Scalable and Efficient Functional Map Computations on Dense Meshes

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dc.contributor.authorMagnet, Robinen_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.editorMyszkowski, Karolen_US
dc.contributor.editorNiessner, Matthiasen_US
dc.date.accessioned2023-05-03T06:09:32Z
dc.date.available2023-05-03T06:09:32Z
dc.date.issued2023
dc.description.abstractWe propose a new scalable version of the functional map pipeline that allows to efficiently compute correspondences between potentially very dense meshes. Unlike existing approaches that process dense meshes by relying on ad-hoc mesh simplification, we establish an integrated end-to-end pipeline with theoretical approximation analysis. In particular, our method overcomes the computational burden of both computing the basis, as well the functional and pointwise correspondence computation by approximating the functional spaces and the functional map itself. Errors in the approximations are controlled by theoretical upper bounds assessing the range of applicability of our pipeline.With this construction in hand, we propose a scalable practical algorithm and demonstrate results on dense meshes, which approximate those obtained by standard functional map algorithms at the fraction of the computation time. Moreover, our approach outperforms the standard acceleration procedures by a large margin, leading to accurate results even in challenging cases.en_US
dc.description.number2
dc.description.sectionheadersShape Correspondance
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume42
dc.identifier.doi10.1111/cgf.14746
dc.identifier.issn1467-8659
dc.identifier.pages89-101
dc.identifier.pages13 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14746
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14746
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectCCS Concepts: Computing methodologies -> Shape analysis; Theory of computation -> Computational geometry
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.subjectTheory of computation
dc.subjectComputational geometry
dc.titleScalable and Efficient Functional Map Computations on Dense Meshesen_US
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