  This paper presents an efficient approach to image segmentation that
approximates the piecewise-smooth (PS) functional in [12] with explicit
solutions. By rendering some rational constraints on the initial conditions and
the final solutions of the PS functional, we propose two novel formulations
which can be approximated to be the explicit solutions of the evolution partial
differential equations (PDEs) of the PS model, in which only one PDE needs to
be solved efficiently. Furthermore, an energy term that regularizes the level
set function to be a signed distance function is incorporated into our
evolution formulation, and the time-consuming re-initialization is avoided.
Experiments on synthetic and real images show that our method is more efficient
than both the PS model and the local binary fitting (LBF) model [4], while
having similar segmentation accuracy as the LBF model.
