Research On High-Quality Point Cloud Resampling Based On Optimal Transport Theory

We call a dataset containing a large number of points in a certain coordinate system a point cloud.The point cloud contains a wealth of information,in general,including three-dimensional coordinate values,color,normal and other data.With the advancement of 3D scanning technology,we can already acquire point cloud data through 3D scanners,thereby achieving the goal of reproducing the world with a point cloud.At the same time,high-quality point clouds are also important inputs for many applications,such as 3D object reconstruction,point-based rendering,and finite element analysis.However,the current point clouds obtained through 3D scanners still have some defects:the point clouds contain noise due to the optical properties of the object surface and the sensor performance;the points are unevenly distributed in different directions;if the scanning process encounters invisible or reflective areas,it will cause parts of the point cloud to be missing,resulting in voids.We have carried out relevant research in response to the above-mentioned challenges.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 express the properties of the denser original point cloud(such as hidden surfaces).The distribution of the resampling points conforms to the target distribution specified by the user in advance,and has certain blue noise properties.Based on the optimal transport theory,we can transform the traditional point cloud resampling problem into an optimization problem,and construct a discrete mesh on the point cloud,so that 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.Finally,we prove the relationship between the capacity of the restricted power cell associated to each resampling point and the density of the point,so that the capacityrelated measures can be compared with other existing algorithms.A large number of experiments show that the resampling point set output by our algorithm can achieve the goal of accurate adaptive density control,and has good blue noise properties.