基于水平集的散乱数据点云曲面重构方法

提出了基于最小能量约束的水平集重构方法，用以解决由三维数据点云自动重构复杂拓扑结构物体模型的问题．其基本思想是将重构曲面看成是一个定义在三维空间的可变形封闭曲面，在曲面自身几何特征以及目标模型力的作用下，逐步逼近目标模型，其演变过程同时也是曲面能量逐步减小的过程．采用偏微分方程来表示曲面能量最小化的过程，将曲面进行三维空间网格划分，采用快速扫描法将三维数据点云转换为有符号的距离场，并给出了离散偏微分方程的数值解法．实验表明，基于水平集的三维曲面重构方法能够从初始表面自动收缩到目标模型，而且能够适应任意拓扑结构的复杂物体．

Level-Set Based 3D Reconstruction Algorithm from Unorganized Data Cloud

A constrained energy minimization based on level set method for 3D reconstruction of object with complex topology is proposed. The basic idea of this method is that the reconstruction surface is defined as a closed deformable surface in three dimensions, and the surface shrinks to the target under the effects of its geometrical features and target model. The evolution of deformable surface can be regarded essentially as the surface energy minimization, thus described by a partial differential equation. To numerically solve the evolution equation, the deformable surface is discretized into 3D grids and transmitted as signed distance field by fast sweeping. The experimental results show that the deformable surface can automatically shrink from initial surface to target object with complex topology.