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INCORPORATING INVARIANTS IN MAHALANOBIS DISTANCE-BASED CLASSIFIERS: APPLICATIONS TO FACE 189 RECOGNITION the preprocessing algorithms, we suspect that much of the improvement is due to similarities between the transformations we handle and differences between images. For example, a smile is probably something like a dilation in the horizontal direction. V. ACKNOWLEDGMENT This work was supported by a LANL 2002 Homeland defense LDRD-ER (PI K. Vixie) and a LANL 2003 LDRD- DR (PI J. Kamm). REFERENCES [1] A.S.Georghiades, P.N.Belhumeur, and D.J.Kriegman, âFrom few to many: Illumination cone models for face recognition under variable lighting and pose,â IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 643â660, June 2001. [2] P.Y.Simard, Y.A. L.Cun, J.S.Denker, and B.Victorri, âTransformation invariance in pattern recognitionâtangent distance and tangent propagation,â in Neural Networks: Tricks of the Trade, G.B.Orr and K.-R.Muller, Eds. Springer, 1998, ch. 12. [3] P.Y.Simard, Y.A.Cun, J.S.Denker, and B.Victorri, âTransformation invariance in pattern recognition: Tangent distance and propagation,â International Journal of Imaging Systems and Technology, vol. 11, no. 3, pp. 181â197, 2000. [4] A.Fraser, N.Hengartner, K.Vixie, and B.Wohlberg, âClassification modulo invariance, with application to face recognition,â Journal of Computational and Graphical Statistics, 2003, invited paper, in preparation. [5] P.J.Phillips, H.Moon, P.J.Rauss, and S.Rizvi, âThe feret evaluation methodology for face recognition algorithms,â IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 10, Oct. 2000, available as report NISTR 6264. [6] J.R.Beveridge, K.She, B.Draper, and G.H.Givens, âA nonparametric statistical comparison of principal component and linear discriminant subspaces for face recognition,â in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2001. [Online]. Available: http://www.cs.colostate.edu/evalfacerec/index.html [7] R.Beveridge, âEvaluation of face recognition algorithms web site.â http://www.cs.colostate.edu/evalfacerec/, Oct. 2002. [8] M.Turk and A.Pentland, âFace recognition using eigenfaces,â in Proc. IEEE Conference on Computer Vision and Pattern Recognition, Maui, HI, USA, 1991. [9] W.Zhao, R.Chellappa, and A.Krishnaswamy, âDiscriminant analysis of principal components for face recognition,â in Face Recognition: From Theory to Applications, Wechsler, Phillips, Bruce, Fogelman-Soulie, and Huang, Eds., 1998, pp. 73â85.