dc.date.accessioned | 2024-04-05T15:28:05Z | |
dc.date.created | 2023-09-28T18:22:12Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Celledoni, Elena Glöckner, Helge Riseth, Jørgen Nilsen Schmeding, Alexander . Deep neural networks on diffeomorphism groups for optimal shape reparametrization. BIT Numerical Mathematics. 2023, 63(4), 1-38 | |
dc.identifier.uri | http://hdl.handle.net/10852/110387 | |
dc.description.abstract | One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally demanding task, typically done by solving an optimization problem on the diffeomorphism group. In this paper, we propose an algorithm for constructing approximations of orientation preserving diffeomorphisms by composition of elementary diffeomorphisms. The algorithm is implemented using PyTorch, and is applicable for both unparametrized curves and surfaces. Moreover, we show universal approximation properties for the constructed architectures, and obtain bounds for the Lipschitz constants of the resulting diffeomorphisms. | |
dc.description.abstract | Deep neural networks on diffeomorphism groups for optimal shape reparametrization | |
dc.language | EN | |
dc.publisher | BMJ Publishing Group | |
dc.title | Deep neural networks on diffeomorphism groups for optimal shape reparametrization | |
dc.title.alternative | ENEngelskEnglishDeep neural networks on diffeomorphism groups for optimal shape reparametrization | |
dc.type | Journal article | |
dc.creator.author | Celledoni, Elena | |
dc.creator.author | Glöckner, Helge | |
dc.creator.author | Riseth, Jørgen Nilsen | |
dc.creator.author | Schmeding, Alexander | |
dc.date.embargoenddate | 2024-09-27 | |
cristin.unitcode | 185,15,13,45 | |
cristin.unitname | Differensiallikninger og beregningsorientert matematikk | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 2180057 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=BIT Numerical Mathematics&rft.volume=63&rft.spage=1&rft.date=2023 | |
dc.identifier.jtitle | BIT Numerical Mathematics | |
dc.identifier.volume | 63 | |
dc.identifier.issue | 4 | |
dc.identifier.doi | https://doi.org/10.1007/s10543-023-00989-5 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0006-3835 | |
dc.type.version | AcceptedVersion | |
cristin.articleid | 50 | |
dc.relation.project | EC/HEU/860124 | |
dc.relation.project | EPSRC/EP/R014604/1 | |