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2017 | Supplement | Buchkapitel

Bridge Simulation and Metric Estimation on Landmark Manifolds

verfasst von : Stefan Sommer, Alexis Arnaudon, Line Kuhnel, Sarang Joshi

Erschienen in: Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics

Verlag: Springer International Publishing

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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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Titel: Bridge Simulation and Metric Estimation on Landmark Manifolds
verfasst von: Stefan Sommer
Alexis Arnaudon
Line Kuhnel
Sarang Joshi
Verlag: Springer International Publishing
Buch: Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics
Print ISBN: 978-3-319-67674-6

Electronic ISBN: 978-3-319-67675-3

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-67675-3_8

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