Learning Spectral Unions of Partial Deformable 3D Shapes

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dc.contributor.authorMoschella, Lucaen_US
dc.contributor.authorMelzi, Simoneen_US
dc.contributor.authorCosmo, Lucaen_US
dc.contributor.authorMaggioli, Filippoen_US
dc.contributor.authorLitany, Oren_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.authorGuibas, Leonidasen_US
dc.contributor.authorRodolĂ , Emanueleen_US
dc.contributor.editorChaine, Raphaëlleen_US
dc.contributor.editorKim, Min H.en_US
dc.date.accessioned2022-04-22T06:29:17Z
dc.date.available2022-04-22T06:29:17Z
dc.date.issued2022
dc.description.abstractSpectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.en_US
dc.description.number2
dc.description.sectionheadersTopology
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume41
dc.identifier.doi10.1111/cgf.14483
dc.identifier.issn1467-8659
dc.identifier.pages407-417
dc.identifier.pages11 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14483
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14483
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.titleLearning Spectral Unions of Partial Deformable 3D Shapesen_US
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