Collaborative Research: An ADT Proposal: Fast Point Cloud Surface Reconstruction Algorithms

传感器数据对我们国家的安全、经济和健康至关重要。 它有各种格式和分辨率：视觉，雷达，激光雷达，激光扫描和多种形式的医学图像。 已经出现了几种方法来表示和可视化的点云数据。 这些发展通常是特别的，适用于一种形式的传感器数据。 该项目将基于以下关键成分开发新的通用加工平台。 适合的质量将 通常不是在最小二乘意义上进行的，而是由与应用领域密切相关的度量确定的 例如Hausdorff度量的变体。 表示平台将是一个融合的隐式（水平集）方法与多尺度（小波）分解。 最佳表示的选择将与非线性近似和学习理论的技术的帮助。 拟议的研究将适用于通用点云数据，但重点将放在处理点云数据上，这些数据出现在机器人和微型飞行器的自主导航、生物和化学污染物来源的识别以及 气候建模 我们生活的世界的信息是通过传感器获得的。 其中包括医学图像（MRI、CAT扫描）、导航工具（雷达、激光雷达、声纳）、监视（卫星图像、视频）。 这些传感器收集的数据由点值阵列（称为点云）组成。 必须对这些数据进行处理和可视化，以提取它们所包含的重要信息。 这样的处理每天要进行数百万次，如何处理决定了信息的质量。目前处理和可视化传感器数据的大多数方法都是建立在图像处理的旧思想上，无法捕捉它们的许多重要特征，如几何形状和拓扑结构。 该项目提出了数学和计算机科学的新的复杂技术，以创建更有效的数据处理。 开发将着眼于处理和渲染发生的准确性和速度的关键问题。该提案特别强调的是日常导航中使用的地形数据，特别是用于机器人和无人空中监视。

Sensor data is vital to the security, economy, and health of our nation. It comes in various formats and resolutions: visual, radar, lidar,laser scans, and multiple forms of medical imagery. There have emerged several approaches to the representation and visualization of point cloud data. These developments have typically been ad hoc, applying to one form of sensor data. This project will develop new generic processing platforms based on the following key ingredients. The quality of fit will typically not be made in the least squares sense but instead will be determined by metrics closely tied to the application domain such as variants of the Hausdorff metric. The representation platform will be a fusion of implicit (level set) methods together with multiscale (wavelet like) decompositions. The selection of optimal representations will be made with the aid of techniques from nonlinear approximation and learning theory. The proposed research will be applicable to generic point cloud data, but an emphasis will be placed on processing point cloud data that arise in applications such as autonomous navigation of robots and micro air vehicles, identification of sources of biological and chemical contaminants and climate modeling. Information about the world in which we live is obtained through sensors. These include medical imagery (MRIs, CAT scans), navigational tools (Radar, LIDAR, Sonar), surveillance (satellite imagery, video). The data gathered by such sensors consist of an array of point values (called a point cloud). This data must be processed and visualized in order to extract the important information they hold. Such processing is done literally millions of times a day and how it is done determines the quality of the information. Mostcurrent methods for processing and visualizing sensor data are built on old ideas from image processing and fail to capture many of their important features such as their geometry and topology. This project proposes new sophisticated techniques from mathematics and computer science to create more effective data processing. The development will be made with an eye towards the critical issues of accuracy and the speed at which the processing and rendering take place. A particular emphasis in the proposal is on terrain datawhich are used daily in navigation, especially for robotics and unmanned air surveillance.