Face Recognition using Tensor Analysis Prahlad R. Enuganti The University of Texas at Austin Literature Survey EE381K – 14 Multidimensional Digital Signal Processing March 25, 2005 Submitted to Prof. Brian Evans ABSTRACT Over the past fifteen years many methods have been developed to tackle the problem of recognizing human faces. Face recognition is currently one of the most researched areas in pattern recognition. Its popularity stems from the fact that its applications are used in a variety of real life situations ranging from human - computer interaction to authentication and surveillance. Although various machine learning techniques have been developed, their success is limited because of the restrictions imposed by data acquisition systems. This literature survey will evaluate some of the methods that have been tested and also discuss the advantages of tensor analysis over traditional methods.INTRODUCTION Human recognition processes consider a broad spectrum of stimuli obtained from many, if not all, of the senses. The human brain is a complex system that probably applies contextual knowledge to recognize faces. It is futile to even attempt developing a computer system using existing technologies that can closely resemble the remarkable ability of facial recognition in humans. However, the key advantage that such a computer system would have over a human classifier is due to the limitation of the human brain to accurately remember a large database of individuals. Over the past couple of decades, face recognition has emerged as one of the primary areas of research in pattern recognition. The fact that it has numerous potential applications in biometrics, surveillance, human-computer interaction, video based communication, and the emergence of technologies that enable the implementation of these algorithms in real-time are the main reasons for this trend. Over the past ten years, new conferences such as the International Conference on Audio and Video-Based Authentication (AVBPA) and International Conference on Automatic Face and Gesture Recognition (AFGR) and systematic empirical evaluations of face recognition techniques (FRT) have been started due to the growing interest in facial recognition among researchers in a variety of disciplines such as image processing, neural networks, computer graphics and psychology. FRT systems can be broadly classified into two groups depending on whether they make use of still images or video. In this study, I will focus only on FRT systems that make use of static images. The problem statement for facial recognition can be formulated as follows: Given an image of a person under varying conditions of illumination, pose or facial expression, verify/identify the person in the stored database of facial images.BACKGROUND : PREVIOUS WORK One of the first attempts at automatic face recognition was made by Kanade [1] in 1973. He used a robust feature detector to locate feature geometric points on the facial image. A feature vector was formed by calculating the geometrical parameters and a weighted Euclidian distance was defined on these features to measure the similarity between faces. This was a very simple algorithm that when tested on a database consisting of images obtained from 20 individuals performed at an accuracy of 45 ~ 75 %. Since Kanade’s algorithm in 1973, different algorithms have been developed to tackle the problem of facial recognition. Some of the techniques involved feature extraction while others involved wavelet transform, principal component analysis, Gabor filters, etc. In this section we will look at some of the popular techniques that have been used over the years. GEOMETRIC FEATURE BASED MATCHING Brunelli and Poggio in 1992 extended Kanade’s algorithm and used “Geometric Feature based Matching” for face recognition [2]. The basic idea behind their algorithm was to describe the overall configuration of the face by a vector of numerical data representing the relative position and size of the main facial features: eyes and eyebrows, nose and mouth. The classification was done using the nearest neighbor classifier on the vector corresponding to the given image with respect to the vectors corresponding to the images in the database. The results, although impressive at the time, were not conclusive since they only considered a database of 47 people with 4 images of each person.EIGENFACES Eigenfaces proposed by Turk et al. [3] are a set of orthonormal basis vectors computed from a collection of training face images. The provide a basis of low dimensional representation of the facial images and are optimal in the minimum least square error sense. If the training set of N facial images is represented by { z1 z2 ….. zN}, Principal Component Analysis is applied to the set of training images to find the N eigenvectors of the covariance matrix ( )()()∑=−−NnTnnzzzzN1/1, where ∑==NnnzNz1)/1(is the average of the ensemble. The eigenvectors corresponding to the largest k (pre-determined) eigenvalues form the basis of an eigenface space. Classification is based on the eigen-feature vectors. The simplest classifier is based on Euclidean distance even though nearest neighbor classifier can also be used. The fact that the algorithm is fast and easy to implement makes Eigenfaces a very appealing technique. However, the main constraint is that one the frontal view of the images can be used and they are sensitive to extreme changes in pose and expression [4]. SUPPORT VECTOR MACHCINES In 2001, Guo et al. [5], incorporated Support Vector Machines (SVM’s) with binary tree recognition for multi-class recognition. Given a set of points belonging to two classes, a traditional SVM finds a hyper-plane that separates the largest fraction of points of the same class on the same side while maximizing the distance from each class to the hyper-plane. However, in the case of Face Recognition, we have multiple classes, where each person belongs to a different class and therefore the authors had to extend SVM’s so that they could be applied to the multi-class problem. They
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