A Parametric Analysis of Discrete Hamiltonian Functional Maps

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dc.contributor.authorPostolache, Emilianen_US
dc.contributor.authorFumero, Marcoen_US
dc.contributor.authorCosmo, Lucaen_US
dc.contributor.authorRodolĂ , Emanueleen_US
dc.contributor.editorJacobson, Alec and Huang, Qixingen_US
dc.date.accessioned2020-07-05T13:26:06Z
dc.date.available2020-07-05T13:26:06Z
dc.date.issued2020
dc.description.abstractIn this paper we develop an in-depth theoretical investigation of the discrete Hamiltonian eigenbasis, which remains quite unexplored in the geometry processing community. This choice is supported by the fact that Dirichlet eigenfunctions can be equivalently computed by defining a Hamiltonian operator, whose potential energy and localization region can be controlled with ease. We vary with continuity the potential energy and study the relationship between the Dirichlet Laplacian and the Hamiltonian eigenbases with the functional map formalism. We develop a global analysis to capture the asymptotic behavior of the eigenpairs. We then focus on their local interactions, namely the veering patterns that arise between proximal eigenvalues. Armed with this knowledge, we are able to track the eigenfunctions in all possible configurations, shedding light on the nature of the functional maps. We exploit the Hamiltonian-Dirichlet connection in a partial shape matching problem, obtaining state of the art results, and provide directions where our theoretical findings could be applied in future research.en_US
dc.description.number5
dc.description.sectionheadersDeformation
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume39
dc.identifier.doi10.1111/cgf.14072
dc.identifier.issn1467-8659
dc.identifier.pages103-118
dc.identifier.urihttps://doi.org/10.1111/cgf.14072
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14072
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectComputing methodologies
dc.subjectSpectral methods
dc.subjectShape analysis
dc.titleA Parametric Analysis of Discrete Hamiltonian Functional Mapsen_US
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