Shape from contour: straight homogeneous generalized cones

The authors analyze the properties of straight homogeneous generalized cones (SHGCs) and derive the types of symmetries, that the limb boundaries and cross sections of these objects produce on the image plane. The constraints on the 3-D shape of the objects are formulated based on the symmetries and from the geometry of the projection models. Finally the methods that recover the 3-D shape from the image of their contours are discussed and recovered surfaces are shown for sample objects