A0562
Title: Nonparametric learning for 3D point cloud data
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)
Lily Wang - George Mason University (United States)
Ming-Jun Lai - University of Georgia (United States)
Abstract: In recent years, there has been an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, a novel and efficient smoothing tool is developed based on multivariate splines over the triangulation to extract the underlying signal and build up a 3D solid model from the point cloud. The proposed method can denoise or deblur the point cloud effectively, provide a multi-resolution reconstruction of the actual signal, and handle sparse and irregularly distributed point clouds to recover the underlying trajectory. In addition, the method provides a natural way of reducing numerosity data. The theoretical guarantees of the proposed method are established, including the convergence rate and asymptotic normality of the estimator, and show that the convergence rate achieves optimal nonparametric convergence. A bootstrap method is also introduced to quantify the uncertainty of the estimators. Through extensive simulation studies and a real data example, the superiority of the proposed method is demonstrated over traditional smoothing methods in terms of estimation accuracy and data reduction efficiency.
