Elastic shape models for face analysis using curvilinear coordinates

Journal of Mathematical Imaging and Vision

Volumn 33, Issue 2, 2009, Pages 253-265

  Srivastava, A ^a   Samir, C ^b   Joshi, S H ^a   Daoudi, M ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b ECOLE CENTRALE DE LILLE   (France)

Author keywords

3D shape matching; Darcyan coordinate system; Elastic deformation; Elastic shape metric; Facial shape analysis; Geodesic paths; Riemannian framework

Indexed keywords

COORDINATE MEASURING MACHINES; DEFORMATION; ELASTIC DEFORMATION; GEODESY; GRAPH THEORY; PROGRAMMING THEORY;

3D SHAPE MATCHING; DARCYAN COORDINATE SYSTEM; ELASTIC SHAPE METRIC; FACIAL SHAPE ANALYSIS; GEODESIC PATHS; RIEMANNIAN FRAMEWORK;

THREE DIMENSIONAL;

EID: 59849126809     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-008-0073-6     Document Type: Article

References (44)

1. P.J. Besl N.D. McKay 1992 A method for registration of 3-D shapes IEEE Trans. Pattern Anal. Mach. Intell. 14 2 239 256
2. C. Beumier M. Acheroy 2000 Automatic 3D face authentication J. Image Vis. Comput. 18 4 315 321
3. A.M. Bronstein M.M. Bronstein R. Kimmel 2006 Efficient computation of isometry-invariant distances between surfaces SIAM J. Sci. Comput. 28 5 1812 1836
4. A.M. Bronstein M.M. Bronstein R. Kimmel 2005 Three-dimensional face recognition Int. J. Comput. Vis. 64 1 5 30
5. K.I. Chang K.W. Bowyer P.J. Flynn 2006 Multiple nose region matching for 3D face recognition under varying facial expression IEEE Trans. Pattern Anal. Mach. Intell. 28 10 1695 1700
6. G. Charpiat O. Faugeras R. Keriven 2005 Approximations of shape metrics and application to shape warping and empirical shape statistics J. Found. Comput. Math. 5 1 1 58
7. Chui, H., Rangarajan, A.: A new algorithm for non-rigid point matching. In: Proc. of IEEE Conferences on CVPR, pp. 44-51 (2000)
8. Do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice Hall, New York (1976)
9. Glaunes, J., Trouvé, A., Younes, L.: Diffeomorphic matching of distributions: A new approach for unlabelled point-sets and sub-manifolds matching. In: CVPR (2), pp. 712-718 (2004)
10. Glaunes, J., Trouve, A., Younes, L.: Modeling planar shape variation via Hamiltonian flows of curves. In: Krim, H., Yezzi, A. (eds.) Statistics and Analysis of Shapes. Birkhauser, Basel (2006)
11. Grenander, U.: General Pattern Theory. Oxford University Press, Oxford (1993)
12. U. Grenander M.I. Miller 1998 Computational anatomy: An emerging discipline Q. Appl. Math. 56 4 617 694
13. U. Grenander A. Srivastava S. Saini 2007 A pattern-theoretic characterization of biological growth IEEE Trans. Med. Imag. 26 5 648 659
14. Gupta, S., Markey, M.K., Aggarwal, J., Bovik, A.C.: Three dimensional face recognition based on geodesic and euclidean distances. In: Proceedings of IS&T/SPIE Symposium on Electronic Imaging: Vision Geometry XV (2007)
15. Hallinan, P.W., Gordon, G.G., Yuille, A.L., Giblin, P., Mumford, D.: Two- and Three-Dimensional Patterns of Face. A.K. Peters, Wellesley (1999)
16. Hesher, C., Srivastava, A., Erlebacher, G.: A novel technique for recognizing faces using range images. In: Proceedings of ISSPA, 2003, Paris, France (2003)
17. Joshi, S., Srivastava, A., Klassen, E., Jermyn, I.H.: Removing shape-preserving transformations in square-root elastic (SRE) framework for shape analysis of curves. In: Proc. of Sixth Workshop on Energy Minimization Methods in CVPR (EMMCVPR) (2007)
18. Joshi, S.H., Klassen, E., Srivastava, A., Jermyn, I.H.: An efficient representation for computing geodesics between n-dimensional elastic shapes. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2007
19. I.A. Kakadiaris G. Passalis G. Toderici M.N. Murtuza N. Karampatziakis T. Theoharis 2007 Three-dimensional face recognition in the presence of facial expressions: An annotated deformable model approach IEEE Trans. Pattern Anal. Mach. Intell. 29 4 1 10
