Face Recognition using Tensor Analysis Prahlad R. Enuganti The University of Texas at Austin Final Report EE381K – 14 Multidimensional Digital Signal Processing May 16, 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 paper tries to develop couple of robust novel techniques, based on Tensor Analysis and Isometric Feature Mapping (ISOMAP), to recognizes human faces.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. All of the existing FRT systems suffer from a dip in performance whenever the data acquisition systems suffer from a change in pose, illumination and expression. FRT systems can be broadly classified into two groups depending on whether they make use of still images or video. In this paper, the focus was only to develop an FRT system that made use of static images. The aim of this project can be described as follows: Given an image of a person under varying conditions of illumination or pose, 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. Thiswas 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, several algorithms have been developed to tackle the problem of facial recognition. Some of involve feature extraction [2] while others were based on principal component analysis [3], Support Vector Machines[5], Wavelet transform [9], Gabor filters [10], etc. Table 1 Table 1 presents a qualitative study of some of the FRT techniques that have been developed over the years. Although some of these algorithms were fast and accurate for small databases, their performance suffered when additional constraints such as varying illumination and pose were imposed on the image acquisition system [4]. From Table 1, it also appears that Tensor Analysis could solve some of the performance related problems faced by the earlier FRT systems. Resistance to Computational Classification Illumination View Expression Efficiency Quality Technique Geometric Features [2] good Poor Good good very poor Eigenfaces [3] average Poor Average good average SVM [5,6] average Average Average good very good Depth and Texture Maps [7] good Good Good average very good Multiresolution Analysis [8] good Good Very good average very good Gabor Feature Classifier [9] good Good Good average very good Tensor Analysis [13] very good Very good Very good average very goodMATERIALS AND METHODS TENSOR ANALYSIS Vasilescu et al. [10] tried to solve the problem of facial recognition using Tensor Analysis. They identified the analysis of an ensemble of facial images resulting from the confluence of multiple factors related to scene structure, illumination, and viewpoint as a problem in multilinear algebra in which the image ensemble is represented as a higher-dimensional tensor. A tensor D can be expressed as a multilinear model of factors as follows [11]: D = Z x1 U1 x2 U2 …. xN UN (1) where Z, known as the core tensor, is analogous to the diagonal matrix in standard SVD and U1 to UN contain the orthonormal vectors spanning the column space of D(n) resulting from the mode-n flattening of D [11]. Using the “N-mode SVD” algorithm, a multilinear extension of conventional matrix singular value decomposition (SVD), the core tensor Z is obtained. This image data tensor is decomposed to separate and parsimoniously represent the constituent factors. In case of facial image data used in our experiments, the various variables are people, views, illumination and pixels. Therefore applying the SVD algorithm results in the following expression D = Z x1 Uviews x2 Uillumination x3 Upixels x4 Upeople (2) Multilinear analysis enables us to represent each person regardless of pose and illumination with the combination of different base tensors (similar to the case of EigenFaces) B = Z x1 Uviews x2 Uillumination x3 Upixels (3) ISOMETRIC FEATURE MAPPING (ISOMAP) The common problem that is faced when working with high dimensional data such as gene expressions or large image databases is to find lower dimensional structures hidden in amuch higher dimensional observation space. Isometric Feature Mapping, popularly known as ISOMAP is often used to solve dimensionality reduction problems [12].
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