Study of Similarity Measures with Linear Discriminant Analysis for Face Recognition

Mohamed A. El-Sayed^1,2, Kadry Hamed^3,4

¹Department of Mathematics, Faculty of Science, Fayoum University, Al Fayoum, Egypt.
²Department of CS, Computers & IT College, Taif University, Taif, KSA.
³Department of CS, Faculty of Computers and Information, Minia University, Minya, Egypt.
⁴Department of CS, College of Computing and Information Technology, Shaqra University, Shaqra, KSA.

DOI: 10.4236/jsea.2015.89046                

Abstract

Face recognition systems have been in the active research in the area of image processing for quite a long time. Evaluating the face recognition system was carried out with various types of algorithms used for extracting the features, their classification and matching. Similarity measure or distance measure is also an important factor in assessing the quality of a face recognition system. There are various distance measures in literature which are widely used in this area. In this work, a new class of similarity measure based on the Lp metric between fuzzy sets is proposed which gives better results when compared to the existing distance measures in the area with Linear Discriminant Analysis (LDA). The result points to a positive direction that with the existing feature extraction methods itself the results can be improved if the similarity measure in the matching part is efficient.

Keywords

Fuzzy Sets, Similarity Measure, Distance Measure, LDA, Face Recognition

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Zhao, W., Chellappa, R., Rosenfeld, A. and Phillips, P.J. (2003) Face Recognition: A Literature Survey. ACM Computing Surveys, 35, 399-458. http://dx.doi.org/10.1145/954339.954342
[2]	Tolba, A.S., El-Baz, A.H. and El-Harby, A.A. (2005) Face Recognition: A Literature Review. Intern-ational Journal of Signal Processing, 2.
[3]	Chellappa, R., Wilson, C.L. and Sirohey, C. (1995) Human and Machine Recognition of Faces: A Survey. Proceedings of the IEEE, 83, 705-740. http://dx.doi.org/10.1109/5.381842
[4]	Yang, M.-H., Kriegman, D.J. and Ahuja, N. (2002) Detecting Faces in Images: A Survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24. http://dx.doi.org/10.1109/34.982883
[5]	Tolba, A.S., El-Baz, A.H. and El-Harby, A.A. (2006) Face Recognition: A Literature Review. Intern-ational Journal of Information and Communication Engineering, 2, 88-103.
[6]	Zhao, W.-Y., Chellappa, R., Jonathon Phillips, P. and Rosenfeld, A. (2003) Face Recognition: A Literature Survey. ACM Computing Surveys, 35, 399-458. http://dx.doi.org/10.1145/954339.954342
[7]	Philips, P.J., Moon, H., Rauss, P. and Rizvi, S.A. (1997) The FERET Evaluation Methodology for Face Recognition Algorithms. Proceedings of the IEEE Conference on Computer Vision and Pattern Recog-nition, 137-143.
[8]	Voitsekhovskii, M.I. (2001) Minkowski Inequality. Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer.
[9]	Cha, S.-H. (2007) Comprehensive Survey on Distance/Similarity Measures between Probability Density Function. International Journal of Mathematical Models and Methods in Applied Sciences, 1.
[10]	Randall, W.D. and Martinez, T.R. (1997) Improved Heterogeneous Distance Functions. Journal of Artificial Intelligence Research, 6, 1-34.
[11]	Hjaltason, G.R. and Samet, H. (2003) Index-Driven Similarity Search in Metric Spaces. Survey Article, ACM Transaction on Database Systems.
[12]	Kwon, S.H. (2001) A Similarity Measure of Fuzzy Sets. Journal of Fuzzy Logic and Intelligent Systems, 11, 270-274.
