Fast and Accurate Smoothing Method Using A Modified Allen–Cahn Equation. (March 2020)

• Record Type: Journal Article
• Authors: Wang, Jian; Li, Yibao; Choi, Yongho; Lee, Chaeyoung; Kim, Junseok
• Is Part Of: Computer aided design. Volume 120(2020)
• Publication Date: 2020-03
• Subjects: Allen–Cahn equation -- Image smoothing -- Explicit numerical method; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2019.102804
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2 D shapes and volume smoothing of 3 D 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. Graphical abstract: Highlights: We present a fast and accurate image smoothing using the AC equation. The fidelity term helps to avoid volume shrinkage or shape distortion. The results demonstrate that the proposed algorithm is fast and efficient. The proposed algorithm is useful for the 3D printing applications.