The Visual Hull of Curved Objects

The visual hull is a geometric tool which relates the 3D shape of a concave object to its silhouettes or shadows. This paper develops the theory of the visual hull of objects bounded by smooth curved surfaces. From the basic definitions of visual hull we determine the surfaces which bound the visual hull of such objects. We show that these surfaces are patches of some surfaces which partition the viewpoint space of the aspect graph of the object. The surfaces concerned are those generated by the visual events tangent crossing and triple point. These ruled surfaces are analyzed for finding their active parts, i.e. the parts which could actually bound the visual hull. This analysis is based on the shape of the surface of the object at the tangency points of the ruled surfaces. An algorithm for computing the visual hull of a smooth curved object is outlined, which exploits the algorithm for computing its aspect graph .