New Enabling Uses of Variational Active Surfaces and PDE s for 3D Sensor Fusion and Constrained Optimal Transport
Abstract
Variational methods based on geometric partial differential equations inspired from physics have played an important role in the development of computer vision and image processing, while in recent years advances in machine learning have produced successful data-driven alternatives to several practical problems. This has not rendered physical model-based methodologies obsolete, but has instead helped us understand where such models offer particular benefits as we begin to push data-driven counterparts to their limits. As such, geometric PDE based methods have taken on a more specialized role yet continue to represent mature and powerful tools that can be brought to bear on new and emerging applications where specific challenges arise. We propose two such novel formulations of variational active surfaces and PDE s which could enable broad advances in both sensor fusion applications for robotics and drone technology as well as in distributed path planning and the management of Multi-Domain Formations. First, noting the growing importance of robotics in the Army modernization Strategy and that computer vision has been the dominant sensing technology for 3D perception, we reformulate earlier variational methods in multiview stereo to accommodate a wide variety of portable sensor modalities to supplement optical images under visually challenging conditions. Some work has already been done in this area (RGB-D, LIDAR, infrared) but most using sensor that provide outputs in the form of 2D images. Radar, which can easily penetrate fog and smoke, be employed at night or even in the presence of strong glare, detect surfaces whose visual features are concealed by snow or deliberately camouflaged, has received far less attention in close range scenarios beyond mere vicinity detection. Over the past few years we have studied the feasibility of performing dense 3D reconstruction in typical computer-vision environments exclusively from 1D radar pulses, and have recently obtained simulated results that offer levels of geometric detail that begin to approach those attainable by image driven multiview stereo. We now wish to develop these into usable algorithms and to combine them with other image based sensors within the context of a unified inversion framework. Second, motivated by the surge in interest in Optimal Mass Transport theory (across the spectrum from computer vision, machine learning, data analysis, meteorology, statistical physics, network theory, and expert systems), but also noting that many realistic problems where it might be exploited add the challenge of dynamically changing domains for the entities to be transported, we propose a novel twist on OMT in which one allows and explicitly models a dynamic time dependent domain. This leads to an interesting synergy of curve evolution theory (for the evolution of the domain boundary) and mass transport for an evolving density within. This synergy of curve evolution theory and OMT, we believe to be novel not only as a formulation, but as a research direction in OMT which prioritizes the incorporation of common realistic constraints into OMT that otherwise preclude many important problems from leveraging recent developed methods trending primarily in the directions computational speed or data abstraction. Once we can explicitly model, control, and optimize the OMT problem with respect to dynamically changing boundaries, we can easily incorporate spatio-temporal constraints about where (and when) mass is allowed or not allow to go. This opens up a whole novel class of optimization problems for real world situations of relevance which could enhance army capabilities for optimal maneuvering, planning, simulation, and war-gaming of multi-domain formations.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 13, 2022
- Source ID
- W911NF2210267
Entities
People
- Anthony Yezzi
Organizations
- Army Contracting Command
- Georgia Tech Research Corporation
- United States Army