Abstract: In this talk, we will present a novel iterative convolution-thresholding method (ICTM) that is applicable to a wide range of variational models for image segmentation and topology optimization for fluid.  A variational model usually minimizes an energy functional consisting of a fidelity term and a regularization term. In the ICTM, the interface is implicitly represented by their characteristic functions and the regularized term is approximated by a functional of characteristic functions in terms of heat kernel convolution. This allows us to design an iterative convolution-thresholding method to minimize the approximate energy. The method is simple, efficient and enjoys the energy-decaying property. Numerical experiments show that the method is easy to implement, robust and applicable to a wide class of models. If time permits, we will also discuss data-driven approaches for interface motions and some future work.