Geometric Methods for Shape Recovery from Line Drawings of Polyhedra

Using structural geometric arguments, Whiteley showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We here enlarge the class of drawings to which this test applies, including those of polyhedral disks, possibly with perforations. This extension is helpful, as it makes the test applicable to verify and reconstruct drawings from usual scenes with opaque objects.The presented results rely on geometric constructions, thus offering an alternativeapproach to line drawing interpretation, complementary to the algebraic-combinatorial treatment given in the classic work by Sugihara.Lluís Ros was born inVilafranca del Penedès (Catalonia), on June 30, 1968. He is currently a research scientist at the Institut de Robótica i Informàtica Industrial of the Spanish High Council for Scientific Research, where he holds a Ramón y Cajal position since February 2003. He received a M.Sc. degree in mechanical engineering in 1992, and a Ph.D. degree (with honors) in advanced robotics in 2000, both from the Polytechnic University of Catalonia. His research interests are in geometry, with applications to machine vision, robot kinematics and computer graphics.Federico Thomas was born in Barcelona, on October 5, 1961. He received the B.S. degree in telecommunications engineering in 1984, and the Ph.D. degree (with honors) in computer science in 1988, both from the Polytechnic University of Catalonia. Since March 1990, he has been a research scientist in the Institut de Robòtica i Informàtica Industrial of the Spanish High Council for Scientific Research. His research interests are in geometry and kinematics, with applications to robotics, computer graphics and machine vision.