Structured Regularization of Functional Map Computations

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dc.contributor.authorRen, Jingen_US
dc.contributor.authorPanine, Mikhailen_US
dc.contributor.authorWonka, Peteren_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.editorBommes, David and Huang, Huien_US
dc.date.accessioned2019-07-11T06:19:07Z
dc.date.available2019-07-11T06:19:07Z
dc.date.issued2019
dc.description.abstractWe consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace-Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well-justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one-parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly-used refinement techniques.en_US
dc.description.number5
dc.description.sectionheadersFunctional Maps
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume38
dc.identifier.doi10.1111/cgf.13788
dc.identifier.issn1467-8659
dc.identifier.pages39-53
dc.identifier.urihttps://doi.org/10.1111/cgf.13788
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13788
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.titleStructured Regularization of Functional Map Computationsen_US
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