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

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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.