Projective Geometry for 3D Modeling of Objects

Abstract

This chapter surveys many fundamental aspects of projective geometry that have been used extensively in computer vision literature. In particular, it discusses the role of this branch of geometry in reconstructing basic entities (e.g., 3D points, 3D lines, and planes) in 3D space from multiple images. The chapter presents the notation of different elements. It investigates the geometrical relationships when one or two cameras are observing the scene creating single-view and two-view geometry. In other words, camera parameters in terms of locations and orientations, with respect to 3D space and with respect to other cameras, create relationships. This chapter discusses these relationships and expresses them mathematically. Finally, different approaches to deal with the existence of noise or inaccuracy in general are presented.