III: Small: Geospatial Data Representation and Analysis through the Stellar Decomposition

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Thanks to recent developments in remote sensing technologies, the amount of spatial and spatio-temporal data currently available has been dramatically increasing. Specifically, LiDAR (Light Detection and Ranging) technologies generate precise three-dimensional information about the shape of the Earth, and its characteristics, in the form of massive point clouds. LiDAR data are used in a variety of different fields, such as urban modeling, climate study, earthquake analysis, disaster management, flood risk mapping, forestry analysis. Capitalizing on the opportunities presented by such massive, high-resolution, data and representing, analyzing and transforming them into useful information poses several challenges. The project focuses on developing scalable data representations, and algorithms for processing and analyzing scattered big geospatial data. The emphasis is on dealing with point clouds of very large size, arising from LiDAR acquisitions, and on applications to terrain modeling and to tree reconstruction from forestry data, with benefits to the research in environmental and Earth science. Being the approach entirely data agnostic, the project has a potential impact on a broader range of applications, including neuroscience, social science, and virtual reality. Software tools for modeling and analysis of very large terrains, and for forestry segmentation will be developed and distributed in the public domain.Currently, raw LiDAR point clouds are processed by first converting them into raster models, with high computational costs, potential loss of information and creation of artifacts due to missing data and to the presence of noise. The innovative aspect of the project is in performing data analysis directly on the LiDAR point clouds. This requires encoding the neighboring relations among the points as a simplicial mesh so as to provide an approximation of the underlying "shape" of the point cloud. In order to be able to deal with massive data sets, the research will develop efficient and effective mesh data structures, based on a new data clustered spatio-topological model, the Stellar decomposition, supporting scalability, and efficient processing of fundamental spatial and connectivity queries. New algorithms, rooted in computational topology, will be developed for terrain simplification and analysis, and for tree reconstruction from forestry data. The new scalable framework will make the analysis of terrain and forest data possible on commodity hardware even for datasets composed of billions of points. Moreover, thanks to the use of the Stellar decomposition, it will be well suited for implementations in a distributed environment for the analysis of such data at global Earth scale. The project website will include, besides resulting publications, the public-domain software tools developed, and benchmark and real datasets used, for demonstration purposes and to ensure reproducibility.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.