Research About Point Cloud Sampling Based On Optimal Transport Theory

Since the advent of 3D scanning device,3D scanning technology has developed rapidly,the shape of objects in real world can be rapidly capture and stored as point clouds.The point cloud data obtained by 3D scanning device inevitably has different degree of defect,so it is necessary to process the point cloud to facilitate the follow-up work.Point cloud sampling is chosen as the focus of our research in this paper.In this paper,the work follow the idea which from theory to application.We first study the relax blue noise sampling,generate a general sampling framework based on the theory of optimal transport and the analysis of the probability measure models.And it can be applied to point cloud sampling,multi-class sampling,color stippling and so on.Research of this paper not only promote the development of sampling theory in computer graphics,but also provides a new idea about the application of optimal transport.The main work of this paper includes:1.Research about point cloud sampling based on optimal transport theoryFirstly,we summarize the latest development of blue noise sampling algorithms and the main point cloud surface sampling algorithms,and analyze the problems and solutions of point cloud sampling algorithm.Next we propose a blue noise sampling algorithm based on the optimal transport theory which combine with probability measure models.We use the Wasserstein barycenter of the probability measure to solve the energy minimization,and form a more general sampling framework.Entropy regularized Wasserstein distance improve sampling efficiency.Finally,according to the characteristics of point cloud data,point cloud sampling is taken from point cloud distribution feature,and the GPU is used to perform parallel processing on the algorithm,so we obtaine a efficient and robust cloud sampling method.2.Multi-class blue noise samplingThe characteristics of the single-class blue noise sampling limit the ability to describe the natural phenomena,So the generalization of sampling will become a new trend of the development of sampling technology.We first combine blue noise sampling algorithm proposed before and construct a multi-class probability measure function.Next,we define a new energy function to solve the problems of conflict between different classes and solution of multi-class sampling model.We have done a series of experiments through the proposed sampling method,include constant density sampling,adaptive sampling,point cloud sampling and reconstruction.The results of experiments show that the algorithm proposed in this paper has a good property of blue noise,and it is also robust to point cloud sampling.Multiclass sampling expands the scope of sampling applications and provides a new direction for the development of sampling technology.