FACE RECOGNITION, EXPERIMENTS WITH RANDOM PROJECTION

Navin Goel

Graduate Student

Advisor: Dr George Bebis

Associate Professor

Department Of Computer Science and Engineering

University of Nevada, Reno

Overview

• Introduction and Thesis Scope

• Principal Component Analysis

• Method of Eigenfaces

• Random Projection

• Properties of Random Projection

• Random Projection for Face Recognition

• Experimental Procedure and Data sets

• Recognition approaches and results

• Conclusion and Future work

Introduction

Problem Statement Identify a person’s face image from face database.

Applications Human-Computer interface,

Static matching of photographs,

Video surveillance,

Biometric security,

Image and film processing.

Challenges

Variations in pose Head positions, frontal view, profile view and head tilt, facial expressions

Illumination Changes Light direction and intensity changes, cluttered background, low quality images

Camera Parameters Resolution, color balance etc.

Occlusion Glasses, facial hair and makeup

Thesis Scope

Investigate the application of Random Projection (RP) in Face Recognition.

Evaluate the performance of RP for face recognition under various conditions and assumptions.

Aim at proposing an algorithm, which replaces the learning step of PCA by cheaper and efficient step.

Principal Component Analysis (PCA)

For a set M of N-dimensional vectors {x1, x2…xM}, PCA finds the

eigenvalues and eigenvectors of the covariance matrix of the vectors

TM

iii xx

MC

1

1 - the average of the image vectors

an image as 1d vector kkk uu uk - Eigenvectors

k - Eigenvalues

Keep only k eigenvectors, corresponding to the k largest eigenvalues.

Method of Eigenfaces

• Apply PCA on the training dataset

• Project the Gallery set images to the reduced dimensional eigenspace.

• For each test set image:

• Project the image to the reduced dimensional eigenspace.

• Measure similarity by calculating the distance between the projection coefficients of two datasets

• The face is recognized if the closest gallery image belongs to same person in test set

Random Projection (RP)

The original N-dimensional data is projected to a d-dimensional subspace, (d << n) using:

Random matrix is calculated using the following steps:

Each entry of the matrix follows N(0,1).

The d rows of the matrix are orthogonalized using Gram-Schmidt algorithm and then are normalized to unit length

NxMdxNdxM xRX xNxM – original data

RdxN – random matrix

2

2

2 2exp

2

1),(

x

N

- Mean

- Variance

Random Projection – Data Independence

Two 1-separated spherical Gaussians were projected onto a random space of dimension 20.

Error bars are for 1 standard deviation and there are 40 trials per dimension.

Digital images, document databases, signal processing.

Random Projection does not depend on the data itself.

S. Dasgupta. Experiments with Random Projection. Uncertainty in Artificial Intelligence, 2000.

Random Projection – Eccentricity

Gaussian in subspace of 50-dimension and eccentricity 1,000 is projected onto lower dimensions.

Conceptually easier to design algorithms for spherical clusters than ellipsoidal ones.

RP makes highly eccentric Gaussian clusters to spherical.

S. Dasgupta. Experiments with Random Projection. Uncertainty in Artificial Intelligence, 2000.

Random Projection – Complexity

Number of floating-point operations needed when reducing the dimensionality of image data using RP (+), SRP (*), PCA () and DCT (), in a logarithmic scale.

Complexity of RP is of the order of quadratic (n2) in contrast to PCA which is cubic (n3).

E. Bingham and H. Mannila. Random projection in dimensionality reduction: applications to image and text data. Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 245-250, August 26-29, 2001.

Random Projection – Lower Bound

1-separated mixtures of k Gaussians of dimension 100 was projected on d = lnk.

PCA cannot be expected to reduce the dimensionality of k Gaussians below Ω(k).

What value of d (lower space) must be chosen ?

S. Dasgupta. Experiments with Random Projection. Uncertainty in Artificial Intelligence, 2000.

Random Projection for Face Recognition

• Generate lower dimensional random subspace.

• Project the Gallery set images to the reduced dimensional random space.

• For each test set image:

• Project the image to the reduced dimensional random space.

• Measure similarity by calculating the distance between the projection coefficients of two datasets.

• The face is recognized if the closest gallery image belongs to same person in test set.

Experimental Procedure

Main steps of the approach

Data Sets

Face images from ORL data set for a particular subject.

Face images from CVL data set for a particular subject.

Face images from AR data set for a particular subject.

Closest Match Approach

Averaging over 5 experiments.

Flowchart for calculating recognition rate using closest match approach.

Closest Match Approach + Majority Voting

Flowchart for calculating recognition rate using closest match approach + majority voting technique.

Closest Match Approach + Scoring

Flowchart for calculating recognition rate using closest match approach + scoring technique.

Results for the ORL database

Experiment on ORL database using closest match approach + majority voting technique, where training set consists of same subjects as in the gallery and testing set.

Experiment on ORL database using closest match approach + majority voting technique, where training set consists of different subjects as in the gallery and testing set.

Results for the CVL database

Experiment on CVL database using closest match approach + majority voting technique, where training set consists of same subjects as in the gallery and testing set.

Experiment on CVL database using closest match approach + majority voting, training set consists of different subjects as in the gallery and testing set.

Results for the AR database

Experiment on AR database using closest match approach + majority voting, training set consists of random subjects, gallery and Test set contains different combinations.

ORL database for Multiple Ensembles

Plot on RCA, Majority-Voting technique for 5 and 30 different random seeds, training set consists of different subjects as in the gallery and testing set.

Results for the ORL database with Scoring Technique

Experiment on ORL database using closest match approach + scoring, training set consists of different subjects as in the gallery and testing set.

Experiment on ORL database using closest match approach + scoring, training set consists of same subjects as in the gallery and testing set.

Results for the CVL database with Scoring Technique

Experiment on CVL database using closest match approach + scoring, training set consists of different subjects as in the gallery and testing set.

Results for the AR database with Scoring Technique

Experiment on AR database using closest match approach + scoring, training set consists of random subjects as in the gallery and Test set contains different combinations.

Conclusion

• We were able to get recognition rate equivalent to PCA and in most cases better than it.

• RP matrix is independent of the training data.

• The main advantage of using RP is the computational complexity, for RP it is quadratic and for PCA cubic.

• RP works better when gallery to test set ratio is higher.

• RP works better than PCA when the training set images differ from gallery and test set.

• RP shows irregularity for single runs, but improves with multiple ensembles.

• Majority-voting over closest match for recognition further improves the performance of RP.

• For scoring technique, greater the number of top hits per image, better the performance.

Future Work

• Combine different random ensembles, that will improve efficiency and accuracy.