Methods of Geodesic Distance in Two-Dimensional Face Recognition

In this paper, we present a comparative study of three
methods of 2D face recognition system such as: Iso-Geodesic Curves
(IGC), Geodesic Distance (GD) and Geodesic-Intensity Histogram
(GIH). These approaches are based on computing of geodesic
distance between points of facial surface and between facial curves.
In this study we represented the image at gray level as a 2D surface in
a 3D space, with the third coordinate proportional to the intensity
values of pixels. In the classifying step, we use: Neural Networks
(NN), K-Nearest Neighbor (KNN) and Support Vector Machines
(SVM). The images used in our experiments are from two wellknown
databases of face images ORL and YaleB. ORL data base was
used to evaluate the performance of methods under conditions where
the pose and sample size are varied, and the database YaleB was used
to examine the performance of the systems when the facial
expressions and lighting are varied.

• Rachid Ahdid
• Said Safi
• Bouzid Manaut

• 2D face recognition
• Geodesic distance
• Iso-Geodesic Curves
• Geodesic-Intensity Histogram
• facial surface
• Neural Networks
• K-Nearest Neighbor
• Support Vector Machines.

[1] C. Samir, A. Srivastava, M. Daoudi: “Three-dimensional face
recognition using shapes of facial curves”. IEEE Transactions on Pattern
Analysis and Machine Intelligence, 1847–1857, (2006).
[2] L. Ballihi, B. Ben Amor, M. Daoudi, A. Srivastava, D. Aboutajdine:
Sélection de courbes de la surface nasale pour l’authentification de
personnes en utilisant Adaboost. hal-00666262, version 1 - 3 Feb 2012.
[3] M. Turk and A. Pentland, “Eigenfaces for Recognition,” Journal of
Cognitive Neuroscience, vol 3no 1, pp. 71-86. 1991.
[4] J. Yang., D. Zhang and D. Frangi: “Two-Dimensional PCA: A New
Approach to Appearance-Based Face Representation and Recognition”,
IEEE Trans On PAMI, 26(1), pp: 131-137, 2004.
[5] P. Yan, K.W. Bowyer: “Biometric recognition using 3D ear shape”.
IEEE Transactions on Pattern Analysis and Machine Intelligence 29, 8,
pp. 1297–1308. (2007).
[6] H. Chen, B. Bhanu: Human ear recognition in 3D. IEEE Transactions on
Pattern Analysis and Machine Intelligence 29, 4, pp. 718–737. (2007).
[7] M. Visani., C. Garcia and J.M. Jolion., “Two- Dimensional-Oriented
Linear Discriminant Analysis for Face Recognition,” Proc. of the Int.
Conf. On Computer Vision and Graphics ICCVG’04, dans la srie
Computational Imaging and Vision, Varsovie, Pologne, 2004.
[8] H. Cevikalp., M. Neamtu., M. Wilkes, A. Barkana.: Discriminative
common vectors for face recognition. IEEE Trans. Pattern Anal.
Machine Intell. 27 (1), 4–13. 2005.
[9] M. Belahcene., A. Ouamane., M. Boumehrez., and A. Benakcha.,
”Comparaison des mthodes de rduction d’espace et l’application des
SVMS pour la classification dans l’authentification de visages,”
COURRIER DU SAVOIR, pp. 117-126, 2012.
[10] J. Lu, J., N. P. Kostantinos, N. V. Anastasios: “Face recognition using
LDA-based algorithms”. IEEE Trans. Neural Networks 14 (1), 195–200.
2003.
[11] B.A. Draper, K. Baek, M.S. Bartlett, J.R. Beveridge, “Recognizing
Faces with PCA and ICA,” Computer Vision and Image Understanding:
special issue on face recognition, in press, pp. 115-137, 2003.
[12] M.S. Bartlett, J.R. Movellan, and T.J. Sejnowski, “Face Recognition by
Independent Component Analysis,” IEEE Trans. Neural Networks, vol.
13, no. 6, pp. 1450-1464, 2002.
[13] W. Xu and E. J. Lee, “Face Recognition Using Wavelets Transform and
2D PCA by SVM Classifier”, International Journal of Multimedia and
Ubiquitous Engineering, Vol.9, No.3, pp.281 -290, (2014).
[14] K. I. Kim., K. Jung., and J. Kim., ”Face recognition using support vector
machines with local correlation kernels,” International Journal of Pattern
Recognition and Artificial Intelligence, vol. 16 no. 1, pp. 97- 111, 2002.
[15] G.D. Guo, H.J. Zhang, and S.Z. Li., ”Pairwise face recognition,” in
Proceedings of 8th IEEE International Conference on Computer Vision.
Vancouver, Canada, July 9-12, 2001.
[16] F. Salimi., M. Sadeghi., M. S. Moin and J. Kittler., “Face Verification
