Correspondence Search Mitigation Using Feature Space Anti-Aliasing

Abstract

Abstract : Image-aided navigation techniques can determine the navigation solution (position, velocity, and attitude) by observing a sequence of images from an optical sensor over time. This operation is based on tracking the location of stationary objects in multiple images, which requires solving the correspondence problem. This is an active area of research and many algorithms exist which attempt to solve this problem by identifying a unique feature in one image and then searching subsequent images for a feature match. The correspondence problem is plagued by feature ambiguity, temporal feature changes, and also occlusions, which are difficult for a computer to address. Constraining the correspondence search to a subset of the image plane has the dual advantage of increasing robustness by limiting false matches and improving search speed. A number of ad-hoc methods to constrain the correspondence search have been proposed in the literature. In this paper, the correspondence problem itself is carefully analyzed from fundamental optical principles. This development results in a general temporal sampling constraint and also reveals the essential connection between the deleterious effects of temporal aliasing and the ambiguities which plague the correspondence search problem. This temporal image sampling constraint is expressed as a function of the navigation trajectory for elementary camera motions. The predicted sampling rates are on the order of those needed for adaptive optics control systems and require very large bandwidths. The temporal image sampling constraint is then re-evaluated by incorporating inertial measurements. The incorporation of inertial measurements is shown to reduce the required temporal sampling rate to practical levels, which evidences the fundamental synergy between image and inertial sensors for navigation and serves as the basis for a real-time, adaptive, antialiasing strategy.