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

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 multiscale 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 highfrequency details on a shape, the proposed method reconstructs and transfers δ-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. CCS Concepts • Computing methodologies → Shape analysis; • Theory of computation → Computational geometry; • Mathematics of computing → Functional analysis;
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https://hal-polytechnique.archives-ouvertes.fr/hal-03028937
Contributor : Maxime Kirgo <>
Submitted on : Friday, November 27, 2020 - 6:34:51 PM
Last modification on : Saturday, December 5, 2020 - 3:29:11 AM

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  • HAL Id : hal-03028937, version 1

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Maxime Kirgo, S Melzi, G Patanè, E Rodolà, M Ovsjanikov. Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis. Computer Graphics Forum, Wiley, In press. ⟨hal-03028937⟩

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