Error analysis of combined stereo/optical-flow passive ranging

The motion of an imaging sensor causes each imaged point of the scene to correspondingly describe a time trajectory on the image plane. The trajectories of all imaged points are reminiscent of a flow (e.g., of liquid) which is the source of the term 'optical flow'. Optical-flow ranging is a method by which the stream of two-dimensional images obtained from a forward-looking forward-moving passive sensor is used to compute depth (or range) to points in the field of view. Another well-known ranging method consists of triangulation based on stereo images obtained from at least two stationary sensors. In this paper we analyze the potential accuracies of a combined optical flow and stereo passive-ranging system in the context of helicopter nap-of-the-earth obstacle avoidance. The Cramer-Rao lower bound is developed for the combined system under the assumption of an unknown angular bias error common to both cameras of a stereo pair. It is shown that the depth accuracy degradations caused by a bias error is negligible for a combined optical-flow and stereo system as compared to a monocular optical-flow system.