Perception of 3-D surfaces from 2-D contours

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. The authors survey classes of techniques proposed in the past and provide a critical analysis. They show that two kinds of symmetries in figures, which are known as parallel and skew symmetries, give significant information about surface shape for a variety of objects. They derive the constraints imposed by these symmetries and show how to use them to infer 3-D shape. They also discuss the zero Gaussian curvature (ZGC) surfaces in depth and show results on the recovery of surface orientation for various ZGC surfaces     

Shape from contour: straight homogeneous generalized cylinders andconstant cross section generalized cylinders

We analyze the properties of straight homogeneous generalized cylinders (SHGCs) and constant cross section generalized cylinders (CGCs), 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 3D shape of the objects are formulated based on the symmetries and from the geometry of the projection models. Finally, the methods that recover the 3D shape from the image of their contours are discussed and recovered surfaces are shown for sample objects