Gradient-based time to contact on paracatadioptric camera

The problem of time to contact or time to collision (TTC) estimation is largely discussed in perspective images. However, a few works have dealt with images of catadioptric sensors despite of their utility in robotics applications. The objective of this paper is to develop a novel model for estimating TTC with catadioptric images relative to a planar surface, and to demonstrate that TTC can be estimated only with derivative brightness and image coordinates. This model, called “gradient based time to contact”, does not need high processing such as explicit estimation of optical flow and feature detection and/or tracking. The proposed method allows to estimate TTC and gives additional information about the orientation of planar surface. It was tested on simulated and real datasets.