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Bridge simulation and metric estimation on landmark manifolds

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Title: Bridge simulation and metric estimation on landmark manifolds
Authors: Sommer, S
Arnaudon, A
Kuhnel, L
Joshi, S
Item Type: Conference Paper
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.
Issue Date: 23-May-2017
Date of Acceptance: 9-Feb-2017
URI: http://hdl.handle.net/10044/1/52732
DOI: https://dx.doi.org/10.1007/978-3-319-59050-9_45
ISSN: 0302-9743
Publisher: Springer Verlag
Start Page: 571
End Page: 582
Journal / Book Title: Lecture Notes in Computer Science
Volume: 10265
Copyright Statement: © Springer International Publishing AG 2017. The final publication is available at Springer via https://link.springer.com/chapter/10.1007%2F978-3-319-59050-9_45
Conference Name: Information Processing in Medical Imaging 2017
Keywords: cs.CV
08 Information And Computing Sciences
Artificial Intelligence & Image Processing
Start Date: 2017-06-25
Finish Date: 2017-06-30
Conference Place: Boone, NC, USA
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences