A modified Chan–Vese model and its theoretical proof

We present a modified Chan–Vese functional and give its theoretical proof. By using the geometric heat flow method to all the Euler–Lagrange equations, a system of evolution equations in level set formulation is derived. We study the existence of solution to this system by Schauder fixed point theorem and the implicit function theorem in Banach space. This variational formulation can detect interior and exterior boundaries of desired object(s) in color images.