Homography-based tracking for central catadioptric cameras

This paper presents a parametric approach for tracking piecewise planar scenes with central catadioptric cameras (including perspective cameras). We extend the standard notion of homography to this wider range of devices through the unified projection model on the sphere. We avoid unwarping the image to a perspective view and take into account the non-uniform pixel resolution specific to non-perspective central catadioptric sensors. The homography is parametrised by the Lie algebra of the special linear group SL(3) to ensure that only eight free parameters are estimated. With this model, we use an efficient second-order minimisation technique leading to a fast tracking algorithm with a complexity similar to a first-order approach. The developed algorithm was tested on the estimation of the displacement of a mobile robot in a real application and proved to be very precise.