Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis
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Date
2021
Journal Title
Journal ISSN
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Publisher
© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd
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 ‐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.
Description
@article{10.1111:cgf.14180,
journal = {Computer Graphics Forum},
title = {{Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis}},
author = {Kirgo, Maxime and Melzi, Simone and Patanè, Giuseppe and Rodolà, Emanuele and Ovsjanikov, Maks},
year = {2021},
publisher = {© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14180}
}