Recovery of Straight Homogeneous Generalized Cylinders Using Contour and Intensity Information

Abstract

Generalized cylinders have been the focus of considerable vision research. Straight homogeneous generalized cylinders are a class of generalized cylinders whose cross sections are scaled versions of a reference curve. In this paper, a general method for recovering straight homogeneous generalized cylinders is outlined. The method proposed in this paper combines constraints derived from both contour and intensity information. First, a method of ruling straight homogeneous generalized cylinder (SHGC) images is given. Next, these ruled images are studied to determine what parameters of the underlying shape can be computed. We show there exist equivalent classes of SHGCs that pro-duce the same set of contours, both extremal and discontinuous, thus one can not recover an SHGC from contour information alone. We also show that the sign and magnitude of the Gaussian curvature at a point varies among members of a contour-equivalent class. This motivates the need for incorporating additional information into the recovery process. Finally, we derive a method for recovering the tilt of the object using the ruled SHGC contour and intensity values along cross-sectional geodesics.