Functional Maps Representation On Product Manifolds

dc.contributor.authorRodolà, E.en_US
dc.contributor.authorLähner, Z.en_US
dc.contributor.authorBronstein, A. M.en_US
dc.contributor.authorBronstein, M. M.en_US
dc.contributor.authorSolomon, J.en_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2019-03-17T09:57:07Z
dc.date.available2019-03-17T09:57:07Z
dc.date.issued2019
dc.description.abstractWe consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.en_US
dc.description.number1
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume38
dc.identifier.doi10.1111/cgf.13598
dc.identifier.issn1467-8659
dc.identifier.pages678-689
dc.identifier.urihttps://doi.org/10.1111/cgf.13598
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13598
dc.publisher© 2019 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectshape matching
dc.subjectfunctional maps
dc.subjectproduct manifolds
dc.subjectComputational Geometry and Object Modelling–Shape Analysis; 3D Shape Matching; Geometric Modelling
dc.titleFunctional Maps Representation On Product Manifoldsen_US
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