Image segmentation is crucial for high-level vision tasks such as object detection and recognition. As in the classic models of Geman-Geman and Mumford-Shah, the complexity and challenge in modeling and computing segmentation are mainly rooted in its innate free-boundary nature. The level-set method of Osher and Sethian has provided a powerful tool for computing segmentation.

In this talk, we will present our recent alternative efforts in employing the diffuse-interface method in Mathematical Material Science to model, analyze, and compute image segmentation. Two novel models will be specifically addressed: the sine-sinc multiphase Modica-Mortola model, and a stochastic-variational model for soft (or fuzzy) image segmentation. The former is a joint work with Prof. Sung-Ha Kang and Dr. Yoon-Mo Jung.