Generalizing Epipolar-Plane Image Analysis on the Spatiotemporal Surface

Abstract

The previous implementations of the authors' epipolar-plane image-analysis mapping technique demonstrated the feasibility and benefits of the approach, but were carried out for restricted camera geometries. The question of more general geometries made the technique's utility for autonomous navigation uncertain. The authors have developed a generalization of the analysis that: (1) enables varying view direction, including varying over time; (2) provides three-dimensional connectivity information for building coherent spatial descriptions of observed objects; and (3) operates sequentially, allowing initiation and refinement of scene feature estimates while the sensor is in motion. To implement this generalization it was necessary to develop an explicit description of the evolution of images over time. They achieved this by building a process that creates a set of two-dimensional manifolds defined at the zeros of a three-dimensional spatiotemporal Laplacian. These manifolds represent explicitly both the spatial and temporal structure of the temporally evolving imagery and are termed spatiotemporal surfaces.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>