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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