卡洛变换的MATLAB程序(Karhunen-Loeve)

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卡洛变换的MATLAB程序，运用于图像处理和统计信号处理

1. % Karhunen-Loeve, for face recognition
   
2. % By Alex Chirokov, Alex.Chirokov@gmail.com
   
3. clear all;
   
4. 
   
5. % Load the ATT image set
   
6. k = 0;
   
7. for i=1:1:40
   
8.     for j=1:1:10
   
9.         filename  = sprintf('C:\\MATLAB\\att_faces\\s%d\\%d.pgm',i,j);
   
10.         image_data = imread(filename);
    
11.         k = k + 1;
    
12.         x(:,k) = image_data(:);
    
13.         anot_name(k,:) = sprintf('%2d:%2d',i,j);   % for plot annotations
    
14.      end;
    
15. end;
    
16. nImages = k;                     %total number of images
    
17. imsize = size(image_data);       %size of image (they all should have the same size)
    
18. nPixels = imsize(1)*imsize(2);   %number of pixels in image
    
19. x = double(x)/255;               %convert to double and normalize
    
20. %Calculate the average
    
21. avrgx = mean(x')';
    
22. for i=1:1:nImages
    
23.     x(:,i) = x(:,i) - avrgx; % substruct the average
    
24. end;
    
25. subplot(2,2,1); imshow(reshape(avrgx, imsize)); title('mean face')
    
26. %compute covariance matrix
    
27. cov_mat = x'*x;
    
28. [V,D] = eig(cov_mat);         %eigen values of cov matrix
    
29. V = x*V*(abs(D))^-0.5;               
    
30. subplot(2,2,2); imshow(ScaleImage(reshape(V(:,nImages  ),imsize))); title('1st eigen face');
    
31. subplot(2,2,3); imshow(ScaleImage(reshape(V(:,nImages-1),imsize))); title('2st eigen face');
    
32. subplot(2,2,4); plot(diag(D)); title('Eigen values');
    
33. 
    
34. %image decomposition coefficients
    
35. KLCoef =  x'*V;
    
36. 
    
37. %reconstruction of Image
    
38. %KLCoef(:,1:1:1)= 0;  % filtration
    
39. image_index = 12;  %index of face to be reconstructed
    
40. reconst = V*KLCoef';
    
41. diff = abs(reconst(:,image_index) - x(:,image_index));
    
42. strdiff_sum = sprintf('delta per pixel: %e',sum(sum(diff))/nPixels);
    
43. figure;
    
44. subplot(2,2,1); imshow((reshape(avrgx+reconst(:,image_index), imsize))); title('Reconstructed');
    
45. subplot(2,2,2); imshow((reshape(avrgx+x(:,image_index), imsize)));title('original');
    
46. subplot(2,2,3); imshow(ScaleImage(reshape(diff, imsize))); title(strdiff_sum);
    
47. 
    
48. for i=1:1:nImages
    
49.     dist(i) = sqrt(dot(KLCoef(1,:)-KLCoef(i,:), KLCoef(1,:)-KLCoef(i,:))); %euclidean
    
50. end;
    
51. subplot(2,2,4); plot(dist,'.-'); title('euclidean distance from the first face');
    
52. 
    
53. %2D plot of first 2 decomposition coefficients, with annotatons
    
54. % annotations have format Face:Extression, i.e 5:6 means image was taken
    
55. % from s5/6.pgm expression 6 of the person in the set s5.
    
56. figure;
    
57. show_faces = 1:1:nImages/2;
    
58. plot(KLCoef(show_faces,nImages), KLCoef(show_faces,nImages-1),'.'); title('Desomposition: Numbers indicate (Face:Expression)');
    
59. for i=show_faces
    
60.     name = anot_name(i,:);
    
61.     text(KLCoef(i,nImages), KLCoef(i,nImages-1),name,'FontSize',8);
    
62. end;
    
63. 
    
64. % Find similar faces,  variable 'image_index' defines face used in comparison
    
65. image_index = 78;
    
66. for i=1:1:nImages
    
67.     dist_comp(i) = sqrt(dot(KLCoef(image_index,:)-KLCoef(i,:), KLCoef(image_index,:)-KLCoef(i,:))); %euclidean
    
68.     strDist(i) = cellstr(sprintf('%2.2f\n',dist_comp(i)));
    
69. end;
    
70. [sorted, sorted_index] = sort(dist_comp); % sort distances
    
71. figure; % open new figure
    
72. for i=1:1:9
    
73.     subplot(3,3,i); imshow((reshape(avrgx+x(:,sorted_index(i)), imsize))); title(strDist(sorted_index(i)));
    
74. end;

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