Elsevier

Pattern Recognition Letters

Volume 25, Issue 6, 19 April 2004, Pages 711-724
Pattern Recognition Letters

Distance measures for PCA-based face recognition

https://doi.org/10.1016/j.patrec.2004.01.011Get rights and content

Abstract

In this article we compare 14 distance measures and their modifications between feature vectors with respect to the recognition performance of the principal component analysis (PCA)-based face recognition method and propose modified sum square error (SSE)-based distance. Recognition experiments were performed using the database containing photographies of 423 persons. The experiments showed, that the proposed distance measure was among the first three best measures with respect to different characteristics of the biometric systems. The best recognition results were achieved using the following distance measures: simplified Mahalanobis, weighted angle-based distance, proposed modified SSE-based distance, angle-based distance between whitened feature vectors. Using modified SSE-based distance we need to extract less images in order to achieve 100% cumulative recognition than using any other tested distance measure. We also showed that using the algorithmic combination of distance measures we can achieve better recognition results than using the distances separately.

Introduction

Principal component analysis (PCA) or Karhunen–Loeve transform (KLT)-based face recognition method was proposed in (Turk and Pentland, 1991). It was studied by computer scientists (Moon and Phillips, 1998; Yilmaz and Gokmen, 2001; Navarrete and Ruiz-del-Solar, 2001, Navarrete and Ruiz-del-Solar, 2002) and psychologists (Abdi et al., 1995; Hancock et al., 1996), used as a baseline method for comparison of face recognition methods (Moghaddam and Pentland, 1998; Phillips et al., 2000) and implemented in commercial applications (Viisage, 2001). Using PCA we find a subset of principal directions (principal components) in a set of training faces. Then we project faces into this principal components space and get feature vectors. Comparison is performed by calculating the distance between these vectors. Usually comparison of face images is performed by calculating the Euclidean distance between these feature vectors. Sometimes the angle-based distance is used. Mathematical formulation of this recognition method is presented in the next section. Although there exist many other distance measures, we were able to find only few attempts to create, compare and use other distance measures (Navarrete and Ruiz-del-Solar, 2002; Phillips et al., 1997, Phillips et al., 2000) in order to achieve better recognition results.

In this article we compare recognition performance of 14 distance measures including Euclidean, angle-based, Mahalanobis and their modifications. Also we propose modified sum square error-based distance and modified Manhattan distance measures. The experiments showed, that the proposed distance measures were among the best distance measures with respect to different characteristics of the biometric systems. For comparison we used the following characteristics of the biometric systems: equal error rate (EER), first one recognition rate, area above cumulative match characteristic (CMC), area below receiver operating characteristic (ROC), percent of images that we need to extract in order to achieve 100% cumulative recognition.

Section snippets

PCA-based face recognition

In this section we will describe Karhunen–Loeve transform (KLT)-based face recognition method, that is often called principal component analysis (PCA) or eigenfaces. We will present only main formulas of this method, whose details could be found in (Groß, 1994).

Let Xj be N-element one-dimensional image and suppose that we have r such images (j=1,…,r). A one-dimensional image-column X from the two-dimensional image (face photography) is formed by scanning all the elements of the two-dimensional

Distance measures

Let X, Y be eigenfeature vectors of length n. Then we can calculate the following distances between these feature vectors (Grudin, 1997; Yambor and Draper, 2002; Phillips et al., 1999, Phillips et al., 2000; Cekanavicius and Murauskas, 2002):

  • (1)

    Minkowski distance (Lp metrics)d(X,Y)=Lp(X,Y)=i=1n|xi−yi|p1/p,here p>0;

  • (2)

    Manhattan distance (L1 metrics, city block distance)d(X,Y)=Lp=1(X,Y)=∑i=1n|xi−yi|;

  • (3)

    Euclidean distance (L2 metrics)d(X,Y)=Lp=2(X,Y)=∥XY∥=i=1n(xi−yi)2;

  • (4)

    Squared euclidean distance (sum

Experiments and results

For experiments we used images from the AR (AR, 1998; Martinez and Benavente, 1998), Bern (1995), BioID (2001), Yale (1997), Manchester (1998), MIT (MIT, 1989; Turk and Pentland, 1991), ORL (ORL, 1992; Samaria and Harter, 1994), Umist (Umist, 1997; Graham and Allinson, 1998), FERET (Phillips et al., 1997) databases. From these databases we collected the database containing photographies of 423 persons (two images per person––one for learning and one for testing). In order to avoid recognition

Conclusions

In this publication we compared 14 distance measures and their modifications for principal component analysis-based face recognition method and proposed modified sum squared error (SSE)-based distance measure. Recognition experiments were performed using the database containing photographies of 423 persons. The experiments showed, that the proposed distance measure is among the first three best measures with respect to different characteristics of the biometric systems. The best recognition

References (34)

  • A. Yilmaz et al.

    Eigenhill vs. eigenface and eigenedge

    Pattern Recognition

    (2001)
  • H. Abdi et al.

    More about the difference between man and women: Evidence from linear neural network and principal component approach

    Perception

    (1995)
  • AR, 1998. The AR face database. Available from...
  • Bern, 1995. Face database at the University of Bern. Available from...
  • BioID, 2001. The BioID face database. Available from...
  • C.M. Bishop

    Neural Networks for Pattern Recognition

    (1995)
  • Bromba, M., 2003. Biometrics FAQ. Available from...
  • V. Cekanavicius et al.

    Statistics and its applications. Part 2

    (2002)
  • B. Efron et al.

    An Introduction to the Bootstrap

    (1993)
  • D.B. Graham et al.

    Characterizing virtual eigensignatures for general purpose face recognition. Face recognition: From theory to applications

    NATO ASI Series F, Computer and Systems Sciences

    (1998)
  • M. Groß

    Visual computing. The integration of computer graphics, visual perception and imaging. Computer Graphics: Systems and Applications

    (1994)
  • Grudin, M.A., 1997. A compact multi-level model for the recognition of facial images. Ph.D. thesis, Liverpool John...
  • P.J.B. Hancock et al.

    Race processing: Human perception and principal component analysis

    Memory Cognition

    (1996)
  • M. Kirby et al.

    Application of the Karhunen–Loeve expansion for the characterization of human faces

    IEEE Trans. PAMI

    (1990)
  • Manchester, 1998. Manchester face database. Available from...
  • Martinez, A.M., Benavente, R., 1998. The AR face database. CVC TR...
  • MIT, 1989. MIT Media Laboratory face database. Available from...
  • Cited by (0)

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