca = PCA(TM);
clear
g_R=0; %r清晰度描述
g_G=0; %g清晰度描述
g_B=0; %b清晰度描述
h_R=0; %熵的描述
h_G=0;
h_B=0;
fenzi_R=0;
fenzi_G=0;
fenzi_B=0;
fenmu_up_R=0;
fenmu_up_G=0;
fenmu_up_B=0;
fenmu_low_R=0;
fenmu_low_G=0;
fenmu_low_B=0;
init_up_R=[];
init_up_G=[];
init_up_B=[];
init_low_R=[];
init_low_G=[];
init_low_B=[];
up=imread('high.jpg'); %读图像
low=imread('low.jpg');
figure(1)
imshow(up); %读RGB数值
title('PCA-RGB表示的高分辨率图像');
figure(2)
imshow(low);
title('PCA-RGB表示的低分辨率图像');
[up_R]=double(up(:,:,1));
[up_G]=double(up(:,:,2));
[up_B]=double(up(:,:,3));
[low_R]=double(low(:,:,1));
[low_G]=double(low(:,:,2));
[low_B]=double(low(:,:,3));
[M,N,color]=size(up);
up_Mx = 0;
low_Mx=0;
for i = 1 : M
for j = 1 : N
up_S = [up_R(i,j),up_G(i,j),up_B(i,j)]'; % 生成由R，G， B组成的三维列向量
up_Mx = up_Mx + up_S;
low_S = [low_R(i,j),low_G(i,j),low_B(i,j)]';
low_Mx = low_Mx + low_S;
end
end
up_Mx = up_Mx / (M*N); % 计算三维列向量的平均值
low_Mx = low_Mx / (M*N);
up_Cx = 0;
low_Cx=0;
for i = 1 : M
for j = 1 : N
up_S = [up_R(i,j),up_G(i,j),up_B(i,j)]';
up_Cx = up_Cx + up_S*up_S';
low_S = [low_R(i,j),low_G(i,j),low_B(i,j)]';
low_Cx = low_Cx + low_S*low_S';
end
end
up_Cx = up_Cx / (M * N)- up_Mx*up_Mx'; % 计算协方差矩陈
low_Cx = low_Cx / (M * N)- low_Mx*low_Mx';
[up_A,up_latent] = eigs(up_Cx); % 协方差矩陈的特征向量组成的矩陈----PCA变换的系数矩陈,特征值
[low_A,low_latent] = eigs(low_Cx);
for i = 1 : M
for j = 1 : N
up_X = [up_R(i,j),up_G(i,j),up_G(i,j)]'; % 生成由R，G， B组成的三维列
up_Y = up_A'*up_X; % 每个象素点进行PCA变换正变换
up_Y = up_Y';
up_R(i,j) = up_Y(1); % 高分辨率图片的第1主分量
up_G(i,j) = up_Y(2); % 高分辨率图片的第2主分量
up_B(i,j) = up_Y(3); % 高分辨率图片的第3主分量
low_X = [low_R(i,j),low_G(i,j),low_G(i,j)]';
low_Y = low_A'*low_X;
low_Y = low_Y';
low_R(i,j) = low_Y(1); % 低分辨率图片的第1主分量
low_G(i,j) = low_Y(2); % 低分辨率图片的第2主分量
low_B(i,j) = low_Y(3); % 低分辨率图片的第3主分量
end
end
for i = 1 : M
for j = 1 : N
up_Y = [up_R(i,j),up_G(i,j),up_B(i,j)]'; % 生成由R，G， B组成的三维列向量
up_X = up_A*up_Y; % 每个象素点进行PCA变换反变换
up_X = up_X';
up_r(i,j) = up_X(1);
up_g(i,j) = up_X(2);
up_b(i,j) = up_X(3);
low_Y = [up_R(i,j),low_G(i,j),low_B(i,j)]';
low_X = low_A*low_Y;
low_X = low_X';
low_r(i,j) = low_X(1);
low_g(i,j) = low_X(2);
low_b(i,j) = low_X(3);
end
end
%RGB(:,:,1)=up_r;
%RGB(:,:,2)=up_g;
%RGB(:,:,3)=up_b;
RGB(:,:,1)=low_r;
RGB(:,:,2)=low_g;
RGB(:,:,3)=low_b;
figure(3)
imshow(uint8(RGB));
title('PCA-RGB表示的转化图像');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 下面是计算相关系数 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
init_up_R=ones(M,N)*mean(up_R(:));
init_up_G=ones(M,N)*mean(up_G(:));
init_up_B=ones(M,N)*mean(up_B(:));
init_low_R=ones(M,N)*mean(low_R(:));
init_low_G=ones(M,N)*mean(low_G(:));
init_low_B=ones(M,N)*mean(low_B(:));
for i=1:M
for j=1:N
fenzi_R=fenzi_R+(up_R(i,j)-init_up_R(i,j))*(low_R(i,j)-init_low_R(i,j));
fenmu_up_R=fenmu_up_R+(up_R(i,j)-init_up_R(i,j))^2;
fenmu_low_R=fenmu_low_R+(low_R(i,j)-init_low_R(i,j))^2;
fenzi_G=fenzi_G+(up_R(i,j)-init_up_G(i,j))*(low_R(i,j)-init_low_G(i,j));
fenmu_up_G=fenmu_up_G+(up_R(i,j)-init_up_G(i,j))^2;
fenmu_low_G=fenmu_low_G+(low_R(i,j)-init_low_G(i,j))^2;
fenzi_B=fenzi_B+(up_R(i,j)-init_up_B(i,j))*(low_R(i,j)-init_low_B(i,j));
fenmu_up_B=fenmu_up_B+(up_R(i,j)-init_up_B(i,j))^2;
fenmu_low_B=fenmu_low_B+(low_R(i,j)-init_low_B(i,j))^2;
end
end
rou_R=fenzi_R/(sqrt(fenmu_up_R*fenmu_low_R));
rou_G=fenzi_G/(sqrt(fenmu_up_G*fenmu_low_G));
rou_B=fenzi_B/(sqrt(fenmu_up_B*fenmu_low_B));
fprintf('\n\n R的相关系数为:%.4f\n G的相关系数为:%.4f\n B的相关系数为:%.4f',rou_R,rou_G,rou_B);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 下面是计算清晰度G %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for ii=1:M-1
for jj=1:N-1
g_R=g_R+sqrt((((low_r(ii+1,jj)-low_r(ii,jj))^2+(low_r(ii,jj+1)-low_r(ii,jj))^2))/2);
g_G=g_G+sqrt((((low_g(ii+1,jj)-low_g(ii,jj))^2+(low_g(ii,jj+1)-low_g(ii,jj))^2))/2);
g_B=g_B+sqrt((((low_b(ii+1,jj)-low_b(ii,jj))^2+(low_b(ii,jj+1)-low_b(ii,jj))^2))/2);
end
end
fprintf('\n\n R的清晰度为:%.4f\n G的清晰度为:%.4f\n B的清晰度为:%.4f',...
g_R/(M-1)/(N-1),g_G/(M-1)/(N-1),g_B/(M-1)/(N-1));
3 仿真结果
4 参考文献
[1]魏交统, 陈平, 潘晋孝. 基于主成分分析的递变能量X射线图像融合[J]. 中国体视学与图像分析, 2013(2):6.
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