Dynamic Stereo: Passive Ranging to Moving Objects from Relative Image Flows

A new concept in passive ranging to moving objects is described which is based on the comparison of multiple image flows. It is well known that if a static scene is viewed by an observer undergoing a known relative translation through space, then the distance to objects in the scene can be easily obtained from the measured image velocities associated with features on the objects (i.e., motion stereo). But in general, individual objects are translating and rotating at unknown rates with respect to a moving observer whose own motion may not be accurately monitored. The net effect is a complicated image flow field in which absolute range information is lost. However, if a second image flow field is produced by a camera whose motion through space differs from that of the first camera by a known amount, the range information can be recovered by subtracting the first image flow from the second. This ``difference flow´´ must then be corrected for the known relative rotation between the two cameras, resulting in a divergent relative flow from a known focus of expansion. This passive ranging process may be termed Dynamic Stereo, the known difference in camera motions playing the role of the stereo baseline. We present the basic theory of this ranging process, along with some examples for simulated scenes.