Point Cloud Repair Method via Convex Set Theory

Abstract

The point cloud is the basis for 3D object surface reconstruction. An incomplete point cloud significantly reduces the accuracy of downstream work such as 3D object reconstruction and recognition. Therefore, point-cloud repair is indispensable work. However, the original shape of the point cloud is difficult to restore due to the uncertainty of the position of the new filling point. Considering the advantages of the convex set in dealing with uncertainty problems, we propose a point-cloud repair method via a convex set that transforms a point-cloud repair problem into a construction problem of the convex set. The core idea of the proposed method is to discretize the hole boundary area into multiple subunits and add new 3D points to the specific subunit according to the construction properties of the convex set. Specific subunits must be located in the hole area. For the selection of the specific subunit, we introduced Markov random fields (MRF) to transform them into the maximal a posteriori (MAP) estimation problem of random field labels. Variational inference was used to approximate MAP and calculate the specific subunit that needed to add new points. Our method iteratively selects specific subunits and adds new filling points. With the increasing number of iterations, the specific subunits gradually move to the center of the hole region until the hole is completely repaired. The quantitative and qualitative results of the experiments demonstrate that our method was superior to the compared method.