Professor Nikolaos Papanikolopoulos

Project Title: 
Topological Methods for 3D Point Cloud Processing

These researchers are investigating new approaches to processing large-scale 3D point cloud datasets using applied topology, specifically topological data analysis (TDA). As robots become widely available and interconnected in society there has been a corresponding increase in the number and size of datasets generated by their on-board sensors. Topological structure, represented by shape, can provide important insights on the nature of these datasets. A desire to exploit this structure gives motivation for the development of efficient algorithms. Inspired by recent advances in TDA, these researchers are interested in creating effective and scalable algorithms for point cloud processing tasks such as 3D reconstruction, (region) segmentation, and object detection and classification. The main tool in TDA, persistent homology, allows the group to study homology (i.e. connected components, holes, and voids) at multiple scales. Persistent homology is based on the nation of a filtration; the researchers build sequences of complexes, composed of simplices (vertices, edges, triangles, tetrahedrons), on the dataset to study its fundamental structure. There are computational challenges that arise when dealing with massive 3D sensor datasets. When applying persistent homology, this occurs in three specific areas: construction of the simplicial complex representation of the data, computing persistent homology, and measuring the topological similarity between datasets. Thus, MSI resources are necessary.

Project Investigators

Bill Beksi
Dario Canelon
Haoyuan Du
Ted Morris
Professor Nikolaos Papanikolopoulos
Haoyi Shi
Felix Su
Are you a member of this group? Log in to see more information.