Stochastic development regression on non-linear manifolds

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

Line Kühnel, Stefan Horst Sommer

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes.

OriginalsprogEngelsk
TitelInformation Processing in Medical Imaging : 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings
Antal sider12
ForlagSpringer
Publikationsdato2017
Sider53-64
ISBN (Trykt)978-3-319-59049-3
ISBN (Elektronisk)978-3-319-59050-9
DOI
StatusUdgivet - 2017
Begivenhed25th International Conference on Information Processing in Medical Imaging - Boone, USA
Varighed: 25 jun. 201730 jun. 2017
Konferencens nummer: 25

Konference

Konference25th International Conference on Information Processing in Medical Imaging
Nummer25
LandUSA
ByBoone
Periode25/06/201730/06/2017
NavnLecture notes in computer science
Vol/bind10265
ISSN0302-9743

Links

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