On Variational and PDE-Based Methods for Accurate Distance Function Estimation

P.-A. Fayolle; A. G. Belyaev

doi:10.1134/S0965542519120066

On Variational and PDE-Based Methods for Accurate Distance Function Estimation

P.-A. Fayolle^*, A. G. Belyaev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and p-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.

Original language	English
Pages (from-to)	2009-2016
Number of pages	8
Journal	Computational Mathematics and Mathematical Physics
Volume	59
Issue number	12
DOIs	https://doi.org/10.1134/S0965542519120066
Publication status	Published - Dec 2019

Keywords

distance function
p-Laplacian
variational methods

ASJC Scopus subject areas

Computational Mathematics

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10.1134/S0965542519120066

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title = "On Variational and PDE-Based Methods for Accurate Distance Function Estimation",

abstract = "A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and p-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.",

keywords = "distance function, p-Laplacian, variational methods",

author = "P.-A. Fayolle and Belyaev, {A. G.}",

note = "Funding Information: The Gargoyle mesh model is courtesy of AIM@SHAPE and the Lucy mesh model is courtesy of the Stanford Graphics Laboratory. Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

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doi = "10.1134/S0965542519120066",

language = "English",

volume = "59",

pages = "2009--2016",

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T1 - On Variational and PDE-Based Methods for Accurate Distance Function Estimation

AU - Fayolle, P.-A.

AU - Belyaev, A. G.

N1 - Funding Information: The Gargoyle mesh model is courtesy of AIM@SHAPE and the Lucy mesh model is courtesy of the Stanford Graphics Laboratory. Publisher Copyright: © 2019, Pleiades Publishing, Ltd.

PY - 2019/12

Y1 - 2019/12

N2 - A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and p-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.

AB - A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the problem can be efficiently solved by the alternating direction method of multipliers. Links between this problem and p-Laplacian diffusion are established and studied. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments.

KW - distance function

KW - p-Laplacian

KW - variational methods

UR - http://www.scopus.com/inward/record.url?scp=85079715420&partnerID=8YFLogxK

U2 - 10.1134/S0965542519120066

DO - 10.1134/S0965542519120066

M3 - Article

AN - SCOPUS:85079715420

SN - 0965-5425

VL - 59

SP - 2009

EP - 2016

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

IS - 12

ER -

On Variational and PDE-Based Methods for Accurate Distance Function Estimation

Abstract

Keywords

ASJC Scopus subject areas

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