research-article

Parameterization for polynomial curve approximation via residual deep neural networks

Authors:

Bert JüttlerAuthors Info & Claims

Volume 85, Issue C

https://doi.org/10.1016/j.cagd.2021.101977

Published: 01 February 2021 Publication History

Abstract

Finding the optimal parameterization for fitting a given sequence of data points with a parametric curve is a challenging problem that is equivalent to solving a highly non-linear system of equations. In this work, we propose the use of a residual neural network to approximate the function that assigns to a sequence of data points a suitable parameterization for fitting a polynomial curve of a fixed degree. Our model takes as an input a small fixed number of data points and the generalization to arbitrary data sequences is obtained by performing multiple evaluations. We show that the approach compares favorably to classical methods in a number of numerical experiments that include the parameterization of polynomial as well as non-polynomial data.

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Cited By

Wang HZhang F(2024)Computing nodes for plane data points by constructing cubic polynomial with constraintsComputer Aided Geometric Design10.1016/j.cagd.2024.102308111:COnline publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1016/j.cagd.2024.102308
Zhan ZWang WChen F(2024)Simultaneous Boundary and Interior Parameterization of Planar Domains Via Deep LearningComputer-Aided Design10.1016/j.cad.2023.103621166:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103621
Barzegar Khalilsaraei SKomar AZheng JAugsdörfer U(2024)InceptCurves: curve reconstruction using an inception networkThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-024-03477-140:7(4805-4815)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s00371-024-03477-1

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Parameterization for polynomial curve approximation via residual deep neural networks

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Published In

cover image Computer Aided Geometric Design

Computer Aided Geometric Design Volume 85, Issue C

Feb 2021

127 pages

ISSN:0167-8396

Issue’s Table of Contents

Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 February 2021

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Cited By

Wang HZhang F(2024)Computing nodes for plane data points by constructing cubic polynomial with constraintsComputer Aided Geometric Design10.1016/j.cagd.2024.102308111:COnline publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1016/j.cagd.2024.102308
Zhan ZWang WChen F(2024)Simultaneous Boundary and Interior Parameterization of Planar Domains Via Deep LearningComputer-Aided Design10.1016/j.cad.2023.103621166:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103621
Barzegar Khalilsaraei SKomar AZheng JAugsdörfer U(2024)InceptCurves: curve reconstruction using an inception networkThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-024-03477-140:7(4805-4815)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s00371-024-03477-1
Zhu ZIglesias AYou LZhang J(2022)A Review of 3D Point Clouds Parameterization MethodsComputational Science – ICCS 202210.1007/978-3-031-08757-8_57(690-703)Online publication date: 21-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-08757-8_57

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