PC-GAU: PCA Basis of Scattered Gaussians for Shape Matching via Functional Maps

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dc.contributor.authorColombo, Micheleen_US
dc.contributor.authorBoracchi, Giacomoen_US
dc.contributor.authorMelzi, Simoneen_US
dc.contributor.editorCabiddu, Danielaen_US
dc.contributor.editorSchneider, Teseoen_US
dc.contributor.editorAllegra, Darioen_US
dc.contributor.editorCatalano, Chiara Evaen_US
dc.contributor.editorCherchi, Gianmarcoen_US
dc.contributor.editorScateni, Riccardoen_US
dc.date.accessioned2022-11-08T11:44:42Z
dc.date.available2022-11-08T11:44:42Z
dc.date.issued2022
dc.description.abstractShape matching is a central problem in geometry processing applications, ranging from texture transfer to statistical shape analysis. The functional maps framework provides a compact representation of correspondences between discrete surfaces, which is then converted into point-wise maps required by real-world applications. The vast majority of methods based on functional maps involve the eigenfunctions of the Laplace-Beltrami Operator (LB) as the functional basis. A primary drawback of the LB basis is that its energy does not uniformly cover the surface. This fact gives rise to regions where the estimated correspondences are inaccurate, typically at tiny parts and protrusions. For this reason, state-of-the-art procedures to convert the functional maps (represented in the LB basis) into point-wise correspondences are often error-prone. We propose PCGAU, a new functional basis whose energy spreads on the whole shape more evenly than LB. As such, PC-GAU can replace the LB basis in existing shape matching pipelines. PC-GAU consists of the principal vectors obtained by applying Principal Component Analysis (PCA) to a dictionary of sparse Gaussian functions scattered on the surfaces. Through experimental evaluation of established benchmarks, we show that our basis produces more accurate point-wise maps —- compared to LB - when employed in the same shape-matching pipeline.en_US
dc.description.sectionheadersGeometry Processing
dc.description.seriesinformationSmart Tools and Applications in Graphics - Eurographics Italian Chapter Conference
dc.identifier.doi10.2312/stag.20221253
dc.identifier.isbn978-3-03868-191-5
dc.identifier.issn2617-4855
dc.identifier.pages29-39
dc.identifier.pages11 pages
dc.identifier.urihttps://doi.org/10.2312/stag.20221253
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/stag20221253
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies -> Shape analysis; Theory of computation -> Computational geometry; Mathematics of computing -> Functional analysis
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.subjectTheory of computation
dc.subjectComputational geometry
dc.subjectMathematics of computing
dc.subjectFunctional analysis
dc.titlePC-GAU: PCA Basis of Scattered Gaussians for Shape Matching via Functional Mapsen_US
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Italian Chapter Conference 2022 - Smart Tools and Apps in Graphics