This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
January 1990 (vol. 12 no. 1)
pp. 103-108

The use of natural symmetries (mirror images) in a well-defined family of patterns (human faces) is discussed within the framework of the Karhunen-Loeve expansion. This results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix, without increasing the complexity of the calculation. The resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average.

[1] L. Sirovich, "Turbulence and the dynamics of coherent structures, Part II: Symmetries and transformations,"Quart. Appl. Math., vol. XLV, no. 3, pp. 573-582, 1987.
[2] S. Watanabe, "Karhunen-Loève expansion and factor analysis theoretical remarks and applications." inProc. 4th Prugue Conf. Inform. Theory. 1965.
[3] M. D. Kelly. "Visual identification of people by computer." Stanford Intelligence Project Memo AI-130, July 1970.
[4] A. J. Goldstein, L. D. Harmon, and A. B. Lesk, "Identification of human faces."Proc. IEEE, vol. 59, May 1971.
[5] Y. Kaya and K. Kobayashi, "A basic study on human face recognition." inProc. Int. Conf. Frontiers of Pattern Recognition, HI, 1971, pp. 265-289.
[6] T. Sakai, M. Nagao, and T. Kanade, "Computer analysis and classification of photographs of human faces," presented at the 1st USA-Japan Comput. Conf., Session 2-7-1, 1972.
[7] L. D. Harmon, M. B. Khan, R. Lasch, and P. F. Ramig, "Machine identification of human faces."Pattern Recognition, vol. 13, no. 2, pp. 97-110, 1981.
[8] T. Kohonen, E. Oja, and P. Lehtiö, "Storage and processing of information in distributed associative memory systems." in G. E. Hinton and J. A. Anderson, Eds.,Parallel Models of Associative Memory. Hillsdale, NJ: Lawrence Erlbaum Associates, 1989, pp. 129- 167.
[9] J. Stoneham, "Practical face recognition and verification with WISARD," in H. Ellis, M. Jeeves, F. Newcombe, and A. Young, Eds.,Aspects of Face Processing. Dordrecht: Martinus Nijhoff, 1986.
[10] V. Bruce and M. Burton, "Computer recognition of faces," in A. W. Young and H. D. Ellis, Eds., Handbook of Research on Face Processing. Amsterdam: North-Holland, 1989, pp. 487-506.
[11] L. Sirovich and M. Kirby, "A low-dimensional procedure for the characterization of human faces,"J. Opt. Soc. Amer. A, vol. 4, no. 3, pp. 519-524, 1987.
[12] A. O'Toole and H. Abdi, "Connectionist approaches to visually-based facial feature extraction," in G. Tiberghien, Ed.,Advances in Cognitive Psychology, Vol. 2, London: Wiley, 1989.
[13] H. Abdi, "A generalized approach for connectionist autoassociative memories: Interpretation, implication and illustration for face processing," in J. Demongeot, T. Hervè, V. Rialle, and C. Roche, Eds.,Artificial Intelligence and Cognitive Sciences. Manchester, England: Manchester Univ. Press, 1988, pp. 149-165.
[14] K. Karhunen, "Uber lineare methoden in der wahrscheinlichkeitsrechnung,"Ann. Acad. Sci. Fennicae, ser. A1,Math. Phys., vol. 37. 1946.
[15] M. M. Loèe. Probability Theory. Princeton, NJ: Van Nostrand, 1955.
[16] K. Fukunaga,Introduction to Statistical Pattern Recognition. New York: Academic, 1972.
[17] R. B. Ash and M. F. Gardner,Topics in Stochastic Processes. New York: Academic. 1975.
[18] I. T. Jolliffe,Principle Component Analysis. New York: Springer-Verlag, 1986.
[19] R.C. Gonzalez and P. Wintz,Digital Image Processing, Addison-Wesley, Reading, Mass., 1987.
[20] K. Pearson, "On lines and planes of closest fit to systems of points in space."Phil. Mag., 6th series, 1901.
[21] H. Hotelling, "Analysis of a complex of statistical variables into principal components,"J. Educational Psyhol., Sept. 1933.
[22] J. A. Anderson and G. E. Hinton, "Models of information processing in the brain," in G. E. Hinton and J. A. Anderson, Eds.,Parallel Models of Associative Memory. Hillsdale, NJ: Lawrence Erlbaum Associates, 1989, pp. 23-62.
[23] L. D. Harmon, "The recognition of faces,"Sci. Amer., pp. 70-84, Nov. 1973.
[24] L. Sirovich, "Turbulence and the dynamics of coherent structures, Part I: Coherent structures,"Quart. Appl. Math., vol. XLV, no. 3, pp. 561-571, 1987.

Index Terms:
pattern recognition; Karhunen-Loeve procedure; human faces; natural symmetries; mirror images; Karhunen-Loeve expansion; eigenfunctions; covariance matrix; eigenvalues and eigenfunctions; matrix algebra; pattern recognition
Citation:
M. Kirby, L. Sirovich, "Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 103-108, Jan. 1990, doi:10.1109/34.41390
Usage of this product signifies your acceptance of the Terms of Use.