Orthogonalized Fourier Polynomials for Signal Approximation and Transfer

F. Maggioli, S. Melzi, M. Ovsjanikov, M. M. Bronstein, E. Rodolà

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)435-447
Number of pages13
JournalComputer Graphics Forum
Volume40
Issue number2
DOIs
StatePublished - May 2021
Externally publishedYes

Funding

FundersFunder number
Horizon 2020 Framework Programme802554
European Research Council758800
Agence Nationale de la Recherche

    Keywords

    • CCS Concepts
    • Computing methodologies → Shape analysis
    • Mathematics of computing → Functional analysis
    • Theory of computation → Computational geometry

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