Laplacian Spectral Kernels and Distances for Geometry Processing and Shape Analysis

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dc.contributor.authorPatané, Giuseppeen_US
dc.contributor.editorJoaquim Madeira and Gustavo Patowen_US
dc.date.accessioned2016-04-26T08:03:55Z
dc.date.available2016-04-26T08:03:55Z
dc.date.issued2016en_US
dc.description.abstractIn geometry processing and shape analysis, several applications have been addressed through the properties of the spectral kernels and distances, such as commute-time, biharmonic, diffusion, and wave distances. Our survey is intended to provide a background on the properties, discretization, computation, and main applications of the Laplace-Beltrami operator, the associated differential equations (e.g., harmonic equation, Laplacian eigenproblem, diffusion and wave equations), Laplacian spectral kernels and distances (e.g., commute-time, biharmonic, wave, diffusion distances). While previous work has been focused mainly on specific applications of the aforementioned topics on surface meshes, we propose a general approach that allows us to review Laplacian kernels and distances on surfaces and volumes, and for any choice of the Laplacian weights. All the reviewed numerical schemes for the computation of the Laplacian spectral kernels and distances are discussed in terms of robustness, approximation accuracy, and computational cost, thus supporting the reader in the selection of the most appropriate method with respect to shape representation, computational resources, and target application.en_US
dc.description.documenttypestar
dc.description.number2en_US
dc.description.sectionheadersState of the Art Reportsen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12866en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages599-624en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12866en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.3 [Numerical Analysis]en_US
dc.subjectApproximation/Image Generationen_US
dc.subjectSpecial function approximationsen_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modeling/Curveen_US
dc.subjectsurfaceen_US
dc.subjectsoliden_US
dc.subjectand object representationsen_US
dc.subjectI.3.6 [Computer Graphics]en_US
dc.subjectMethodology and Techniquesen_US
dc.subjectKeywordsen_US
dc.subjectLaplaceen_US
dc.subjectBeltrami operatoren_US
dc.subjectLaplacian spectrumen_US
dc.subjectharmonic equationen_US
dc.subjectLaplacian eigenmproblemen_US
dc.subjectheat equationen_US
dc.subjectdiffusion geometryen_US
dc.subjectLaplacian spectral distance and kernelsen_US
dc.subjectspectral geometry processingen_US
dc.subjectshape analysisen_US
dc.subjectnumerical analysis.en_US
dc.titleLaplacian Spectral Kernels and Distances for Geometry Processing and Shape Analysisen_US
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