Canonical Representation and Three View Geometry of Cylinders

This paper first introduces a canonical representation for cylinders. The canonical representation introduced here is closely related to the Plücker line respresentation. It then drives the general equation of a cylinder using this representation. In this paper, we also show that this representation is an appropriate one for computer vision applications. In particular, it allows us to easily develop a series of mathematical methods for pose estimation, 3D reconstruction and motion estimation. Finally, one of the main objectives of this paper is to introduce the main equations dominating the three view geometry of cylinders. We show the relationship between cylinders’ three-view geometry and that of lines (Spetsakis and Aloimonos, 1990, Weng et al., 1993) and points (Shashua, 1995) defined by the trilinear tensor (Hartley, 1997), and propose a linear method, which uses the correspondences between six cylinders over three views in order to recover the motion and structure.