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

Datalogisk Institut

10 Citationer (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.

Originalsprog	Engelsk
Titel	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
Redaktører	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
Antal sider	13
Forlag	Springer
Publikationsdato	2017
Sider	79-91
ISBN (Trykt)	978-3-319-67674-6
ISBN (Elektronisk)	978-3-319-67675-3
DOI	https://doi.org/10.1007/978-3-319-67675-3_8
Status	Udgivet - 2017
Begivenhed	6th International Workshop on Mathematical Foundations of Computational Anatomy - Québec City, Canada Varighed: 10 sep. 2017 → 14 sep. 2017 Konferencens nummer: 6

Konference

Konference	6th International Workshop on Mathematical Foundations of Computational Anatomy
Nummer	6
Land/Område	Canada
By	Québec City
Periode	10/09/2017 → 14/09/2017

Navn	Lecture notes in computer science
Vol/bind	10551
ISSN	0302-9743

Adgang til dokumentet

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

http://arxiv.org/pdf/1705.10943

Citationsformater

Sommer, S. H., Arnaudon, A., Kühnel, L., & Joshi, S. (2017). Bridge simulation and metric estimation on landmark manifolds. I 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 (red.), 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 (s. 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. red. / 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. s. 79-91 (Lecture notes in computer science, Bind 10551).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Sommer, SH, Arnaudon, A, Kühnel, L & Joshi, S 2017, Bridge simulation and metric estimation on landmark manifolds. i 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 (red), 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, bind 10551, s. 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. I 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, red., 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. s. 79-91. (Lecture notes in computer science, Bind 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. red. / 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. s. 79-91 (Lecture notes in computer science, Bind 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.",

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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 - Dalca, A.

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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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