When using eigen faces to reconstruct images final image comes out fuzzy even when using all eigen faces

I am trying to reconstruct these images using eigen faces but keep having the same issue.

I attatched all of the images along with the average face that is created. Unfortunatly, I am unable to attach allFaces.mat as it is too large. However it is just the data from the Yale faces database. I have linked a copy of it thought I dont believe this is the same one I am using as the one I am using has 38 participants. If you have any suggestions on how to deal with this please let me know.

I have seen code very similar to this work but everytime I try to replicate it I run into this same issue.

https://www.kaggle.com/datasets/olgabelitskaya/yale-face-database

clear all, close all, clc

r1 = im2double(im2gray(imread('r1-168x192.png')),'indexed');
r2 = im2double(im2gray(imread('r2-168x192.jpg')),'indexed');
r3 = im2double(im2gray(imread('r3-168x192.jpg')),'indexed');
r4 = im2double(im2gray(imread('r4-168x192.jpg')),'indexed');
r5 = im2double(im2gray(imread('r5-168x192.jpg')),'indexed');
r6 = im2double(im2gray(imread('r6-168x192.jpg')),'indexed');
r7 = im2double(im2gray(imread('r7-168x192.jpg')),'indexed');
r8 = im2double(im2gray(imread('r8-168x192.jpg')),'indexed');
r9 = im2double(im2gray(imread('r9-168x192.jpg')),'indexed');
r10 = im2double(im2gray(imread('r10-168x192.jpg')),'indexed');
m1 = im2double(rgb2gray(imread('m1-168x192.jpg')),'indexed');
m2 = im2double(im2gray(imread('m2-168x192.jpg')),'indexed');
m3 = im2double(im2gray(imread('m3-168x192.jpg')),'indexed');
m4 = im2double(im2gray(imread('m4-168x192.jpg')),'indexed');
m5 = im2double(im2gray(imread('m5-168x192.jpg')),'indexed');
m6 = im2double(im2gray(imread('m6-168x192.jpg')),'indexed');
m7 = im2double(im2gray(imread('m7-168x192.jpg')),'indexed');
m8 = im2double(im2gray(imread('m8-168x192.jpg')),'indexed');
m9 = im2double(im2gray(imread('m9-168x192.jpg')),'indexed');
m10 = im2double(im2gray(imread('m10-168x192.jpg')),'indexed');
load allFaces.mat        % Load data file of faces 

r1 = reshape(r1,32256,1);
r2 = reshape(r2,32256,1);
r3 = reshape(r3,32256,1);
r4 = reshape(r4,32256,1);
r5 = reshape(r5,32256,1);
r6 = reshape(r6,32256,1);
r7 = reshape(r7,32256,1);
r8 = reshape(r8,32256,1);
r9 = reshape(r9,32256,1);
r10 = reshape(r10,32256,1);

m1 = reshape(m1,32256,1);
m2 = reshape(m2,32256,1);
m3 = reshape(m3,32256,1);
m4 = reshape(m4,32256,1);
m5 = reshape(m5,32256,1);
m6 = reshape(m6,32256,1);
m7 = reshape(m7,32256,1);
m8 = reshape(m8,32256,1);
m9 = reshape(m9,32256,1);
m10 = reshape(m10,32256,1);


Mfaces = [r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 m1 m2 m3 m4 m5 m6 m7 m8 m9 m10];


%% Use the first 36 people for training data

trainingFaces = faces(:,1:sum(nfaces(1:38)));
avgFace = mean(trainingFaces,2);  % size n*m by 1;

% compute eigenfaces on mean-subtracted training data
X = trainingFaces-avgFace*ones(1,size(trainingFaces,2));


[U,S,V] = svd(X,'econ');

figure(3)               % Open new figure to plot average face 
axes('position',[0  0  1  1]), axis off
imagesc(reshape(avgFace,n,m)), colormap gray

im = m6;
figure(6)               % Open new figure to plot reconstructed image
subplot(2,4,1), imagesc(reshape(im,n,m)), colormap gray
title('Person #37 Original')


%% Plot first 64 eigenfaces
count = 1;
testFaceMS =  im - avgFace ;
for r=[400 800 2282]  % Error in original code; 50 not 0 between 25 and 100
    count=count+1;
    subplot(2,4,count)
    reconFace = avgFace + (U(:,1:r)*(U(:,1:r)'*testFaceMS));
    imagesc(reshape(reconFace,n,m)), colormap gray % Plot reconstructed face
    title(['r=',num2str(r,'%d')]);
    pause(0.1)
end

[Walter Roberson]

To test we will need the rest of the images as well, and also allfaces.mat

[te]

I can upload the other jpgs but I was unable to upload the allfaces.mat as the file size was too large even when compressed. however the allfaces.mat is just the yale faces database.

[te]

Everything should be uploaded as much as possible now.

Answer 1

[Christine Tobler]

Is the face you are working with (m6) one of the columns in the trainingFaces matrix from which the SVD is constructed?

I would expect an exact reconstruction in that case, since norm(U*(U'*X)) should be small and that should mean every column of X is reconstructed to high precision.