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。目前已经出现了几种点云数据的表示和可视化方法。这些发展通常是临时的，适用于一种形式的传感器数据。本项目将基于以下关键成分开发新的通用加工平台。拟合质量通常不会在最小二乘意义上进行，而是由与应用领域密切相关的度量来确定，例如Hausdorff度量的变体。表示平台将隐式（水平集）方法与多尺度（类小波）分解相融合。最优表示的选择将借助非线性逼近和学习理论的技术进行。拟议的研究将适用于一般的点云数据，但重点将放在处理机器人和微型飞行器自主导航、生物和化学污染物来源识别以及气候建模等应用中出现的点云数据。我们生活的世界的信息是通过传感器获得的。这些包括医学图像（核磁共振成像，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一组点值组成（称为点云）。必须对这些数据进行处理和可视化，以便提取其中包含的重要信息。这样的处理每天要进行数百万次，处理的方式决定了信息的质量。目前大多数处理和可视化传感器数据的方法都是建立在图像处理的旧思想之上的，并且无法捕捉到它们的许多重要特征，例如它们的几何和拓扑结构。这个项目从数学和计算机科学中提出了新的复杂技术，以创造更有效的数据处理。该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。该提案特别强调地形数据，这些数据每天用于导航，特别是用于机器人和无人驾驶空中监视。

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.