Line extraction in central hyper-catadioptric systems

In central hyper-catadioptric systems the 3D lines are projected into conics in the image plane. The general representation of conics considers five parameters. These conics can be represented by two parameters if the hyper-catadioptric camera calibration is known. In this paper we present a new approach to extract these projected lines that we name catadioptric image lines (CILs). We propose an approximation to the geometric distance from point to conic that combined with the two point representation inside a RANSAC approach allows us to extract the CILs present in a hyper-catadioptric image. We also perform an exhaustive analysis on the elements that can affect the CILs extraction accuracy. Particularly we analyze the effect of calibration errors of the omnidirectional system and the effect of the distribution of the image points on the projected line, i. e. the conic in the image and its length. We present simulations with different hyper-catadioptric systems, and experiments with real images.