The projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using uncalibrated cameras

Abstract

In this paper we present an algorithm for the simultaneous projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using Bundle Adjustment. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. Furthermore, for the reconstruction of quadrics (both full-rank and degenerate) and plane conics, a novel algorithm for the rectification of the outlines projected in n views is presented. Finally, we found out that due to the noise in the data, the global minimum of the classic cost function used in Bundle Adjustment may unfortunately break the topology of the quadrics. Hence, during the iterations of this method, we need to add the constraints to keep the quadrics within acceptable limits to preserve their topology.