Analyzing Generalized Tubes

Many objects in the real world are tubular in shape and this paper is about understanding this object class, which we refer to in the paper as generalized tubes (hereafter GTs). Intuitively, a GT is constructed by sweeping some planar closed curve (the GT cross-section) along a 3D space curve (the GT axis). First, we examine the GT class as a whole and identify two important GT subclasses where the parametric curves and the set of intrinsic directions are related: i) GTs with circular cross-sections (hereafter CGTs) and ii) GTs with zero-torsion axes (hereafter ZGTs). Then, these two classes of generalized tube are analyzed with respect to their surface and projective properties. For example, CGT occluding edges are shown to project to parallel contours, and the contour image of a CGT is shown to have at least one degree of freedom. An algorithm is then given that uses both image contour and reflectance to recover CGT shape parameters modulo scale.