水平集方法在点云建模中的应用研究

Research on Level Set Method Applied to Point Cloud Modeling

描述了一种利用偏微分方程和变分法进行点采样几何模型的重建算法。把符号距离函数与任意函数的度量函数作为内部能量,根据能量约束最小化条件,通过水平集方法求解曲面的梯度流,使初始曲面随时间产生演化变形,直至逼近目标模型,完全消除重新初始化过程。实验表明,通过水平集方法能够把初始曲面快速自动演化变形到目标模型,对任意拓扑结构和带噪声的点云具有很强的适应能力。

An algorithm based on partial differential equation （PDE） and variational calculus for reconstruction point sampled geometry model is presented. Metric function between signed distance function and any function is internal energy, the original surface evolution is driven by solving its gradient flow under the condition of constrained energy minimization, and the re-initialization progress is eliminated. The experimental results show that the surface can automatically evolve into target model with complex topology and noise quickly.