卡洛变换的MATLAB程序(Karhunen-Loeve)
卡洛变换的MATLAB程序，运用于图像处理和统计信号处理% 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('C:\\MATLAB\\att_faces\\s%d\\%d.pgm',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;
= 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;
= 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;
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