Motion recovery in light-attenuating media from image-shading variations

One of the requirements for providing some autonomy in the operation of robotic vehicles is an accurate knowledge of position, orientation, and motion relative to nearby objects and the environment. Passive-vision sensing provides a useful tool for extracting such information from the images of the scene. Some applications, including the operation of undersea vehicles, involve working under artificial lighting in an attenuating medium. The extraction of motion, position, and orientation information requires models of image brightness that incorporate the effects that are due to the illumination attenuation and the illumination variation resulting from the motion of the light source. We investigate the problem of motion recovery from image-shading variations for a configuration common in many undersea applications. On the basis of the image model developed earlier [J. Opt. Soc. Am. A 8, 217 (1991)], we show that the motion of a vehicle can be determined in closed form by using three Lambertian planar surfaces as optical beacons.