带噪声散乱数据的光滑曲面重构——变分水平集方法  

Smooth Surface Reconstruction from Noisy Scattered Data—Variational Level Set Methods

作　　者：徐国良[1] 张琴[1] 刘丹[1] 

机构地区：[1]中国科学院数学与系统科学研究院计算数学研究所,北京100080

出　　处：《计算机辅助设计与图形学学报》2007年第7期840-848,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(10371130);国家"九七三"重点基础研究发展规划项目(2004CB318000)

摘　　要：带噪声散乱数据点的光滑曲面重构应用广泛,基于变分水平集方法提出一种求解该问题的新的能量模型,并由此能量得到一新的微分方程,该微分方程演化后得到的极限曲面即为要重构的光滑曲面.给出了一种快速建立初始曲面的方法,节约了重构时间;然后对该微分方程的初值问题运用水平集方法求解,其中的空间方向离散化采用本质无震荡或加权本质无震荡技术,时间方向采用具有高精度的TVDRunge-Kutta技术.提出一种变步长的TVDRunge-Kutta方法来重新初始化符号距离函数,保证了Runge-Kutta方法中每一欧拉步都满足迎风设计要求.实验结果表明,该方法高效且能产生良好的重建效果.Smooth surface reconstruction from noisy scattered data owns a large application background. A new energy model is proposed to solve this problem based on variational level set methods and a partial differential equation （PDE） is thus deduced. The limit surface obtained by PDE evolution is the reconstructed smooth surface. We provide a fast method to construct the initial surface, which saves the temporal cost of reconstruction. Then level set methods are utilized to solve the initialization problem of the PDE, where we discretize space by essentially non-oscillatory or weighted essentially non-oscillatory technique and discretize time by total variation diminishing （TVD） Runge-Kutta method of high precision. A TVD Runge-Kutta method with varying time steps is proposed to reinitialize the signed distance function, which guarantees the upwind design of each Euler step. The experiments show that the method proposed is efficient and can produce visual pleasing reconstruction results.

关 键 词：带噪声散乱数据 光滑重构 水平集方法 变步长总变差减少Runge-Kutta方法 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]