Direct estimation of time-to-impact from optical flow

The estimation of time to impact is of vital importance for animals as well as for autonomous robots. The optical flow is used to estimate the time to impact. The authors demonstrate 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. In the former case, the time-to-impact can be directly computed from the velocity field and its derivatives. The analysis takes place considering a 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 relating the optical flow, represented in a polar or log-polar coordinate system, with the time-to-impact. Experiments performed on images acquired from real scenes are presented