Facial recognition, eigenfaces and synthetic discriminant functions

Muller, Neil (2000-12)

Thesis (PhD)--University of Stellenbosch, 2001.

Thesis

ENGLISH ABSTRACT: In this thesis we examine some aspects of automatic face recognition, with specific reference to the eigenface technique. We provide a thorough theoretical analysis of this technique which allows us to explain many of the results reported in the literature. It also suggests that clustering can improve the performance of the system and we provide experimental evidence of this. From the analysis, we also derive an efficient algorithm for updating the eigenfaces. We demonstrate the ability of an eigenface-based system to represent faces efficiently (using at most forty values in our experiments) and also demonstrate our updating algorithm. Since we are concerned with aspects of face recognition, one of the important practical problems is locating the face in a image, subject to distortions such as rotation. We review two well-known methods for locating faces based on the eigenface technique.e These algorithms are computationally expensive, so we illustrate how the Synthetic Discriminant Function can be used to reduce the cost. For our purposes, we propose the concept of a linearly interpolating SDF and we show how this can be used not only to locate the face, but also to estimate the extent of the distortion. We derive conditions which will ensure a SDF is linearly interpolating. We show how many of the more popular SDF-type filters are related to the classic SDF and thus extend our analysis to a wide range of SDF-type filters. Our analysis suggests that by carefully choosing the training set to satisfy our condition, we can significantly reduce the size of the training set required. This is demonstrated by using the equidistributing principle to design a suitable training set for the SDF. All this is illustrated with several examples. Our results with the SDF allow us to construct a two-stage algorithm for locating faces. We use the SDF-type filters to obtain initial estimates of the location and extent of the distortion. This information is then used by one of the more accurate eigenface-based techniques to obtain the final location from a reduced search space. This significantly reduces the computational cost of the process.

AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons sommige aspekte van automatiese gesigs- herkenning met spesifieke verwysing na die sogenaamde eigengesig ("eigen- face") tegniek. ‘n Deeglike teoretiese analise van hierdie tegniek stel ons in staat om heelparty van die resultate wat in die literatuur verskyn te verduidelik. Dit bied ook die moontlikheid dat die gedrag van die stelsel sal verbeter as die gesigte in verskillende klasse gegroepeer word. Uit die analise, herlei ons ook ‘n doeltreffende algoritme om die eigegesigte op te dateer. Ons demonstreer die vermoë van die stelsel om gesigte op ‘n doeltreffende manier te beskryf (ons gebruik hoogstens veertig eigegesigte) asook ons opdateringsalgoritme met praktiese voorbeelde. Verder ondersoek ons die belangrike probleem om gesigte in ‘n beeld te vind, veral as rotasie- en skaalveranderinge plaasvind. Ons bespreek twee welbekende algoritmes om gesigte te vind wat op eigengesigte gebaseer is. Hierdie algoritme is baie duur in terme van numerise berekeninge en ons ontwikkel n koste-effektiewe metode wat op die sogenaamde "Synthetic Discriminant Functions" (SDF) gebaseer is. Vir hierdie doel word die begrip van lineêr interpolerende SDF’s ingevoer. Dit stel ons in staat om nie net die gesig te vind nie, maar ook ‘n skatting van sy versteuring te bereken. Voorts kon ons voorwaardes aflei wat verseker dat ‘n SDF lineêr interpolerend is. Aangesien ons aantoon dat baie van die gewilde SDF-tipe filters aan die klassieke SDF verwant is, geld ons resultate vir ‘n hele verskeidenheid SDF- tipe filters. Ons analise toon ook dat ‘n versigtige keuse van die afrigdata mens in staat stel om die grootte van die afrigstel aansienlik te verminder. Dit word duidelik met behulp van die sogenaamde gelykverspreidings beginsel ("equidistributing principle") gedemonstreer. Al hierdie aspekte van die SDF’s word met voorbeelde geïllustreer. Ons resultate met die SDF laat ons toe om ‘n tweestap algoritme vir die vind van ‘n gesig in ‘n beeld te ontwikkel. Ons gebruik eers die SDF-tipe filters om skattings vir die posisie en versteuring van die gesig te kry en dan verfyn ons hierdie skattings deur een van die teknieke wat op eigengesigte gebaseer is te gebruik. Dit lei tot ‘n aansienlike vermindering in die berekeningstyd.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/51756
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