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.

Maggioli, F., Melzi, S., Ovsjanikov, M., Bronstein, M., Rodolà, E. (2021). Orthogonalized Fourier Polynomials for Signal Approximation and Transfer. COMPUTER GRAPHICS FORUM, 40(2), 435-447 [10.1111/cgf.142645].

Orthogonalized Fourier Polynomials for Signal Approximation and Transfer

Melzi, S.;
2021

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.
Articolo in rivista - Articolo scientifico
CCS Concepts; Computing methodologies → Shape analysis; Mathematics of computing → Functional analysis; Theory of computation → Computational geometry;
English
435
447
13
Maggioli, F., Melzi, S., Ovsjanikov, M., Bronstein, M., Rodolà, E. (2021). Orthogonalized Fourier Polynomials for Signal Approximation and Transfer. COMPUTER GRAPHICS FORUM, 40(2), 435-447 [10.1111/cgf.142645].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/350556
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