曲面扩散的变分水平集方法  

A Variational Level Set Method for Surface Diffusion

作　　者：姚军生[1] 李然[2] 魏伟波[2] 潘振宽[2] 

机构地区：[1]西北工业大学航海学院,陕西西安710072 [2]青岛大学信息工程学院,山东青岛266071

出　　处：《计算机仿真》2010年第4期240-244,共5页Computer Simulation

摘　　要：基于变分水平集方法提出了一种通用的曲面扩散变分模型,其数据项为演化曲面与原曲面的水平集函数Heaviside函数差的平方,规则项为基于整体曲率的通用函数,通过图像扩散模型中的总变差与该模型中的总曲率类比设计该规则项,以实现曲面扩散的任务。为了避免水平集函数的重新初始化,在本文的能量泛函中增加了水平集函数为符号距离函数的惩罚项。所得到的演化方程为4阶偏微分方程,对其对流项采用经典迎风差分格式离散,对其中的扩散项采用中心差分格式。最后通过数值算例验证了模型用于曲面光滑、边缘保持与边缘增强的可行性。Based on variational level set method, a variational formulation is presented in this paper. The energy functional includes three parts. The first one is data term which is expressed as square of difference between Heavi- side function of the original level set function and the evolved level set function. The second part is a regularized term in general form which is expressed as total curvature similar to total variation term used in image diffusion. The third part is a penalty term to avoid re - initialization of level set function. The derived evolution equation is a fourth order partial differential equation which includes advection term and diffusion term. The advection part is diseretized by u- sing classic upwind difference scheme, and the diffusion part is diseretized by using central difference scheme. Finally, some numerical examples are presented to validate the model for surface diffusion, edge preserving and edge en- hancement.

关 键 词：曲面扩散 变分方法 水平集方法 总曲率 曲面演化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]