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.

Kirgo, M., Melzi, S., Patane, G., Rodolà, E., Ovsjanikov, M. (2021). Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis. COMPUTER GRAPHICS FORUM, 40(1 (February 2021)), 165-179 [10.1111/cgf.14180].

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

Melzi S.
;
2021

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.
Articolo in rivista - Articolo scientifico
3D shape matching; computational geometry; modelling; modelling;
English
165
179
15
Kirgo, M., Melzi, S., Patane, G., Rodolà, E., Ovsjanikov, M. (2021). Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis. COMPUTER GRAPHICS FORUM, 40(1 (February 2021)), 165-179 [10.1111/cgf.14180].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/350550
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