Towards structure from motion for linear features through reference points

The 3D reconstruction from projections and feature correspondence between projections are two major problems in structure from motion. The authors show a geometric method on how a 3D affine shape is obtained from two parallel projections through general 4 reference points, or from two central projections when additional vanishing points are available. And they show also that correspondences can be established through reference points; the reference points configuration for central projections should contain at least a set of 4 coplanar points. The method is developed both for point and line segment features. Apart from that the correspondence of the necessary reference points should be known in advance, one needs neither to calibrate cameras nor to have any knowledge of its position and displacement. Projective geometry and affine geometry invariants are manipulated to perform both reconstruction and correspondence