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

Maxime Kirgo, Simone Melzi, Giuseppe Patanè, Emanuele Rodolà, Maks Ovsjanikov

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In 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 (Formula presented.) -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.
Original languageEnglish (US)
Pages (from-to)165-179
Number of pages15
JournalComputer Graphics Forum
Volume40
Issue number1
DOIs
StatePublished - Nov 3 2020
Externally publishedYes

ASJC Scopus subject areas

  • Computer Networks and Communications

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