Fast central catadioptric line extraction, estimation, tracking and structure from motion

In this paper we present an analysis of 3D line projections for central catadioptric cameras from a projective perspective. Most algorithms consider the projection of lines as general conics in the image plane with five degrees of freedom. However, in the calibrated case, only two parameters are needed to represent lines. We describe methods to obtain fast extraction and estimation algorithms. We then explain how classical edge-tracking algorithms can be adapted to these sensors. To this avail, we introduce two parametric equations for lines in central catadioptric images. We then propose a minimal representation for the euclidean transformation in the structure from motion problem and introduce possible metrics between a point and a central catadioptric line. These metrics are evaluated on simulated data. The structure from motion algorithm, from the line extraction process to the tracking and the reconstruction is tested on a real sequence