Invariant properties of straight homogeneous generalized cylinders and their contours

A fundamental group in computer vision is the recovery of three-dimensional shape from image data. While this problem is in general underconstrained, the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders. They consider the class of straight homogeneous generalized cylinders (SHGCs), without any further assumption on the viewing direction or the precise shape of these objects. They present a rigorous mathematical study of the geometry of SHGCs and characterize their Gaussian curvature and occluding contours, and use these results to prove several new invariant properties of the contours of SHGCs. These properties are, in turn, used in two implemented algorithms for recovering SHGC descriptions from image contours. Several examples of segmentation of real images are given. Other applications are also discussed