Handle URI:
http://hdl.handle.net/10754/597649
Title:
Bayesian data assimilation in shape registration
Authors:
Cotter, C J; Cotter, S L; Vialard, F-X
Abstract:
In this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well-defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterization in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterization vector field ν, informed by regularity results about the forward model. Having done this, we illustrate how maximum likelihood estimators can be used to find regions of high posterior density, but also how we can apply recently developed Markov chain Monte Carlo methods on function spaces to characterize the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem. © 2013 IOP Publishing Ltd.
Citation:
Cotter CJ, Cotter SL, Vialard F-X (2013) Bayesian data assimilation in shape registration. Inverse Problems 29: 045011. Available: http://dx.doi.org/10.1088/0266-5611/29/4/045011.
Publisher:
IOP Publishing
Journal:
Inverse Problems
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
28-Mar-2013
DOI:
10.1088/0266-5611/29/4/045011
Type:
Article
ISSN:
0266-5611; 1361-6420
Sponsors:
The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 239870. This publication was based on work supported in part by award no KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), and the results were obtained using the Imperial College High Performance Computing Centre cluster. SLC would also like to thank St Cross College Oxford for support via a Junior Research Fellowship.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCotter, C Jen
dc.contributor.authorCotter, S Len
dc.contributor.authorVialard, F-Xen
dc.date.accessioned2016-02-25T12:43:42Zen
dc.date.available2016-02-25T12:43:42Zen
dc.date.issued2013-03-28en
dc.identifier.citationCotter CJ, Cotter SL, Vialard F-X (2013) Bayesian data assimilation in shape registration. Inverse Problems 29: 045011. Available: http://dx.doi.org/10.1088/0266-5611/29/4/045011.en
dc.identifier.issn0266-5611en
dc.identifier.issn1361-6420en
dc.identifier.doi10.1088/0266-5611/29/4/045011en
dc.identifier.urihttp://hdl.handle.net/10754/597649en
dc.description.abstractIn this paper we apply a Bayesian framework to the problem of geodesic curve matching. Given a template curve, the geodesic equations provide a mapping from initial conditions for the conjugate momentum onto topologically equivalent shapes. Here, we aim to recover the well-defined posterior distribution on the initial momentum which gives rise to observed points on the target curve; this is achieved by explicitly including a reparameterization in the formulation. Appropriate priors are chosen for the functions which together determine this field and the positions of the observation points, the initial momentum p0 and the reparameterization vector field ν, informed by regularity results about the forward model. Having done this, we illustrate how maximum likelihood estimators can be used to find regions of high posterior density, but also how we can apply recently developed Markov chain Monte Carlo methods on function spaces to characterize the whole of the posterior density. These illustrative examples also include scenarios where the posterior distribution is multimodal and irregular, leading us to the conclusion that knowledge of a state of global maximal posterior density does not always give us the whole picture, and full posterior sampling can give better quantification of likely states and the overall uncertainty inherent in the problem. © 2013 IOP Publishing Ltd.en
dc.description.sponsorshipThe research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 239870. This publication was based on work supported in part by award no KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST), and the results were obtained using the Imperial College High Performance Computing Centre cluster. SLC would also like to thank St Cross College Oxford for support via a Junior Research Fellowship.en
dc.publisherIOP Publishingen
dc.titleBayesian data assimilation in shape registrationen
dc.typeArticleen
dc.identifier.journalInverse Problemsen
dc.contributor.institutionImperial College London, London, United Kingdomen
dc.contributor.institutionUniversity of Manchester, Manchester, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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