Orthogonalized Fourier Polynomials for Signal Approximation and Transfer
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We propose a novel approach for the approximation and transfer of signals across 3D shapes. The proposed solution is based on taking pointwise polynomials of the Fourier-like Laplacian eigenbasis, which provides a compact and expressive representation for general signals defined on the surface. Key to our approach is the construction of a new orthonormal basis upon the set of these linearly dependent polynomials. We analyze the properties of this representation, and further provide a complete analysis of the involved parameters. Our technique results in accurate approximation and transfer of various families of signals between near-isometric and non-isometric shapes, even under poor initialization. Our experiments, showcased on a selection of downstream tasks such as filtering and detail transfer, show that our method is more robust to discretization artifacts, deformation and noise as compared to alternative approaches.
Description
@article{10.1111:cgf.142645,
journal = {Computer Graphics Forum},
title = {{Orthogonalized Fourier Polynomials for Signal Approximation and Transfer}},
author = {Maggioli, Filippo and Melzi, Simone and Ovsjanikov, Maks and Bronstein, Michael M. and RodolĂ , Emanuele},
year = {2021},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.142645}
}