Linear multiview reconstruction of points, lines, planes and cameras using a reference plane

Abstract

This paper presents a new linear method for reconstructing simultaneously 3D features (points, lines and planes) and cameras from many perspective views by solving a single linear system. It assumes that a real or virtual reference plane is visible in all views. We call it the Direct Reference Plane (DRP) method. It is well known that the projection relationship between uncalibrated cameras and 3D features is nonlinear in the absence of a reference plane. With a known reference plane, points and cameras have a linear relationship, as shown by Rother and Carlsson (2001). The main contribution of this paper is that lines and cameras, as well as, planes and cameras also have a linear relationship. Consequently, all 3D features and all cameras can be reconstructed simultaneously from a single linear system, which handles missing image measurements naturally. A further contribution is an extensive experimental comparison, using real data, of different reference plane and nonreference plane reconstruction methods. For difficult reference plane scenarios, with point or line features, the DRP method is superior to all compared methods. Finally, an extensive list of reference plane scenarios is presented, which shows the wide applicability of the DRP method.