On the advantages of polar and log-polar mapping for direct estimation of time-to-impact from optical flow

The application of an anthropomorphic retina-like visual sensor and the advantages of polar and log-polar mapping for visual navigation are investigated. It is demonstrated that the motion equations that relate the egomotion and/or the motion of the objects in the scene to the optical flow are considerably simplified if the velocity is represented in a polar or log-polar coordinate system, as opposed to a Cartesian representation. The analysis is conducted for tracking egomotion but is then generalized to arbitrary sensor and object motion. The main result stems from the abundance of equations that can be written directly that relate the polar or log-polar optical flow with the time to impact. Experiments performed on images acquired from real scenes are presented