Computational topology has rapidly progressed to become a useful tool for processing and analyzing diverse data from a topological perspective. Computational topology converts relationships between data into topological relationships, which can be analyzed using topological techniques such as homology, cohomology, and homotopy. In this paper we apply techniques from computational topology to the problem of path planning for vision aided navigation of aerial platforms in GPS-denied regions. Navigation in GPS-denied areas requires external aiding to reduce the drift that naturally occurs with un-aided Inertial Measurement Units. One aiding mechanism, vision aided navigation (VAN), generates vision based measurements by registering imagery acquired from an onboard camera to geo-located reference imagery of the fly-over region. Successful VAN requires distinct, stable, and discriminative image scene content to permit successful image registration. Previously, we developed a probabilistic path planning approach for VAN. The path planner operates on image fiducials that generate reliable and accurate vision measurements. In this paper, we develop a principled approach to refine image fiducial selection using topological techniques. We describe the application of computational topology and provide numerical examples. We first motivate and describe the image fiducial selection problem. We also briefly describe an application of computational topology to analysis of the shape of image fiducial match score data, and an application of cohomology for path planning.

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Stephen DelMarco, "Application of computational topology to vision aided navigation in GPS-denied regions," Proc. SPIE 12526, Multimodal Image Exploitation and Learning 2023 , 1252608 (Presented at SPIE Defense + Commercial Sensing: May 01, 2023; Published: 15 June 2023); https://doi.org/10.1117/12.2662933.