Visual contact with catadioptric cameras

• Two methods for Time to Contact (TTC) are proposed for catadioptric cameras.
• These methods take into account the distortion introduced by the mirror and adapt two classical methods developed for perspective images.
• The first method based optical flow computes a TTC for each pixel of the omnidirectional image.
• The second method estimates the TTC on a planar surface without an estimation of the optical flow.
• The methods are evaluated and compared on synthetic and real images.

Time to contact or time to collision (TTC) is utmost important information for animals as well as for mobile robots because it enables them to avoid obstacles; it is a convenient way to analyze the surrounding environment. The problem of TTC estimation is largely discussed in perspective images. Although a lot of works have shown the interest of omnidirectional camera for robotic applications such as localization, motion, monitoring, few works use omnidirectional images to compute the TTC. In this paper, we show that TTC can be also estimated on catadioptric images. We present two approaches for TTC estimation using directly or indirectly the optical flow based on de-rotation strategy. The first, called “gradient based TTC”, is simple, fast and it does not need an explicit estimation of the optical flow. Nevertheless, this method cannot provide a TTC on each pixel, valid only for para-catadioptric sensors and requires an initial segmentation of the obstacle. The second method, called “TTC map estimation based on optical flow”, estimates TTC on each point on the image and provides the depth map of the environment for any obstacle in any direction and is valid for all central catadioptric sensors. Some results and comparisons in synthetic and real images will be given.