Cellular Automata based Level Set Method for Image Segmentation

Abstract

Level set equation can be substituted by the convection-diffusion equation. But the two equations are very difficult to solve. When both of the equations become non-differentiable for certain initial data, appropriate weak solutions must be built. This may undermine the quality of the segmentation. In recent years the Cellular Automata (CA), for example the lattice Boltzmann method (LBM), has attracted much attention as an alternative approach for solving partial differential equations. CA is an inherent discrete system and do not require the differentiability of the initial condition. For this reason, CA is very appropriate for the numerical solution of the partial differential equation. In this paper, the LBM is used to solve the convection-diffusion equation. The experiments show that the LBM can solve the advection equation accurately and stably, and the segmentation is good.