B1440
Title: A new smoothing method for 3D imaging data: Efficiency vs. accuracy
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)
Abstract: Over the past two decades, increased demand for 3D visualization and simulation software is seen in medicine, architectural design, engineering, and many other areas, which have boosted the investigation of geometric data analysis and raised the demand for further advancement in statistical analytic approaches. We propose a class of spline smoothers appropriate for approximating geometric data over 3D complex domains, which can be represented in terms of a linear combination of spline basis functions with some smoothness constraints. We start with introducing the tetrahedral partitions, Barycentric coordinates, Bernstein basis polynomials, and trivariate spline on tetrahedra. Then, we propose a penalized spline smoothing method for identifying the underlying signal in a complex 3D domain from potential noisy observations. Simulation studies are conducted to compare the proposed method with traditional smoothing methods on 3D complex domains.
