Statistical M-estimation and consistency in large deformable models for image warping

Journal of Mathematical Imaging and Vision

Volumn 34, Issue 3, 2009, Pages 270-290

  Bigot, Jérémie ^a   Gadat, Sébastien ^a   Loubes, Jean Michel ^a  

^a UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Asymptotic statistics; Clustering; Image warping; Large deformable models; M estimation; Random diffeomorphism; Template extraction

Indexed keywords

ASYMPTOTIC STATISTICS; CLUSTERING; IMAGE WARPING; LARGE DEFORMABLE MODELS; M-ESTIMATION; RANDOM DIFFEOMORPHISM; TEMPLATE EXTRACTION;

ASYMPTOTIC ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; DEFORMATION; IMAGE ANALYSIS; IMAGE ENHANCEMENT; STATISTICS; WEAVING;

ESTIMATION;

EID: 67651068021     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-009-0146-1     Document Type: Article

References (42)

1. S. Allassonière Y. Amit A. Trouvé 2007 Toward a coherent statistical framework for dense deformable template estimation J. Stat. R. Soc. B 69 3 29
2. Y. Amit U. Grenander M. Piccioni 1991 Structural image restoration through deformable template J. Am. Stat. Assoc. 86 376 387
3. A. Antoniadis J. Fan 2001 Regularization of wavelet approximations J. Am. Stat. Assoc. 96 939 967
4. Allassonière, S., Kuhn, E., Trouvé, A.: Bayesian deformable models building via stochastic approximation algorithm: a convergence study. Technical Report (2007)
5. Y. Amit A. Trouvé 2007 Pop: patchwork of parts models for object recognition Int. J. Comput. Vis. 75 267 282 (Pubitemid 47293422)
6. R.J. Biscay C.M. Mora 2001 Metric sample spaces of continuous geometric curves and estimation of their centroids Math. Nachr. 229 15 49 (Pubitemid 33572618)
7. E. Candès D. Donoho 2000 Recovering edges in ill-posed inverse problems: optimality of curvelet frames Ann. Stat. 30 784 842 (Pubitemid 37095352)
8. G. Charpiat O. Faugeras R. Keriven 2005 Approximations of shape metrics and application to shape warping and empirical shape statistics Found. Comput. Math. 5 1 58 (Pubitemid 41310096)
9. Charpiat, G., Faugeras, O.D., Keriven, R.: Image statistics based on diffeomorphic matching. In: ICCV, pp. 852-857. IEEE Computer Society, Los Alamitos (2005) (Pubitemid 44055044)
10. Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines, 2001. Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
11. De Boor, C.: A Practical Guide to Splines. Applied Mathematical Sciences, vol. 27. Springer, New York (1978)
12. Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. Wiley, New York (1998)
13. O. Faugeras G. Hermosillo 2002 Well-posedness of eight problems of multi-modal statistical image-matching Biomed. Imaging 15 23 64
14. F. Gamboa J.-M. Loubes E. Maza 2007 Semi-parametric estimation of shifts Electron. J. Stat. 1 616 640
15. U. Grenander M.I. Miller 1998 Computational anatomy: an emerging discipline Q. Appl. Math. 56 4 617 694 Current and future challenges in the applications of mathematics (Providence, RI, 1997) (Pubitemid 128597100)
16. C.A. Glasbey K.V. Mardia 2001 A penalized likelihood approach to image warping J. R. Stat. Soc. Ser. B Stat. Methodol. 63 3 465 514
17. Grenander, U.: General Pattern Theory a Mathematical Study of Regular Structures. Oxford University Press, New, York (1994)
18. J. Glaunès M. Vaillant M.I. Miller 2004 Landmark matching via large deformation diffeomorphisms on the sphere J. Math. Imaging Vis. 20 1-2 179 200 Special issue on mathematics and image analysis
19. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, Berlin (2003), Chap. 10
20. L. Huilling 1998 On the consistency of procrustean mean shapes Adv. Appl. Probab. 30 53 63
21. Jain, A.K.: Fundamentals of Digital Image Processing. Prentice-Hall, Upper Saddle River (1989)
22. Kendall, D.G., Barden, D., Carne, T.K., Le, H.: Shape and Shape Theory. Wiley Series in Probability and Statistics. Wiley, Chichester (1999)
23. Korostelëv, A.P., Tsybakov, A.B.: Minimax Theory of Image Reconstruction. Lecture Notes in Statistics, vol. 82. Springer, New York (1993)
24. Y. LeCun L. Bottou Y. Bengio P. Haffner 1998 Gradient-based learning applied to document recognition Proc. IEEE 86 11 2278 2324
25. J.-M. Loubes S. van de Geer 2002 Adaptive estimation with soft thresholding penalties Stat. Neerl. 56 4 454 479 (Pubitemid 36086535)
26. MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Le Cam, L.M., Neyman, J. (eds.) Proc. of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281-297. University of California Press, Berkeley (1967)
27. Mallat, S.: A Wavelet Tour of Signal Processing. AP Professional, 2nd edn. Academic Press, San Diego (1998)
28. Markussen, B.: A statistical approach to large deformation diffeomorphisms. In: CVPRW'04: Proceedings of the 2004 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'04), vol. 12, p. 181. IEEE Computer Society, Los Alamitos (2004)
29. B. Markussen 2007 Large deformation diffeomorphisms with application to optic flow Comput. Vis. Image Underst. 106 1 97 105 (Pubitemid 46528764)
30. X. Pennec 2006 Intrinsic statistics on Riemannian manifolds: basic tools for geometric measurements J. Math. Imaging Vis. 25 1 127 154 (Pubitemid 44544744)
31. Samaria, F.S., Harter, A.: Parameterisation of a stochastic model for human face identification, pp. 138-142 (1994)
32. Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)
33. A. Trouvé L. Younes 2005 Local geometry of deformable templates SIAM J. Math. Anal. 37 1 17 59 (electronic) (Pubitemid 43265726)
34. A. Trouvé L. Younes 2005 Metamorphoses through lie group action Found. Comput. Math. 5 2 173 198 (Pubitemid 41025459)
35. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)
36. van de Geer, S.A.: Applications of Empirical Process Theory. Cambridge Series in Statistical and Probabilistic Mathematics, vol. 6. Cambridge University Press, Cambridge (2000)
37. Van der Waart, A.: Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics, vol. 27. Cambridge Univ. Press, New York (1998)
38. Van der Waart, A.: Semiparametric Statistics. Lectures on Probability Theory, Ecole d'Ete de Probabilites de St. Flour XXIX- 1999. Springer, Berlin (2002)
39. Vimond, M.: Efficient estimation in homothetic shifted in regression models. Ann. Stat. (2006, in press)
40. M. Vaillant M.I. Miller A. Trouvé L. Younes 2004 Statistics on diffeomorphisms via tangent space representations NeuroImage 23 161 169
41. Younes, L.: Deformation analysis for shape and image processing. Lecture Notes available at: http://cis.jhu.edu/~younes/LectureNotes/deformationAnalysis. pdf
42. Younes, L.: Invariance, Déformations et Reconnaissance de Formes Mathématiques & Applications (Berlin) [Mathematics & Applications], vol. 44. Springer, Berlin (2004)