Straight homogeneous generalized cylinders: analysis of reflectance properties and a necessary condition for class membership

Consideration is given to two membership tests for straight homogeneous generalized cylinders to determine if an object in the image is a member of the shape class. It is shown that contour information alone is insufficient to recover a straight homogeneous generalized cylinder uniquely. It is then shown that the sign and magnitude of the Gaussian curvature at a point vary among members of a contour-equivalent class. Next, a method of ruling straight homogeneous generalized cylinder images is developed. This ruling of the surface serves two functions. First, the ruling algorithm provides a heuristic test of whether or not the image is consistent with that of a straight homogeneous generalized cylinder. Secondly, the ruling makes explicit certain parameters of the underlying straight homogeneous generalized cylinder that the authors use in their second membership test. The second membership test is an intensity-based method which assumes that the surface has geodesics and that the albedo is constant. The method compares intensity values at corresponding meridian points along cross-sectional geodesics