A set theoretic approach for time to contact estimation in dynamic vision

This paper deals with the estimation of the time-to-contact in dynamic vision. It is well known that di2erential invariants of the image velocity 4eld can be used to characterize the shape changes of objects in the scene, due to relative motion between the observer and the scene. Under the hypothesis of constant velocity along the optical axis, the time-to-contact turns out to be a function of the area enclosed by the object contour and its time derivative. In the paper, a novel approach based on set membership estimation theory is proposed to estimate the variables involved in the computation of the time-to-contact. Both errors in the motion model and image measurement noise are described as unknown-but-bounded disturbances, without requiring any statistical assumption. The proposed technique allows for the computation of guaranteed bounds on the time-to-contact estimates in 4nite time, a crucial issue in all problems where a robust evaluation of the time-to-contact is in order.