[13]	Liu, X. (1992) Entropy, Distance Measure and Similarity Measure of Fuzzy Sets and Their Relations. Fuzzy Sets and Systems, 52, 305-318. http://dx.doi.org/10.1016/0165-0114(92)90239-Z
[14]	Wang, X., DeBaets, B. and Kerre, E.E. (1995) A Comparative Study of Similarity Measures. Fuzzy Sets and Systems, 73, 259-268. http://dx.doi.org/10.1016/0165-0114(94)00308-T
[15]	Chen, S.M. (1995) Measures of Similarity between Vague Sets. Fuzzy Sets and Systems, 74, 217-223. http://dx.doi.org/10.1016/0165-0114(94)00339-9
[16]	Wang, W.J. (1997) New Similarity Measure on Fuzzy Sets and on Elements. Fuzzy Sets and Systems, 85, 305-309. http://dx.doi.org/10.1016/0165-0114(95)00365-7
[17]	Van der Weken, D., Nachtegael, M. and Kerre, E.E. (2002) An Overview of Similarity Measures for Images. Proceeding of ICASSP 2002 (IEEE International Conference on Acoustics, Speech and Signal processing), Orland, 13-17 May 2002, 3317-3320.
[18]	Van der Weken, D., Nachtegael, M. and Kerre, E.E. (2004) Using Similarity Measures and Homogeneity for the Comparison of Images. Image and Vision Computing, 22, 695-702. http://dx.doi.org/10.1016/j.imavis.2004.03.002
[19]	Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[20]	Huang, A. (2008) Similarity Measures for Text Document Clustering. NZCSRSC 2008, Christchurch, 14-18 April 2008.
[21]	Taghva, K. and Veni, R. (2010) Effects of Similarity Metrics on Document Clustering. 2010 7th International Conference on Information Technology, Las Vegas, 12-14 April 2010, 222-226. http://dx.doi.org/10.1109/itng.2010.65
[22]	Omran, S. and Hassaballah, M. (2006) A New Class of Similarity Measures for Fuzzy Sets. International Journal of Fuzzy Logic and Intelligent Systems, 6, 100-104. http://dx.doi.org/10.5391/IJFIS.2006.6.2.100
[23]	Wang, W. and Xin, X. (2005) Distance Measure between Intuitionistic Fuzzy Sets. Pattern Recognition Letters, 26, 2063-2069. http://dx.doi.org/10.1016/j.patrec.2005.03.018
[24]	Mika, S., Ratsch, G., Weston, J., Scholkopf, B. and Muller, K. (1999) Fisher Discriminant Analysis with Kernels. IEEE Conference on Neural Networks for Signal Processing IX, Madison, 23-25 August 1999, 41-48. http://dx.doi.org/10.1109/nnsp.1999.788121
[25]	Zhao, W., Chellappa, R. and Phillips, J. (1999) Subspace Linear Discriminant Analysis for Face Recognition. Technical Report, CFAR-TR99-914, University of Maryland.
[26]	Beveridge, J.R., She, K., Draper, B. and Givens, G.H. (2001) A Nonparametric Statistical Comparison of Principal Component and Linear Discriminant Subspaces for Face Recognition. Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Kauai, 8-14 December 2001, 535-542. http://dx.doi.org/10.1109/cvpr.2001.990520
[27]	Martinez, A. and Kak, A. (2001) PCA versus LDA. IEEE Transactions on Pattern Analysis Machine Intelligence, 23, 228-233. http://dx.doi.org/10.1109/34.908974
[28]	Navarrete, P. and Ruiz-del-Solar, J. (2002) Analysis and Comparison of Eigen Space Based Face Recognition Approaches. International Journal on Pattern Recognition and Artificial Intelligence, 16, 817-830. http://dx.doi.org/10.1142/S0218001402002003
[29]	The ORL Database of Faces. http://www.face-rec.org/databases/
[30]	Nefian, A.V., Khosravi, M. and Hayes III, M.H. (1997) Real-Time Human Face Detection from Uncontrolled Environments. SPIE Visual Communications on Image Processing.
[31]	Turk, M. and Pentland, A. (1991) Eigenfaces for Recognition. Journal of Cognitive Neuroscience, 3, 71-86. http://dx.doi.org/10.1162/jocn.1991.3.1.71