KL.rar_K-L变换_K._KL_k-l_kl 人脸识别

% Karhunen-Loeve, for face recognition % By Alex Chirokov, Alex.Chirokov@gmail.com clear all; % Load the ATT image set k = 0; for i=1:1:40 for j=1:1:10 filename = sprintf('005.bmp',i,j); image_data = imread(filename); k = k + 1; x(:,k) = image_data(:); anot_name(k,:) = sprintf('%2d:%2d',i,j); % for plot annotations end; end; nImages = k; %total number of images imsize = size(image_data); %size of image (they all should have the same size) nPixels = imsize(1)*imsize(2); %number of pixels in image x = double(x)/255; %convert to double and normalize %Calculate the average avrgx = mean(x')'; for i=1:1:nImages x(:,i) = x(:,i) - avrgx; % substruct the average end; subplot(2,2,1); imshow(reshape(avrgx, imsize)); title('mean face') %compute covariance matrix cov_mat = x'*x; [V,D] = eig(cov_mat); %eigen values of cov matrix V = x*V*(abs(D))^-0.5; subplot(2,2,2); imshow(ScaleImage(reshape(V(:,nImages ),imsize))); title('1st eigen face'); subplot(2,2,3); imshow(ScaleImage(reshape(V(:,nImages-1),imsize))); title('2st eigen face'); subplot(2,2,4); plot(diag(D)); title('Eigen values'); %image decomposition coefficients KLCoef = x'*V; %reconstruction of Image %KLCoef(:,1:1:1)= 0; % filtration image_index = 12; %index of face to be reconstructed reconst = V*KLCoef'; diff = abs(reconst(:,image_index) - x(:,image_index)); strdiff_sum = sprintf('delta per pixel: %e',sum(sum(diff))/nPixels); figure; subplot(2,2,1); imshow((reshape(avrgx+reconst(:,image_index), imsize))); title('Reconstructed'); subplot(2,2,2); imshow((reshape(avrgx+x(:,image_index), imsize)));title('original'); subplot(2,2,3); imshow(ScaleImage(reshape(diff, imsize))); title(strdiff_sum); for i=1:1:nImages dist(i) = sqrt(dot(KLCoef(1,:)-KLCoef(i,:), KLCoef(1,:)-KLCoef(i,:))); %euclidean end; subplot(2,2,4); plot(dist,'.-'); title('euclidean distance from the first face'); %2D plot of first 2 decomposition coefficients, with annotatons % annotations have format Face:Extression, i.e 5:6 means image was taken % from s5/6.pgm expression 6 of the person in the set s5. figure; show_faces = 1:1:nImages/2; plot(KLCoef(show_faces,nImages), KLCoef(show_faces,nImages-1),'.'); title('Desomposition: Numbers indicate (Face:Expression)'); for i=show_faces name = anot_name(i,:); text(KLCoef(i,nImages), KLCoef(i,nImages-1),name,'FontSize',8); end; % Find similar faces, variable 'image_index' defines face used in comparison image_index = 78; for i=1:1:nImages dist_comp(i) = sqrt(dot(KLCoef(image_index,:)-KLCoef(i,:), KLCoef(image_index,:)-KLCoef(i,:))); %euclidean strDist(i) = cellstr(sprintf('%2.2f\n',dist_comp(i))); end; [sorted, sorted_index] = sort(dist_comp); % sort distances figure; % open new figure for i=1:1:9 subplot(3,3,i); imshow((reshape(avrgx+x(:,sorted_index(i)), imsize))); title(strDist(sorted_index(i))); end;