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.
Bibliographical noteFunding Information:
Yibao Li was supported by the National Natural Science Foundation of China (nos. 11601416 and 11631012). Junseok Kim was supported by the National Research Foundation (NRF), Korea, under project no. BK21 FOUR.
© 2021 Yibao Li et al.
ASJC Scopus subject areas
- General Mathematics
- General Engineering