An Algorithm to Recover Generalized Cylinders from a Single Intensity View

Understanding a scene involves the ability to recover the shape of objects in an environment. Generalized cylinders are a flexible. loosely defined class of parametric shapes capable of modeling many real-world objects. Straight homogeneous generalized cylinders are an important subclass of generalized cylinders whose cross sections are scaled versions of a reference curve. In this paper. a general method is presented for recovering straight homogeneous generalized cylinders from monocular intensity images. The algorithm is much more general in scope than any other developed to date. combining constraints derived from both contour and intensity information. We first demonstrate that contour information alone is insufficient to recover a straight homogeneous generalized cylinder uniquely. Next. we show that the sign and magnitude of the Gaussian curvature at a point varies among members of a contour-equivalent class. The image contour fails to constrain two parameters required to recover the shape of a generalized cylinder. the 3D axis location and the object tilt. Next. a method for "ruling" straight homogeneous generalized cylinder images is developed. Once the rulings of the image have been recovered. we show that all parameters derivable from contour alone can be recovered. To recover the two remaining parameters (modulo scale) not constrained by image contour requires incorporating additional information into the recovery process. e.g. intensity information. We derive a method for recovering the tilt of the object using the ruled contour image and intensity values along cross-sectional geodesics. In addition. we derive a method for recovering the location of the object's 3D axis from intensity values along meridians of the surface. Using the different methods outlined in this paper constitutes an algorithm for recovering all the shape pardmeters (modulo scale) of a straight homogeneous generalized cylinder.