一种基于扩散理论的水平集方程演化算法

摘要

The level set method has been widely applied to the field of image segmentation and Interface tracking.In order to keep the level set function close to signed distance function,we have to initialize the level set function periodically,which is actually contrary to the theory itself.We can get the level set function in a proper way without the initialization by bringing in diffusion theory,which can solve various problems in the process of the level set initialization, and adding diffusion term as well as using piecewise constant numerical method.successfully applying diffusion theory to level set method, the implementation procedure is both simple and stable by means of the finite difference method.The proposed method shows very good performance on boundary antileakage,and it can be readily extended to high dimensional level set method.%水平集方法已被广泛地应用于界面追踪和图像分割领域内。为了保证水平集函数演化时能够保持在符号距离函数附近，必须周期性地对水平集函数进行初始化，这一过程其实是与水平集理论本身是相悖的。为了合理解决水平集函数的初始化过程，本文引进了扩散理论，通过在水平集函数添加扩散项，并利用分段常数数值方法求解，从而实现了水平集函数无需初始化过程。引入扩散理论，依靠简单的有限差分求解方法，不仅保证实现过程的简单性，也是对实现过程稳定性的保证。这一方法对边界具有高敏感度，而且可以延伸至更高维的水平集理论。