Time to collision (TTC) estimation maps based on optical flow in paracatadioptric vision [Estimation des cartes du temps de collision (TTC) basée sur le flot optique en vision para-catadioptrique]

The present paper deals with time to collision (TTC) for a mobile robot equipped with a catadioptric camera. This type of cameras is very useful in robotics because it provides a panoramic view field. The time to collision has been extensively studied in the case of perspective cameras. Nevertheless, the methods used are not directly applicable due to strong distortions in the images produced by the omnidirectional camera and they, therefore, need to be adapted. In this work, we propose to compute the TTC thanks to the estimation of the optical flow on omnidirectional images between the robot and the obstacle. We see that the double projection of a 3D point on the mirror and then on the camera plane leads to a new formulation of the TTC for catadioptric cameras. This formulation enables us to know, at each moment and at each pixel of the image, the TTC from the optical flow at this point. Our approach is validated on synthetic data and real experiments. Finally, we show that this calculation can detect obstacles in the motion direction of the robot. © 2014 Lovoisier.