A new variational model for shape graph registration with partial matching constraints Article Swipe
Yashil Sukurdeep
,
Martin Bauer
,
Nicolas Charon
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2105.00678
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2105.00678
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and topological inconsistencies. Weighted shape graphs are the union of an arbitrary number of component curves in Euclidean space with potential connectivity constraints between some of their boundary points, together with a weight function defined on each component curve. The framework of higher order invariant Sobolev metrics is particularly well suited for constructing notions of distances and geodesics between unparametrized curves. The main difficulty in adapting this framework to the setting of shape graphs is the absence of topological consistency, which typically results in an inadequate search for an exact matching between two shape graphs. We overcome this hurdle by defining an inexact variational formulation of the matching problem between (weighted) shape graphs of any underlying topology, relying on the convenient measure representation given by varifolds to relax the exact matching constraint. We then prove the existence of minimizers to this variational problem when we choose Sobolev metrics of sufficient regularity and a total variation (TV) regularization on the weight function. We propose a numerical optimization approach which adapts the smoothed fast iterative shrinkage-thresholding (SFISTA) algorithm to deal with TV norm minimization and allows us to reduce the matching problem to solving a sequence of smooth unconstrained minimization problems. We finally illustrate the capabilities of our new model through several examples showcasing its ability to tackle partially observed and topologically varying data.
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- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.48550/arxiv.2105.00678
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
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- DOI
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https://doi.org/10.48550/arxiv.2105.00678Digital Object Identifier
- Title
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A new variational model for shape graph registration with partial matching constraintsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-05-03Full publication date if available
- Authors
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Yashil Sukurdeep, Martin Bauer, Nicolas CharonList of authors in order
- Landing page
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https://doi.org/10.48550/arxiv.2105.00678Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://doi.org/10.48550/arxiv.2105.00678Direct OA link when available
- Concepts
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Mathematics, Geodesic, Mathematical optimization, Matching (statistics), Algorithm, Topology (electrical circuits), Mathematical analysis, Combinatorics, StatisticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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