Integrating PCA

.gitignore

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+capture.pgm
+/training/positive
+mean.png
+negative_eigenface.png
+positive_eigenface.png

pca/EFace1_demo.m

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+
+%UNDERSTANDING PRINCIPAL COMPONENT ANALYSIS On face images
+
+%Here K=Total number of pixels of image=MN=112x92
+
+%RMSE averaged over all images..........Change value of q for PCA
+%components
+
+%When q=6(All principal components retained)     err =  00
+%When q=5( 5 principal components retained)     err =  9.3270
+%When q=4( 4 principal components retained)     err =  21.6476
+%When q=3( 3 principal components retained)     err =    29.9518
+%--------------------------------------------------------------------------
+
+clc;
+clear all;
+close all;
+
+%Reading and displaying 6 face images
+
+F1=imread('f1.pgm');
+F2=imread('f2.pgm');
+F3=imread('f3.pgm');
+F4=imread('f4.pgm');
+F5=imread('f5.pgm');
+F6=imread('f6.pgm');
+
+figure;imshow(F1);title('First image');
+figure;imshow(F2);title('Second image');
+figure;imshow(F3);title('Third  image');
+figure;imshow(F4);title('Forth  image');
+figure;imshow(F5);title('Fifth image');
+figure;imshow(F6);title('Sixth  image');
+
+S=cat(3,F1,F2,F3,F4,F5,F6);    %Representing images in 3 dimension stack
+[X,R]=imstack2vectors(S);       %Convert images from matrix (MxN) to corresponding column vector [ColF1;ColF2;ColF3;ColF4;ColF5;ColF6]
+
+%Covariance matrix Generation  (6x6)
+
+[K,n]=size(X);          
+X=double(X);
+
+if n==1
+    C=0;
+    m=X;
+else
+    m=sum(X,1)/K;           
+    X1=X-m(ones(K,1),:);    
+    C=(X1'*X1)/(K-1);       %Covariance  matrix C . size=6x6
+    m=m';                   
+end
+
+
+% PRINCIPAL COMPONENT IMPLEMENTATION
+
+m=m';                    
+[V,D]=eig(C);            %V =EIGEN VECTORED column matrix; D=Eigen valued diagonal matrix
+
+d=diag(D);               %Extract diagonal elements of D
+
+[d,idx]=sort(d);
+d=flipud(d);
+idx=flipud(idx);
+
+D=diag(d);
+V=V(:,idx);
+
+
+q=input('Enter the number of principal eigenvectors (<= 6): ');                                       %Use only first q principle components
+
+A=V(:,1:q)';             %q x n principal components x'formation matrix;rows are eigen vectors of C corresponding to the
+                                %first q largest eigenvalues.
+
+Mx=repmat(m,K,1);    % Kx6 mean matrix 
+
+X=X-Mx;                     %Mean subtracted images
+
+Y=A*(X') ;                  %size of Y=(qx6)*(6xK)=qxK
+
+X2=(A'*Y)';             %size of X2=((6x3)*(3xK))'=(6xK)'=Kx6
+
+X2=X2+Mx;           % Mean added to reconstruct the images
+
+Y=Y';                   %Kxq  matrix
+
+
+% m=m';                    %nx1 vector
+
+d=diag(D);
+ems=sum(d(q+1:end));
+
+%Covariance matrix of transformed images
+    m2=sum(Y,1)/K;           
+    Y1=Y-m2(ones(K,1),:);    
+    CY=(Y1'*Y1)/(K-1);       %Covariance  matrix C . size=6x6
+
+
+%%Cy=A*C*A';
+
+% Displaying principal component images
+
+% g1=Y(:,1);
+% g1=reshape(g1,112,92);
+% figure;imshow(g1,[]);
+% title('First principle component image');
+% 
+% g2=Y(:,2);
+% g2=reshape(g2,112,92);
+% figure;imshow(g2,[]);
+% title('Second principle component image');
+% 
+% g3=Y(:,3);
+% g3=reshape(g3,112,92);
+% figure;imshow(g3,[]);
+% title('Third principle component image');
+% 
+% g4=Y(:,4);
+% g4=reshape(g4,112,92);
+% figure;imshow(g4,[]);
+% title('Fourth principle component image');
+% 
+% g5=Y(:,5);
+% g5=reshape(g5,112,92);
+% figure;imshow(g5,[]);
+% title('Fifth principle component image');
+% 
+% g6=Y(:,6);
+% g6=reshape(g6,112,92);
+% figure;imshow(g6,[]);
+% title('Sixth principle component image');
+% %--------------------------------------------------------------------------
+% Reconstructing images
+%--------------------------------------------------------------------------
+h1=X2(:,1);
+h1=reshape(h1,112,92);
+figure;imshow(h1,[]);
+title('Reconstructed image1');
+
+ h2=X2(:,2);
+ h2=reshape(h2,112,92);
+ figure;imshow(h2,[]);
+ title('Reconstructed image2');
+
+h3=X2(:,3);
+h3=reshape(h3,112,92);
+figure;imshow(h3,[]);
+title('Reconstructed image3');
+
+h4=X2(:,4);
+h4=reshape(h4,112,92);
+figure;imshow(h4,[]);
+title('Reconstructed image4');
+
+h5=X2(:,5);
+h5=reshape(h5,112,92);
+figure;imshow(h5,[]);
+title('Reconstructed image5');
+
+h6=X2(:,6);
+h6=reshape(h6,112,92);
+figure;imshow(h6,[]);
+title('Reconstructed image6');
+
+%Finding Reconstruction error (rmse)
+
+
+
+disp('RMSE Errors in reconstruction:');
+ D1=double(F1(:,:))-double(h1);
+ err1=sqrt(sum(sum(D1.^2))/(K))
+
+ D2=double(F2)-double(h2);
+err2=sqrt(sum(sum(D2.^2))/(K))
+
+ D3=double(F3)-double(h3);
+ err3=sqrt(sum(sum(D3.^2))/(K))
+
+ D4=double(F4)-double(h4);
+ err4=sqrt(sum(sum(D4.^2))/(K))
+
+ D5=double(F5)-double(h5);
+ err5=sqrt(sum(sum(D5.^2))/(K))
+
+ D6=double(F6)-double(h6);
+err6=sqrt(sum(sum(D6.^2))/(K))
+
+
+ err=(err1+err2+err3+err4+err5+err6)/6;
+ disp('RMSE averaged over all images=');
+ disp(err);

