Bridge simulation and metric estimation on landmark manifolds

Stefan Horst Sommer; Alexis Arnaudon; Line Kühnel; Sarang Joshi

doi:10.1007/978-3-319-67675-3_8

Bridge simulation and metric estimation on landmark manifolds

Stefan Horst Sommer, Alexis Arnaudon, Line Kühnel, Sarang Joshi

Department of Computer Science

10 Citations (Scopus)

Abstract

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood.

Original language	English
Title of host publication	Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics : First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings
Editors	J. Cardoso, T. Arbel, E. Ferrante, X. Pennec, A. Dalca, S. Parisot, N. K. Batmanghelich, A. Sotiras, M. Nielsen, M. R. Sabuncu, T. Fletcher, L. Shen, S. Durrleman, S. Sommer
Number of pages	13
Publisher	Springer
Publication date	2017
Pages	79-91
ISBN (Print)	978-3-319-67674-6
ISBN (Electronic)	978-3-319-67675-3
DOIs	https://doi.org/10.1007/978-3-319-67675-3_8
Publication status	Published - 2017
Event	6th International Workshop on Mathematical Foundations of Computational Anatomy - Québec City, Canada Duration: 10 Sept 2017 → 14 Sept 2017 Conference number: 6

Conference

Conference	6th International Workshop on Mathematical Foundations of Computational Anatomy
Number	6
Country/Territory	Canada
City	Québec City
Period	10/09/2017 → 14/09/2017

Series	Lecture notes in computer science
Volume	10551
ISSN	0302-9743

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10.1007/978-3-319-67675-3_8

http://arxiv.org/pdf/1705.10943

Cite this

Sommer, S. H., Arnaudon, A., Kühnel, L., & Joshi, S. (2017). Bridge simulation and metric estimation on landmark manifolds. In J. Cardoso, T. Arbel, E. Ferrante, X. Pennec, A. Dalca, S. Parisot, N. K. Batmanghelich, A. Sotiras, M. Nielsen, M. R. Sabuncu, T. Fletcher, L. Shen, S. Durrleman, & S. Sommer (Eds.), Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics: First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings (pp. 79-91). Springer. https://doi.org/10.1007/978-3-319-67675-3_8

Bridge simulation and metric estimation on landmark manifolds. / Sommer, Stefan Horst; Arnaudon, Alexis; Kühnel, Line et al.
Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics: First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings. ed. / J. Cardoso; T. Arbel; E. Ferrante; X. Pennec; A. Dalca; S. Parisot; N. K. Batmanghelich; A. Sotiras; M. Nielsen; M. R. Sabuncu; T. Fletcher; L. Shen; S. Durrleman; S. Sommer. Springer, 2017. p. 79-91 (Lecture notes in computer science, Vol. 10551).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Sommer, SH, Arnaudon, A, Kühnel, L & Joshi, S 2017, Bridge simulation and metric estimation on landmark manifolds. in J Cardoso, T Arbel, E Ferrante, X Pennec, A Dalca, S Parisot, NK Batmanghelich, A Sotiras, M Nielsen, MR Sabuncu, T Fletcher, L Shen, S Durrleman & S Sommer (eds), Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics: First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings. Springer, Lecture notes in computer science, vol. 10551, pp. 79-91, 6th International Workshop on Mathematical Foundations of Computational Anatomy, Québec City, Canada, 10/09/2017. https://doi.org/10.1007/978-3-319-67675-3_8

Sommer SH, Arnaudon A, Kühnel L, Joshi S. Bridge simulation and metric estimation on landmark manifolds. In Cardoso J, Arbel T, Ferrante E, Pennec X, Dalca A, Parisot S, Batmanghelich NK, Sotiras A, Nielsen M, Sabuncu MR, Fletcher T, Shen L, Durrleman S, Sommer S, editors, Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics: First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings. Springer. 2017. p. 79-91. (Lecture notes in computer science, Vol. 10551). doi: 10.1007/978-3-319-67675-3_8

Sommer, Stefan Horst ; Arnaudon, Alexis ; Kühnel, Line et al. / Bridge simulation and metric estimation on landmark manifolds. Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics: First International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and Third International Workshop, MICGen 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 10–14, 2017, Proceedings. editor / J. Cardoso ; T. Arbel ; E. Ferrante ; X. Pennec ; A. Dalca ; S. Parisot ; N. K. Batmanghelich ; A. Sotiras ; M. Nielsen ; M. R. Sabuncu ; T. Fletcher ; L. Shen ; S. Durrleman ; S. Sommer. Springer, 2017. pp. 79-91 (Lecture notes in computer science, Vol. 10551).

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abstract = "We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood.",

author = "Sommer, {Stefan Horst} and Alexis Arnaudon and Line K{\"u}hnel and Sarang Joshi",

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AB - We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood.

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A2 - Batmanghelich, N. K.

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Bridge simulation and metric estimation on landmark manifolds

Abstract

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