Active, Foveated, Uncalibrated Stereovision

Biological vision systems have inspired and will continue to inspire the development of computer vision systems. One biological tendency that has never been exploited is the symbiotic relationship between foveation and uncalibrated active, binocular vision systems. The primary goal of any binocular vision system is the correspondence of the two retinal images. For calibrated binocular rigs the search for corresponding points can be restricted to epipolar lines. In an uncalibrated system the precise geometry is unknown. However, the set of possible geometries can be restricted to some reasonable range; and consequently, the search for matching points can be confined to regions delineated by the union of all possible epipolar lines over all possible geometries. We call these regions epipolar spaces. The accuracy and complexity of any correspondence algorithm is directly proportional to the size of these epipolar spaces. Consequently, the introduction of a spatially variant foveation strategy that reduces the average area per epipolar space is highly desirable. This paper provides a set of sampling theorems that offer a path for designing foveation strategies that are optimal with respect to average epipolar area.