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

Bibliographical note

KAUST Repository Item: Exported on 2022-06-14
Acknowledged KAUST grant number(s): CRG-2017-3426
Acknowledgements: Parts of this work were supported by the KAUST OSR Award No. CRG-2017-3426, the ERC Starting Grant No. 758800 (EXPROTEA), ANR AI Chair AIGRETTE, and the ERC Starting Grant No. 802554 (SPECGEO).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Computer Networks and Communications

Fingerprint

Dive into the research topics of 'Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis'. Together they form a unique fingerprint.

Cite this