ITR: Distances and Generalized Geodesics for High-Dimensional Implicit and Point Cloud Surfaces:Theory, Computational Framework, and Applications in Information Sciences and Eng.

ITR：高维隐式和点云表面的距离和广义测地线：理论、计算框架以及信息科学和工程中的应用。

• 批准号: 0309575
• 负责人: Guillermo Sapiro
• 金额: $ 24万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-15 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0309575&HistoricalAwards=false
• 关键词: ITR; Distances; Generalized; Geodesics; Dimensional

Almost all disciplines in information sciences and engineering use and need to compute the distance between events and geodesics or optimal paths between them. Geodesics are used for example for pathplanning in robotics, brain analysis in computational neuroscience, image segmentation, and finding fundamental geometric objects on surfaces. In high dimensions, they are the building blocks for problems in data mining and information discovery, with applications ranging from finance to biology to image and video processing. In general spaces, generalized geodesics also have numerous applications, from brain imaging to color image enhancement to computer graphicsSince distance functions and geodesics are fundamental for the interpretation and utilization ofdata and the knowledge and information embedded in it, it is important to have a good theoretical understanding of generalized distance functions and geodesics, and to develop efficient techniques for their accurate and fast computation. The work is needed in high dimensions and for diverse types of data representations, including implicit hyper-surfaces, sets of unorganized points such as manifold samples obtained when learning high dimensional information from examples, and point clouds from popular 3D range scanners. This project addresses these theoretical and computational issues, and concentrates on specific important applications in the areas mentioned above. These applications can be efficiently approached only once the theoretical and computational frameworks here studied have been derived.In the educational arena, the goal is to continue with current efforts in the interdisciplinary aspects of advanced education and in the distribution and popularization of the developed techniques,including making software publicly available.

信息科学和工程使用中的几乎所有学科都需要计算事件与测量学之间的距离或它们之间的最佳路径。 例如，用于机器人技术的路径规划，计算神经科学中的大脑分析，图像分割以及在表面上找到基本几何对象。在高维度中，它们是数据挖掘和信息发现问题的基础，其应用程序从金融到生物学到图像和视频处理。在一般的空间中，广义的大地学也具有许多应用，从大脑成像到彩色图像增强到计算机图形的距离功能和大地测量学对于DATA的解释和利用以及嵌入其中的知识和信息至关重要，重要的是对良好的理论了解对通用距离的函数良好的理解非常重要，以便开发有效的技术和快速的技术，以便有效地计算精确的技术。需要在高维度和各种类型的数据表示中需要进行工作，包括隐式超曲面，一组无组织的点，例如从示例中学习高维信息以及来自流行的3D范围扫描仪的点云时获得的歧管样本。该项目解决了这些理论和计算问题，并集中于上述领域的特定重要应用。只有在此处研究的理论和计算框架得出的理论和计算框架之后才能有效地接触这些应用程序。在教育领域，目标是在高级教育的跨学科方面以及开发技术的分布和普及中继续进行当前的努力，包括公开软件。