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Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis
Author(s) -
Kirgo Maxime,
Melzi Simone,
Patanè Giuseppe,
Rodolà Emanuele,
Ovsjanikov Maks
Publication year - 2021
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.14180
Subject(s) - wavelet , kernel (algebra) , eigenfunction , heat kernel , heat kernel signature , computation , computer science , algorithm , basis function , laplace transform , mathematics , artificial intelligence , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , physics , active shape model , quantum mechanics , segmentation
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 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.