Fast and Efficient Numerical Finite Difference Method for Multiphase Image Segmentation. (20th November 2021)

• Record Type: Journal Article
• Authors: Li, Yibao; Yoon, Sungha; Wang, Jian; Park, Jintae; Kim, Sangkwon; Lee, Chaeyoung; Kim, Hyundong; Kim, Junseok
• Other Names: Gálvez Akemi Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-11-20
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/2414209
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We present a simple numerical solution algorithm for a gradient flow for the Modica–Mortola functional and numerically investigate its dynamics. The proposed numerical algorithm involves both the operator splitting and the explicit Euler methods. A time step formula is derived from the stability analysis, and the goodness of fit of transition width is tested. We perform various numerical experiments to investigate the property of the gradient flow equation, to verify the characteristics of our method in the image segmentation application, and to analyze the effect of parameters. In particular, we propose an initialization process based on target objects. Furthermore, we conduct comparison tests in order to check the performance of our proposed method.