EIE522 Pattern Recognition Laboratory 1: Face Image Analysis and Representation Using Principal Component Analysis (PCA)
EIE522 Laboratory 1:
Please generate a single PDF file for online submission. Please write your name and student number on the top of the first page of your Lab report. Since you need to submit MATLAB code, only a typewritten report is acceptable.
(NO late submission is allowed)
Face Image Analysis and Representation Using Principal Component Analysis (PCA)
Objectives:
In this laboratory exercise, you are given 20 face images, which are used as training samples for PCA. You are required to produce the eigenfaces of the training samples, which are then used to form an eigenspace for face representation and recognition based on 4 testing images. Through this exercise, you will learn the following:
1. representation of a face image as a high-dimensional vector;
2. generation of the principal components of a set of training images;
3. approximation of images using the principal components; and
4. face recognition using PCA.
For each procedure in the following, please provide the answer with detailed explanation and programming codes in the report.
Software Tools: MATLAB is used throughout this laboratory. You may refer to the HELP menu for the MATLAB commands used in this laboratory.
ORL Database： https://github.com/boenomarcus/face-recognition/tree/main/imgs/orl
Procedures:
(a) Reading the Training Images:
The 20 training face images：1_1, 11_2, 21_3, 31_4,41_5, 51_6, 61_7, 71_8, 81_9, 91_10, 101_11, 111_12, 121_13, 131_14, 141_15, 151_16, 161_17, 171_18, 181_19, 191_20
The images are in jpg format. Please rename the image files based on the following rule.
xx_1.jpg -> 1.jpg,
xx_2.jpg -> 2.jpg,
xx_3.jpg -> 3.jpg, and so on.
The filenames of these image files are “i.jpg”, where i = 1, …, 20. Run the following MATLAB codes to read the training face images:
clear;
NumOfSamples = 20;
str_Path = 'c:\???\Training\';
for i = 1: NumOfSamples
str_Load = strcat(str_Path, num2str(i), '.jpg');
Image = imread(str_Load);
TrainingImage(:,i) = double(reshape(Image, [ ], 1));
end
What is the dimension of TrainingImage? What do the columns of this matrix represent? You may use the command “size(A)” to check the size of A.
- 2 -
(b) Calculating the Mean Face and the Demeaned Faces:
You can calculate the mean of the training face images using the following MATLAB codes:
for i = 1: NumOfSamples
MeanFace = MeanFace+TrainingImage(:,i);
end
MeanFace = MeanFace/NumOfSamples;
The demeaned faces of the training samples can be computed as follows:
for i = 1: NumOfSamples
DemeanFace(:,i) = TrainingImage(:,i) − MeanFace;
end
Display the mean face image and the demeaned face images. Note that the demeaned images can be displayed with grayscale bars using the following MATLAB codes:
for i = 1: NumOfSamples
Display = DemeanFace(:,i);
Display = reshape(Display, [ImageHeight ImageWidth]);
figure(i), imagesc(Display), colorbar, colormap(gray), title(‘Demeaned Face’);
end
You may save the figure in a particular image file format.
(c) Computing the Eigenvalues and Eigenvectors/Eigenfaces:
(i) With the demeaned face images DemeanFace, write a MATLAB code to compute the covariance matrix. Denote this covariance matrix as CovFace1. Note that the transpose of a vector x is x’ in MATLAB.
What is the dimension of CovFace1?
(ii) The MATLAB command [EV, ED] = eig(A) computes the eigenvectors and eigenvalues of the square matrix A and stores them in EV and ED, respectively. Use this command to compute the eigenvalues and eigenvectors of CovFace1. What observation can you see? Discuss your observation.
(iii) Use another method, which computes the eigenvalues and eigenvectors with a smaller covariance matrix.
Compare the runtime required for Parts (ii) and (iii). Discuss your answer.
How many non-zero eigenvectors or non-zero eigenvalues are available? Discuss your answer.
Display the eigenvectors, in the form of image, according to the eigenvalues in descending order.
- 3 -
(d) Image Representation using Eigenfaces:
(i) You should use an array, say order, to store the indices of the eigenvalues in descending order.
(ii) Select a demeaned image Demeanface(:,i) in the training set, and project it onto the eigenvectors as follows:
for j = 1:N % N is the number of eigenvectors available
coef(i,j) = DemeanFace(:,i)’*EV(:,order(j));
end
(iii) Reconstruct the training image using M = 4, 8, … eigenfaces as follows:
for j = 1:M
ReconstImage = ReconstImage+coef(i,j)*EV(:,order(j));
end
ReconstImage = MeanFace + ReconstImage;
Display the reconstructed images using different values of M, and compute the corresponding differences to the original image in terms of the mean squared error. Discuss your results.
Note that the sum of squared error between two images A and B can be computed as follows:
Difference = A − B;
SSE = sum(sum(Difference.*Difference));
(iv) Reading the Testing Images:
The 4 testing face images: 7_1, 37_4, 201_21, 231_24
Please rename the image files based on the following.
7_1.jpg -> 1.jpg,
37_4_2.jpg -> 2.jpg,
201_21.jpg -> 3.jpg,
231_24.jpg -> 4.jpg
Project these images to the eigenspace and then reconstruct them with all the eigenfaces available. Display the original images and the corresponding reconstructed images, and compute their errors. Discuss your results.
(e) Face Recognition using Eigenfaces:
Suppose the coefficients of projecting the two testing face images are stored in TCoeff(i,:), where i = 1, 2. Compute the Euclidean distances of the projection coefficients between the testing images and the training images.
Display the two testing images and their corresponding three training images which have the smallest computed Euclidean distances. Discuss your results.
Your report should also include conclusion, discussion and full MATLAB code with remarks.
ORL Face Database References:
ORL database: The Olivetti Research Laboratory (ORL), AT&T Laboratories Cambridge.
F. Samaria, A. Harter, "Parameterisation of a Stochastic Model for Human Face Identification". IEEE Workshop on Applications of Computer Vision 1994.
Link: https://github.com/boenomarcus/face-recognition/tree/main/imgs/orl
− END −
