Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis

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dc.contributor.authorKirgo, Maximeen_US
dc.contributor.authorMelzi, Simoneen_US
dc.contributor.authorPatanè, Giuseppeen_US
dc.contributor.authorRodolà, Emanueleen_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.editorBenes, Bedrich and Hauser, Helwigen_US
dc.date.accessioned2021-02-27T19:02:29Z
dc.date.available2021-02-27T19:02:29Z
dc.date.issued2021
dc.description.abstractIn this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well‐established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi‐scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high‐frequency details on a shape, the proposed method reconstructs and transfers ‐functions more accurately than the Laplace‐Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large‐scale shape matching. An extensive comparison to the state‐of‐the‐art shows that it is comparable in performance, while both simpler and much faster than competing approaches.en_US
dc.description.number1
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume40
dc.identifier.doi10.1111/cgf.14180
dc.identifier.issn1467-8659
dc.identifier.pages165-179
dc.identifier.urihttps://doi.org/10.1111/cgf.14180
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14180
dc.publisher© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltden_US
dc.subject3D shape matching
dc.subjectmodelling
dc.subjectcomputational geometry
dc.subjectmodelling
dc.titleWavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysisen_US
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