@article {Benamar2014197,
	title = {Time to collision (TTC) estimation maps based on optical flow in paracatadioptric vision [Estimation des cartes du temps de collision (TTC) bas{\'e}e sur le flot optique en vision para-catadioptrique]},
	journal = {Traitement du Signal},
	volume = {31},
	number = {1-2},
	year = {2014},
	note = {cited By 0},
	pages = {197-219},
	abstract = {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. {\textcopyright} 2014 Lovoisier.},
	doi = {10.3166/ts.31.197-219},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84930250224\&doi=10.3166\%2fts.31.197-219\&partnerID=40\&md5=1ed78d09cceb5f059e5db87be3aa812f},
	author = {Benamar, F.Z.a d and Fkihi, S.E.b and Demonceaux, C.c and Mouaddib, E.M.d and Aboutajdine, D.a}
}
@conference {Benamar20135,
	title = {Gradient-based time to contact on paracatadioptric camera},
	booktitle = {2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings},
	year = {2013},
	note = {cited By 2},
	pages = {5-9},
	abstract = {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 {\textquoteright}gradient based time to contact{\textquoteright}, 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. {\textcopyright} 2013 IEEE.},
	doi = {10.1109/ICIP.2013.6738002},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84897697160\&doi=10.1109\%2fICIP.2013.6738002\&partnerID=40\&md5=2d096a6f98a59c3c442f3c24ffca4bbc},
	author = {Benamar, F.a d and El Fkihi, S.a b and Demonceaux, C.c and Mouaddib, E.d and Aboutajdine, D.a}
}
