Geometric approach for simultaneous projective reconstruction of points, lines, planes, quadrics, plane conies and degenerate quadrics

We present an algorithm for the simultaneous projective reconstruction of points, lines, planes, quadrics, plane conies 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 conies, a novel algorithm for the rectification of the outlines projected in n views is presented. Finally, we show that reaching the global minimum during bundle adjustment is not always necessary or desirable since this state might break the topology of the quadrics being reconstructed.