Using Colour Kernels,” Springer-Verlag Berlin Heidelberg, pp. 522-531,
2009.
[17] M. Agarwal, N. Jain, M. Kumar and H. Agrawal, “Face Recognition
Using Eigen Faces and Artificial Neural Network”, International Journal
of Computer Theory and Engineering, Vol. 2, No. 4, August, 1793-8201,
2010.
[18] V. More and A. Wagh, “Improved Fisher Face Approach for Human
Recognition System using Facial Biometrics”, International Journal of
Information and Communication Technology Research, Volume 2 No.
2, February 2012.
[19] L. Chen, H. Liao, M. Ko, J. Lin and G. Yu. A new LDA-based face
recognition system which can solve the small sample size problem. In
IEEE Pattern Recognition 33 (10), 2000.
[20] A. Nefian and M. Hayes, ” An embedded hmm-based approach for face
detection and recognition,” In Proc. IEEE International Conference on
Acoustics, Speech, and Signal Processing, vol. 6, pp. 3553–3556, 1999.
[21] R. Kimmel and J. A. Sethian, “Computing geodesic on manifolds,” in
Proc. US National Academy of Science, 1998, vol. 95, pp. 8431–8435.
1998.
[22] X. Desquesnes, A. Elmoataz, O. Lézoray: “Eikonal equation adaptation
on weighted graphs: fast geometric diffusion process for local and non -
local image and data processing”. Journal of Mathematical Imaging and
Vision 46, 2 (2013), pp. 238-257, 2014.
[23] E. Carlini, M. Falcone, N. Forcadel, R. Monneau: “Convergence of a
generalized fast-marching method for an eikonal equation with a
velocity-changing sign”. SIAM J. Numer. Anal. 46, 2920– 2952 (2008).
[24] E.W. Dijkstra, A Note on Two Problems in Connection with Graphs,
Numerische Mathematik, 1 (1959), pp. 269–271, 1959.
[25] A. M.Bronstein, M. M. Bronstein, E. Gordon, R. Kimmel: “Fusion of
2D and 3D Data in Three-Dimensional Face Recognition”. Image
Processing, 2004. ICIP '04. 2004 International Conference on (Volume:
1), IEEE, p.p: 87 - 90. (2004).
[26] A. M.Bronstein, M. M. Bronstein, A. Spira, R. Kimmel: “Face
Recognition from Facial Surface Metric”, Lecture Notes in Computer
Science Volume 3022, 2004, Springer Berlin Heidelberg, p.p: 225-237.
(2004).
[27] R. Ahdid., S. Safi and B. Manaut, “Approach of Facial Surfaces
by Contour,” IEEE Xplore, International Conference Multimedia
Computing and Systems (ICMCS), pp: 465-468, (2014).[28] H. Ling and D. Jacobs. Deformation invariant image matching. In ICCV,
2005.
[29] S. Miao, H. Krim: “3D Face Recognition Based on Evolution of Iso-
Geodesic Distance Curves”, Acoustics Speech and Signal Processing
(ICASSP), 2010 IEEE International Conference on, pp: 1134 – 1137.
2010.
[30] S. Jahanbin, H. Choi, Y. Liu, A. C. Bovik: “Three Dimensional Face
Recognition Using Iso-Geodesic and Iso-Depth Curves”, Biometrics:
Theory, Applications and Systems, 2008. BTAS 2008. 2nd IEEE
International Conference on, pp: 1-6. 2008.
[31] L. Ballihi, A. Srivastava, B. B. Amor, M. Daoudi, D. Aboutajdine:
“Which 3D geometric facial features give up your identity?”, ICB 2012,
pp: 119-124. 2012.
[32] L. Ballihi, B. B. Amor, M. Daoudi, A. Srivastava, D. Aboutajdine:
“Boosting 3-D-Geometric Features for Efficient Face Recognition and
Gender Classification”. IEEE Transactions on Information Forensics and
Security 7(6), pp: 1766-1779. 2012.
[33] E. Klassen and A. Srivastava, Geodesics Between 3D Closed Curves
Using Path Straightening, Proceedings of ECCV, Lecture Notes in
Computer Science, 2006, p. 95-106. Springer Berlin Heidelberg. 2006.
[34] S. Joshi, E. Klassen, A. Srivastava, and I. Jermyn: “An Efficient
Representation for Computing Geodesics between n-Dimensional
Elastic Shapes”, IEEE Conference on Computer Vision and Pattern
Recognition (CVPR), June 2007.
[35] A. Maalej, B. Ben Amor, M. Daoudi, A. Srivastava, S. Berretti: “Shape
analysis of local facial patches for 3D facial expression
recognition”. Pattern Recognition (Volume 44, Issue 8), pp: 1581-
1589 (2011).
[36] R. Ahdid, S. Safi and B. Manaut: “Three Dimensional Face Surfaces
Analysis using Geodesic Distance”, Journal of Computer Sciences and
Applications, (Volume 3, Issue 3), pp: 67-72. (2015).