Real-time Processing Algorithms for LiDAR Point Cloud Data

该项目将为通过光探测和测距(LiDAR)技术获取的地理空间调查数据开发一个实时处理系统。由于激光雷达点云数据的自然表面粗糙度、噪声的多样性和数据量的巨大，使得激光雷达点云数据的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，曲面重建的方法有多种，如反距离加权法、克立格法、样条法、小波法等。然而，该问题是不适定的，当数据点数量增加时，传统的重建方法要么引入可观测的内插伪影，要么变得过于昂贵。研究人员将开发和分析一种有效的基于偏微分方程(PDE)的曲面重建算法，称为递归曲率插值法(R-CIM)，它可以产生最小振荡的光滑图像曲面，其计算成本与图像大小的量级有关。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局的合作，开发一种针对LiDAR点云数据的最优图像重建算法。所提出的算法(R-CIM)是最优的，因为它具有最小的振荡行为，并且其计算代价是图像大小的量级，与数据大小无关。这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向现实世界。同时，提出的研究还包括为各种激光雷达数据处理任务开发和实现最先进的算法。该项目培养了一名农业工程师和具有偏微分方程、数值分析和图像处理背景的数学家之间的合作；它将支持一名研究生和一名本科生三年。所有新开发的软件都将免费与社区共享。

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.