基于最优传输理论的高质量点云重采样方法

目前通过3D扫描仪获取的点云仍旧存在一些缺陷:点云含有噪声,点云在不同方向上分布不均匀等.本文针对上述问题开展研究.主要工作为提出一种新的算法用于在点云上进行高质量的重采样,即使用较为稀疏的重采样点集去表达较为密集的原始点云的几何形状,同时重采样点集的分布可以满足用户预先指定的目标分布,并具备一定的蓝噪声性质.在最优传输理论的基础之上,本文方法将传统的点云重采样问题转化为一个最优化问题,并在点云上构建离散网格,使得针对网格的受限制的Power剖分方法能够迁移至点云上.随后利用交叉优化框架对该优化问题进行求解,并对每一个重采样点执行精确的容积约束.大量实验结果表明,本文算法输出的重采样点集可以实现精确自适应控制密度的目标,并且具备较好的蓝噪声性质.

High-Quality Point Cloud Resampling Method Based on Optimal Transport Theory

Point clouds obtained through 3D scanners have some defects:the point clouds may contain noise,and the points are unevenly distributed in different directions.In this paper,we carry out research to deal with the above problems.The main contribution is to propose a new algorithm for performing high-quality resampling tasks on point clouds,that is,using a sparse set of resampling points to represent the geometric shape of the original dense point cloud.The distribution of the resampling points conforms to a target distribution specified by the user in advance,and has certain blue noise properties.Based on the optimal transport theory,the traditional point cloud resampling problem can be transformed into an optimization problem,and a discrete mesh can be constructed on the point cloud,so that the restricted power tessellation on surfaces can be applied to point clouds.Then we solve the optimization problem by using an interleaving optimization framework and enforce an exact capacity constraint for each resampling point.A large number of experiments show that the resampling point sets generated by our algorithm conform precisely to the target density function,and show good blue noise properties.