Recovering planar surfaces by stereovision based on projective geometry

The planar surfaces (3-D faces) of the objects of a polyhedral scene are built using a trinocular stereovision system. Before the reconstruction step and after the step of matching, a search is conducted among the set of triplets of matched 2-D faces (supposed to be the projection of 3-D faces) for the triplets which really correspond to planar 3-D surfaces. To accurately reconstruct the surface, a check is conducted in 2-D space for the classes of triplets of faces which correspond to 3-D coplanar structures. It is shown how these 3-D properties are checked in the 2-D space, using tools of projective geometry, allowing the constraint of the 3-D reconstruction in order to maintain these 3-D properties