Description
1. Eigenface implementation
Read carefully and understand the steps of the eigenface approach. Use jacobi.c from
“Numerical Recipes in C” for computing the eigenvalues/eigenvectors of a symmetric
matrix (Warning: the [0] location of an array is NOT used in “Numerical Recipes”; start
storing your data at location [1]). Your program should run in two modes: training and
testing.
Training: In training mode, your program will read in the training face images and compute
the average face and eigenfaces. Then, it will decide how many eigenfaces to keep (i.e.,
this could be done in an interactive mode where the user determines the percentage of the
information to be preserved). It will then project each training face image onto the
eigenspace and compute its representation in that space (i.e., the coefficients of
projection Ωk , k=1,2,..,M, where M is the number of training face images). Finally, your
program will store into a file the coefficients Ωk , the average face, and the eigenfaces.
Testing: In testing mode, your program will read in the coefficients Ωk , the average face,
and the eigenfaces. Use the images in a test set (see below) to evaluate face recognition
performance. Given a test image, your program will need to project it onto the eigenspace
and compute its projection coefficients Ω. To recognize the face in the test image, you will
need to find the closet match Ωk to Ω (i.e., distance in face space (difs)). Let’s call ek = ||Ωk
− Ω|| where the distance is computed using the Mahalanobis distance.
Very important: to make sure that your program works correctly, try the following: given
an image I, (i) project it onto the eigen-space, (ii) reconstruct it using all eigenfaces; let’s
call the reconstructed image ˆ
I , (iii) compute ||I – ˆ
I || (i.e., distance from face space (dffs)
using Euclidean distance). The difference should be very small; if it is not, then your code
is not working correctly. Do not proceed unless you have been able to verify this step.
2. Datasets
To test eigenface recognition, you will use images from the FERET face database [1].
FERET contains a large number of images acquired during different photo sessions and
has a good variety of gender, ethnicity and age groups. The lighting conditions, face
orientation and time of capture vary. In this project, you will concentrate on frontal face
poses named as fa (frontal image) or fb (alternative frontal image, taken during a different
photo session). All faces have been normalized with regards to orientation, position, and
size. Also, they have been masked to include only the face region (i.e., upper body and
background were cropped out). The first subset (fa) contains 1204 images from 867
subjects while the second subset (fb) contains 1196 images from the 866 subjects (i.e.,
there is one subject in fa who is not in fb). You have been provided with two different sizes
for each image: low resolution (16 x 20) and high resolution (48 x 60). All datasets can be
downloaded from the course’s webpage:
FA_L (fa, low resolution), FA_H (fa, high resolution)
FB_L (fb, low resolution), FB_H (fb, high resolution)
The file naming convention for the FERET database is as follows:
nnnnn_yymmdd_xx_q.pgm
where nnnnn is a five digit integer that uniquely identifies the subject, yymmdd indicates
the year, month, and date when the photo was taken, xx is a lowercase character string
(i.e., either fa or fb), and q is a flag (e.g., indicating whether the subject wears glasses – not
always present).
3. Experiments
(a) Use fa_H for training (i.e., to compute the eigenfaces and build the gallery set) and
fb_H for testing. So, there will be 1203 images for training and 1196 images for testing
(query).
(a.I) Show (as images) the following:
o The average face
o The eigenfaces corresponding to the 10 largest eigenvalues.
o The eigenfaces corresponding to the 10 smallest eigenvalues.
(a.II) Choose the top eigenvectors (eigenfaces) preserving 80% of the information
in the data as the basis. Project both training and query images onto this basis
after subtracting the average face to obtain the eigen-coefficients. Then, compute
the Mahalanobis distance between the eigen-coefficient vectors for each pair of
training and query images as the matching distance. Please note that for each
query image, there will be 1203 matching distances (i.e., obtained by matching the
query with each image in the gallery dataset).Choose the top N face gallery
images (i.e., N is a parameter, see below) having the highest similarity score with
the query face. (i.e., N smallest matching distances). If the query image is among
the N most similar faces retrieved, then it is considered as a correct match,
otherwise; it is considered as an incorrect match.
Count the number of correct matches and divide it by the total number of images in
the test set (e.g., 1196) to report the identification accuracy. Draw the Cumulative
Match Characteristic (CMC) curve [1] by varying N from 1 to 50. CMC shows the
probability of the query being among the top N faces retrieved from the gallery. The
faster the CMC curve approaches the value one, the better the matching algorithm
is (see graph below).
(Part a.III) Assuming N=1, show 3 query images which are correctly matched,
along with the corresponding best matched training samples.
(Part a.IV) Assuming N=1, show 3 query images which are incorrectly matched,
along with the corresponding mismatched training samples.
(Part a.V) Repeat (a.II – a.IV) by keeping the top eigenvectors corresponding to
90% and 95% of the information in the data. Plot the CMC curves on the same
graph for comparison purposes. If there are significant differences in terms of
identification accuracy in (a.II) and (a.V), try to explain why. If there are no
significant differences, explain why too.
(b) In this experiment, you will test the performance of the eigenface approach on faces
not in the gallery set (i.e., intruders). For this, remove all the images of the first 50 subjects
from fa_H; let’s call the reduced set as fa2_H. Perform recognition using fa2_H for training
(gallery) and fb_H for testing (query). In this experiment, use the eigenvectors
corresponding to 95% of the information in the data. To reject intruders, you would need to
threshold ek (i.e., accept the match only of ek < T). In this case, the choice of the threshold
T is very important. A high threshold value will increase False Positives (FP) while a low
threshold value will decrease the number of True Positives (TP). To find out what is a good
threshold value, you would need to vary the value of T and compute (FP, TP) for each
value. Then, you would need to plot the (FP, TP) values in a graph (i.e., ROC graph; see
below).
0.7
0 1
1
false positive rate
true
positive
rate
# true positives
# non-intruders (positives)
0.1
# false positives
# intruders (negatives)
Graduate Students Only – Experiments using low-resolution face images.
(c) Repeat experiment (a) using fa_L for training (gallery) and fb_L for testing.
(d) Remove all the images of the first 50 subjects from fa_L; let’s call the reduced set as
fa2_L. Repeat experiment (b) using fa2_L for training (gallery) and fb_L for testing.
(e) What is the effect of using low-resolution images? Are there any significant differences
in identification performance? Explain.
References
[1] Phillips, J. and Moon, H. and Risvi, S. and Rauss, J., “The FERET Evaluation
Methodology for Face Recognition Algorithms”, IEEE Transactions on Pattern Analysis
and Machine Intelligence, vol. 22, no. 10, pp. 1090-1104, 2000.
[2] M. Turk and A. Pentland, Face Recognition Using Eigenfaces, Computer Vision and
Pattern Recognition Conference, 1991.
PROJECT REPORT SUBMISSION REQUIREMENTS
1. Cover Page. The cover page should contain Project title, Project number, Course
number, Student’s name, Date due, and Date handed in.
2. Technical discussion. This section should include the techniques used and the
principal equations (if any) implemented.
3. Discussion of results. A discussion of results should include major findings in terms
of the project objectives, and make clear reference to any figures generated.
4. Division of work: Include a statement that describes how the work was divided
between the two group members.
5. Program listings. Includes listings of all programs written by the student. Standard
routines and other material obtained from other sources should be acknowledged
by name, but their listings should not be included.
A hard copy is required for items 1-4, submitted to the instructor in the beginning of the
class on the due date. Item 5 should be emailed to the instructor, as a zip file, before class
on the due date.