pca/image_resize.py

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+import PIL
+from PIL import Image
+
+# taking 1 image and resizing as: 92x112
+basewidth = 92
+img = Image.open('../training/positive/positive_000.pgm')
+wpercent = (basewidth / float(img.size[0]))
+hsize = int((float(img.size[1]) * float(0.525)))
+img = img.resize((basewidth, hsize), PIL.Image.ANTIALIAS)
+img.save('f1.pgm')
+
+# taking 2 image and resizing as: 92x112
+img = Image.open('../training/positive/positive_001.pgm')
+wpercent = (basewidth / float(img.size[0]))
+hsize = int((float(img.size[1]) * float(0.5)))
+img = img.resize((basewidth, hsize), PIL.Image.ANTIALIAS)
+img.save('f2.pgm')
+
+# taking 3 image and resizing as: 92x112
+img = Image.open('../training/positive/positive_002.pgm')
+wpercent = (basewidth / float(img.size[0]))
+hsize = int((float(img.size[1]) * float(0.408)))
+img = img.resize((basewidth, hsize), PIL.Image.ANTIALIAS)
+img.save('f3.pgm')
+
+# taking 4 image and resizing as: 92x112
+img = Image.open('../training/positive/positive_003.pgm')
+wpercent = (basewidth / float(img.size[0]))
+hsize = int((float(img.size[1]) * float(0.395)))
+img = img.resize((basewidth, hsize), PIL.Image.ANTIALIAS)
+img.save('f4.pgm')
+
+# taking 5 image and resizing as: 92x112
+img = Image.open('../training/positive/positive_004.pgm')
+wpercent = (basewidth / float(img.size[0]))
+hsize = int((float(img.size[1]) * float(0.4)))
+img = img.resize((basewidth, hsize), PIL.Image.ANTIALIAS)
+img.save('f5.pgm')
+
+# taking 6 image and resizing as: 92x112
+img = Image.open('../training/positive/positive_005.pgm')
+wpercent = (basewidth / float(img.size[0]))
+hsize = int((float(img.size[1]) * float(0.365)))
+img = img.resize((basewidth, hsize), PIL.Image.ANTIALIAS)
+img.save('f6.pgm')

pca/imstack2vectors.m

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+function [X, R] = imstack2vectors(S, MASK) 
+%IMSTACK2VECTORS Extracts vectors from an image stack. 
+%   [X, R] = imstack2vectors(S, MASK) extracts vectors from S, which 
+%   is an M-by-N-by-n stack array of n registered images of size 
+%   M-by-N each (see Fig. 11.24). The extracted vectors are arranged 
+%   as the rows of array X. Input MASK is an M-by-N logical or 
+%   numeric image with nonzero values (1s if it is a logical array) 
+%   in the locations where elements of S are to be used in forming X 
+%   and 0s in locations to be ignored. The number of row vectors in X 
+%   is equal to the number of nonzero elements of MASK. If MASK is 
+%   omitted, all M*N locations are used in forming X.  A simple way 
+%   to obtain MASK interactively is to use function roipoly. Finally, 
+%   R is an array whose rows are the 2-D coordinates containing the 
+%   region locations in MASK from which the vectors in S were 
+%   extracted to form X.   
+
+%   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins 
+%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004 
+%   $Revision: 1.6 $  $Date: 2003/11/21 14:37:21 $ 
+
+% Preliminaries. 
+[M, N, n] = size(S); 
+if nargin == 1 
+   MASK = true(M, N); 
+else 
+   MASK = MASK ~= 0; 
+end 
+
+% Find the set of locations where the vectors will be kept before 
+% MASK is changed later in the program. 
+[I, J] = find(MASK); 
+R = [I, J]; 
+
+% Now find X. 
+
+% First reshape S into X by turning each set of n values along the third 
+% dimension of S so that it becomes a row of X. The order is from top to 
+% bottom along the first column, the second column, and so on. 
+Q = M*N; 
+X = reshape(S, Q, n); 
+
+% Now reshape MASK so that it corresponds to the right locations  
+% vertically along the elements of X. 
+MASK = reshape(MASK, Q, 1); 
+
+% Keep the rows of X at locations where MASK is not 0. 
+X = X(MASK, :);