A1007
Title: An efficient spline smoothing for 3D point cloud learning
Authors: Xinyi Li - Clemson University (United States) [presenting]
Shan Yu - University of Virginia (United States)
Yueying Wang - Iowa State University (United States)
Guannan Wang - College of William & Mary (United States)
Ming-Jun Lai - University of Georgia (United States)
Lily Wang - George Mason University (United States)
Abstract: Over the past two decades, we have seen an exponentially increased amount of point clouds of irregular shapes collected in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient smoothing tool based on multivariate splines over the tetrahedral partitions to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can be used to denoise or deblur the point cloud effectively and provide a multi-resolution reconstruction of the actual signal. In addition, it can handle sparse and irregularly distributed point clouds and recover the underlying trajectory from globally and locally missing data. Furthermore, we establish the theoretical guarantees of the proposed method. Specifically, we derive the convergence rate and asymptotic normality of the proposed estimator and illustrate that the convergence rate achieves the optimal nonparametric convergence rate, and the asymptotic normality holds uniformly. We demonstrate the efficacy of the proposed method over traditional smoothing methods through extensive simulation examples.
