Enhanced Level Set Method with Chan-Vese Model Evolution

This document presents an enhanced level set method, a widely adopted numerical technique for simulating phase transition phenomena in physical systems. The implementation employs the Chan-Vese (C_V) model evolution, which provides superior capability for modeling multi-phase processes. This approach finds extensive applications across physics, chemistry, biology, and related disciplines. The method typically involves solving partial differential equations through finite difference schemes, where key functions manage interface evolution using curvature-dependent speed functions and region-based energy minimization. Through this enhanced methodology, researchers can gain deeper insights into the fundamental nature of phase transition behaviors, while obtaining more precise computational tools for advanced scientific investigations. The algorithm implementation often includes regularization terms to maintain stable curve evolution and prevent re-initialization issues common in traditional level set methods.