基于变分水平集方法的散乱数据曲面重构研究

Surface Reconstruction from Scattered Data Based on Variational Level Set Method

摘要: 工程学和医学等领域中的很多问题进行抽象后可转化为散乱数据的光滑曲面重构问题。在散乱数据附近设定初始轮廓，将初始轮廓间接地表示为水平集函数的零水平集形式，最终将初始活动轮廓的演化转化成水平集函数的演化。定义一个以水平集函数为自变量的能量泛函来度量它与散乱点的逼近程度，利用改进的变分水平集方法演化初始轮廓，达到重构目的。本文中，一是对Heaviside函数进行改进，使初始轮廓能更好的收敛于目标轮廓；二是给出了模型数值计算的具体过程，并以二维实例说明散乱数据重构的效果。

Abstract: A lot of problems in the field of engineering and medicine after abstraction can be converted into scattered data reconfiguration problems. We set initial contour near the scattered data, expressed as the zero level set of the level set function, which will eventually turn the evolution of initial active contour into the evolution of the level set function. We define an energy functional who takes the level set function as its independent variable, to measure approximation degree with the scattered data, and use the improved variational level set method to evolve the initial contour and achieve reconstruction. In this paper, firstly, putting forward an improved Heaviside function to make the initial contour can better converge in the target contour; secondly, the specific process of numerical calculation model is given, and a two-dimensional example illustrates the effect of the scattered data reconstruction.