Fast and Accurate Smoothing Method Using A Modified Allen–Cahn Equation

Jian Wang; Yibao Li; Yongho Choi; Chaeyoung Lee; Junseok Kim

doi:10.1016/j.cad.2019.102804

Fast and Accurate Smoothing Method Using A Modified Allen–Cahn Equation

Jian Wang, Yibao Li, Yongho Choi, Chaeyoung Lee, Junseok Kim

Department of Mathematics

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

9 Citations (Scopus)

Abstract

This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2D shapes and volume smoothing of 3D shapes. The modified AC equation has a good smoothing dynamics and it is coupled with a fidelity term. The fidelity term forces the solution of the equation to be a close approximation to the original data. We use a hybrid explicit finite difference method to solve the equation. Therefore, we do not have any restriction on the shape of the computational domains. Several numerical tests for both the curve and surface smoothing problems are performed to demonstrate the robustness and efficiency of the proposed method. In particular, the proposed algorithm is useful for the 3D printing applications.

Original language	English
Article number	102804
Journal	CAD Computer Aided Design
Volume	120
DOIs	https://doi.org/10.1016/j.cad.2019.102804
Publication status	Published - 2020 Mar

Bibliographical note

Funding Information:
The first author (Jian Wang) was supported by the China Scholarship Council ( 201808260026 ). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416 , No. 11631012 ) and by the China Postdoctoral Science Foundation (No. 2018M640968 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), Republic of Korea funded by the Ministry of Education ( NRF-2016R1D1A1B03933243 ). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

Allen–Cahn equation
Explicit numerical method
Image smoothing

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

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10.1016/j.cad.2019.102804

Cite this

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title = "Fast and Accurate Smoothing Method Using A Modified Allen–Cahn Equation",

abstract = "This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2D shapes and volume smoothing of 3D shapes. The modified AC equation has a good smoothing dynamics and it is coupled with a fidelity term. The fidelity term forces the solution of the equation to be a close approximation to the original data. We use a hybrid explicit finite difference method to solve the equation. Therefore, we do not have any restriction on the shape of the computational domains. Several numerical tests for both the curve and surface smoothing problems are performed to demonstrate the robustness and efficiency of the proposed method. In particular, the proposed algorithm is useful for the 3D printing applications.",

keywords = "Allen–Cahn equation, Explicit numerical method, Image smoothing",

author = "Jian Wang and Yibao Li and Yongho Choi and Chaeyoung Lee and Junseok Kim",

note = "Funding Information: The first author (Jian Wang) was supported by the China Scholarship Council ( 201808260026 ). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416 , No. 11631012 ) and by the China Postdoctoral Science Foundation (No. 2018M640968 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), Republic of Korea funded by the Ministry of Education ( NRF-2016R1D1A1B03933243 ). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper. Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2020",

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doi = "10.1016/j.cad.2019.102804",

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AU - Choi, Yongho

AU - Lee, Chaeyoung

AU - Kim, Junseok

N1 - Funding Information: The first author (Jian Wang) was supported by the China Scholarship Council ( 201808260026 ). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416 , No. 11631012 ) and by the China Postdoctoral Science Foundation (No. 2018M640968 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF), Republic of Korea funded by the Ministry of Education ( NRF-2016R1D1A1B03933243 ). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper. Publisher Copyright: © 2019 Elsevier Ltd

PY - 2020/3

Y1 - 2020/3

N2 - This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2D shapes and volume smoothing of 3D shapes. The modified AC equation has a good smoothing dynamics and it is coupled with a fidelity term. The fidelity term forces the solution of the equation to be a close approximation to the original data. We use a hybrid explicit finite difference method to solve the equation. Therefore, we do not have any restriction on the shape of the computational domains. Several numerical tests for both the curve and surface smoothing problems are performed to demonstrate the robustness and efficiency of the proposed method. In particular, the proposed algorithm is useful for the 3D printing applications.

AB - This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2D shapes and volume smoothing of 3D shapes. The modified AC equation has a good smoothing dynamics and it is coupled with a fidelity term. The fidelity term forces the solution of the equation to be a close approximation to the original data. We use a hybrid explicit finite difference method to solve the equation. Therefore, we do not have any restriction on the shape of the computational domains. Several numerical tests for both the curve and surface smoothing problems are performed to demonstrate the robustness and efficiency of the proposed method. In particular, the proposed algorithm is useful for the 3D printing applications.

KW - Allen–Cahn equation

KW - Explicit numerical method

KW - Image smoothing

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ER -

Fast and Accurate Smoothing Method Using A Modified Allen–Cahn Equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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