Real-time Processing Algorithms for LiDAR Point Cloud Data

该项目将开发一个实时处理系统，用于通过光探测和测距（LiDAR）技术获取地理空间调查数据。由于激光雷达点云数据的自然表面粗糙度、各种噪声和庞大的数据规模，表面重建和属性检测具有挑战性。在现有的文献和商业软件中，曲面重构已经通过各种方法进行，如逆距离加权、克里格、样条和小波。然而，问题是病态的，传统的重建方法要么引入可观察到的插值伪像，要么在数据点数量增加时计算成本太高。研究者将开发和分析一种有效的基于偏微分方程（PDE）的表面重建算法，称为递归曲率插值法（R-CIM），该算法产生最小振荡的光滑图像表面，其计算成本与图像尺寸的顺序相同。该项目将通过密西西比州立大学数学与统计系和美国农业部农业研究服务处的合作，开发激光雷达点云数据的最佳图像重建算法。所提出的算法（R-CIM）是最优的，因为它具有最小的振荡行为，其计算成本在图像大小的顺序上，与数据大小无关。它将有助于图像重建的研究，并将涉及非均匀采样数据的各种实时应用推进到现实世界。同时，提出的研究包括开发和实施各种激光雷达数据处理任务的最先进算法。该项目培育农业工程师与具有偏微分方程、数值分析和图像处理背景的数学家之间的合作；它将支持一个研究生和一个本科生三年的学习。所有新开发的软件都将与社区免费共享。

The project will develop a real-time processing system for geospatial survey data acquired by light detection and ranging (LiDAR) technology. Surface reconstruction and attribute detection for LiDAR point cloud data are challenging due to natural surface roughness, diverse noises, and huge data sizes. In the existing literature and commercial software, surface reconstruction has been carried out by various methods such as the inverse-distance weighting, kriging, splines, and wavelets. However, the problem is ill-posed and the conventional reconstruction methods either introduce observable interpolation artifacts or become too computationally expensive when the number of data points increases. The investigator will develop and analyze an effective partial differential equation (PDE)-based surface reconstruction algorithm, called the recursive curvature interpolation method (R-CIM), which produces a smooth image surface of a minimum oscillation, and of which the computational cost is in the order of the image size.This project will develop an optimal image reconstruction algorithm for LiDAR point cloud data via collaboration between the Department of Mathematics and Statistics, Mississippi State University, and Agriculture Research Service, United States Department of Agriculture. The proposed algorithm (R-CIM) is optimal in the sense that it possesses a minimum oscillatory behavior and its computational cost is in the order of the image size, independent of the data size. It will contribute to research on image reconstruction and advance various real-time applications towards the real world which involve nonuniformly sampled data. At the same time, the proposed researh includes the development and implementation of the state-of-the-art algorithms for various LiDAR data processing tasks. The project nurtures collaborations between an agricultural engineer and mathematicians having backgrounds on PDEs, numerical analysis, and image processing; it would support a graduate student and an undergraduate student for three years. All the newly-developed software will be freely shared with the community.