MCS: Reconstructing and Inferring Topology and Geometry from Point Cloud Data

MCS：从点云数据重建和推断拓扑和几何形状

• 批准号: 0915996
• 负责人: Tamal Dey
• 金额: $ 42万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0915996&HistoricalAwards=false
• 关键词: MCS; Reconstructing; Inferring; Topology; Geometry

Point cloud data (PCD) is pervasive across numerous areas in science and engineering. This project addresses two issues, namely reconstruction in three dimension and inference from PCD in high dimensions. In reconstruction, the problem of approximating a three dimensional shape from its PCD is considered. This problem becomes hopeless from computational view point for shapes sitting in high dimensional spaces. Here, the project focuses on inferring topological and geometric properties of the hidden object from its sampled representation rather than reconstructing it completely.A successful implementation of this project will enable many areas of science and engineering to enhance their scope in modeling, analyzing, prototyping, and visualizing input data with assurance of accuracy. Designing machine parts in automotive industry, creating virtual environments with buildings, simulating cracks and shocks in scientific studies are few examples where new algorithms are needed for reconstructing shapes in presence of non-smoothness. This will be addressed in the reconstruction section of the project. Various scientific and social studies such as the ones in medicine, economics, climate, disease control produce data that presumably sample a hidden parameter space (a manifold). They will benefit from the research on the topology and geometry inference section of the project.

点云数据（PCD）在科学和工程的许多领域都很普遍。该项目主要解决两个问题，即三维重建和从高维PCD推断。 在重建中，考虑了从PCD近似三维形状的问题。从计算的角度来看，对于位于高维空间中的形状来说，这个问题变得毫无希望。 该项目的成功实施将使许多科学和工程领域在保证准确性的前提下，在建模、分析、原型设计和可视化输入数据等方面得到更大的发展。在汽车工业中设计机器零件，在建筑物中创建虚拟环境，在科学研究中模拟裂缝和冲击，这些都是需要新算法来重建非光滑形状的例子。 这将在项目的重建部分加以解决。各种科学和社会研究，如医学、经济学、气候、疾病控制等，产生的数据可能会对隐藏的参数空间（流形）进行采样。他们将受益于该项目的拓扑和几何推理部分的研究。