20. D.G. Kendall 1984 Shape manifolds, procrustean metrics and complex projective spaces Bull. Lond. Math. Soc. 16 81 121
21. Kilian, M., Mitra, N.J., Pottmann, H.: Geometric modeling in shape space. In: Proceedings of SIGGRAPH (2007)
22. Klassen, E., Srivastava, A.: Geodesics between 3D closed curves using path straightening. In: European Conference on Computer Vision, vol. 1, pp. 95-106 (2006)
23. E. Klassen A. Srivastava W. Mio S.H. Joshi 2004 Analysis of planar shapes using geodesic paths on shape spaces IEEE Trans. Pattern Anal. Mach. Intell. 26 3 372 383
24. C. Kotropoulos A. Tefas I. Pitas 2000 Frontal face authentication using morphological elastic graph matching IEEE Trans. Image Process. 9 4 555 560
25. Litke, N., Droske, M., Rumpf, M., Schröder, P.: An image processing approach to surface matching. In: Desbrun, M., Pottmann, H. (eds.) Third Eurographics Symposium on Geometry Processing, pp. 207-216 (2005)
26. Lu, X., Jain, A.K.: Deformation analysis for 3D face matching. In: Proc. 7th IEEE Workshop on Applications of Computer Vision, pp. 99-104. Breckenridge (2005)
27. X. Lu A.K. Jain D. Colbry 2006 Matching 2.5D face scans to 3D models IEEE Trans. Pattern Anal. Mach. Intell. 28 1 31 43
28. F. Memoli G. Sapiro 2005 A theoretical and computational framework for isometry invariant recognition of point cloud data Found. Comput. Math. 5 3 313 347
29. P.W. Michor D. Mumford 2006 Riemannian geometries on spaces of plane curves J. Eur. Math. Soc. 8 1 48
30. M.I. Miller L. Younes 2001 Group actions, homeomorphisms, and matching: A general framework Int. J. Comput. Vis. 41 1/2 61 84
31. W. Mio A. Srivastava S.H. Joshi 2007 On shape of plane elastic curves Int. J. Comput. Vis. 73 3 307 324
32. I. Mpiperis S. Malassiotis M.G. Strintzis 2007 3-D face recognition with the geodesic polar representation IEEE Trans. Information Forensics Security 2 3 537 547
33. Osada, R., Funkhouser, T., Chazells, B., Dobkin, D.: Matching 3D models with shape distributions. In: IEEE Shape Modeling International, May 2001
34. C. Samir A. Srivastava M. Daoudi 2006 Three-dimensional face recognition using shapes of facial curves IEEE Trans. Pattern Anal. Mach. Intell. 28 11 1858 1863
35. Samir, C., Srivastava, A., Daoudi, M.: 3D face recognition using shapes of facial curves. In: Proceedings of ICASSP, 2006, Special Session on Statistical Inferences on Nonlinear Manifolds with Applications in Signal and Image Processing, May 2006
36. Samir, C., Srivastava, A., Daoudi, M., Klassen, E.: An intrinsic framework for analysis of facial surfaces. Int. J. Comput. Vis. (2007, in review)
37. Schmidt, F.R., Clausen, M., Cremers, D.: Shape matching by variational computation of geodesics on a manifold. In: Pattern Recognition (Proc. DAGM). LNCS, vol. 4174, pp. 142-151. Springer, Berlin (2006)
38. T.B. Sebastian P.N. Klein B.B. Kimia 2003 On aligning curves IEEE Trans. Pattern Anal. Mach. Intell. 25 1 116 125
39. Spivak, M.: A Comprehensive Introduction to Differential Geometry, vol. I and II. Publish or Perish, Berkeley (1979)
40. Wang, S., Wang, Y., Jin, M., Gu, X., Samaras, D.: 3D surface matching and recognition using conformal geometry. In: CVPR (2), pp. 2453-2460 (2006)
41. Wang, Y., Chiang, M.-C., Thompson, P.: Mutual information-based 3D surface matching with applications to face recognition and brain mapping. In: International Conference on Computer Vision (2005)
42. Wiskott, L., Fellous, J.-M., Krüger, N., von der Malsburg, C.: Face recognition by elastic bunch graph matching. In: Jain, L.C., Halici, U., Hayashi, I., Lee, S.B. (eds.) Intelligent Biometric Techniques in Fingerprint and Face Recognition, pp. 355-396. CRC Press, Boca Raton (1999). Chap. 11
43. Yezzi, A.-J., Mennucci, A.: Conformal metrics and true "gradient flows" for curves. In: Proceedings of the Tenth IEEE International Conference on Computer Vision, vol. 1, pp. 913-919 (2005)
44. L. Younes 1998 Computable elastic distance between shapes SIAM J. Appl. Math. 58 2 565 586