Level set-based bimodal segmentation with stationary global minimum

In this paper, we propose a new level set-based partial differential equation (PDE) for the purpose of bimodal segmentation. The PDE is derived from an energy functional which is a modified version of the fitting term of the Chan-Vese model. The energy functional is designed to obtain a stationary global minimum, i.e., the level set function which evolves by the Euler-Lagrange equation of the energy functional has a unique convergence state. The existence of a global minimum makes the algorithm invariant to the initialization of the level set function, whereas the existence of a convergence state makes it possible to set a termination criterion on the algorithm. Furthermore, since the level set function converges to one of the two fixed values which are determined by the amount of the shifting of the Heaviside functions, an initialization of the level set function close to those values can result in a fast convergence.