Default Shape Theory: With Application to the Computation of the Direction of the Light Source

Humans appear to have the ability to infer the three-dimensional shape of an object from its outline or occluding contour. In computer vision, an occluding contour is an important clue in the shape recovery process. So far, only a small family of shapes, in particular, shapes generated by generalized cylinders, and shapes of polyhedrons, has been investigated in computer vision. However, there are many instances where these types of surfaces are not applicable, e.g., a solid with holes or a solid with no planar surfaces. This paper proposes a new concept called the default shape theory which includes the solid of revolution as a special case. A default shape is a function whose domain is a closed contour and whose range is a vector representation of a three-dimensional solid. The application of this new concept to recover the direction of the light source is demonstrated in this paper. Experimental results show that the default-shape-based method has comparable performance as the Pentland light source determination algorithm. This paper also proves the relationship between one particular type of default shape with the solid of revolution. Other possible definitions of default shape are also discussed.