Canonical Representation and Multi-View Geometry of Cylinders

This paper first introduces a canonical representation for cylinders. The canonical representation introduced here is closely related to the Pl¨ucker line representation. In this paper, we 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. One of the major novelties in this paper is the introduction of the main equations dominating the three view geometry of cylinders.We showthe relationship between cylinders’ three-viewgeometry 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 across three views in order to recover the motion and structure. Cylindrical pipes and containers are the main components in the majority of chemical, water treatment and power plants, oil platforms, refineries and many other industrial installations.We have developed a professional software, called CyliCon, which allows efficient as-built reconstruction of such installations from a series of pre-calibrated images. Markers are used for this pre-calibration process. The theoretical and practical results in this paper represent the first steps towards marker-less calibration and reconstruction of such industrial sites. Here, the experimental results take advantage of the two-view and three-view geometry of cylinders introduced in this paper to provide initial camera calibration results.