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.
Bibliographical noteFunding 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.
© 2019 Elsevier Ltd
- 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