HOW FAR 3D SHAPES CAN BE UNDERSTOOD FROM 2D SILHOUETTES

Each 2D silhouette of a 3D unknown object O constrains O inside the volume obtained by back-projecting the silhouette from the corresponding viewpoint. A set of silhouettes specifies a boundary volume R, obtained by intersecting the volumes due to each silhouette, R more or less closely approximates O, depending on the viewpoints and the object itself. This approach to the reconstruction of 3D objects is usually referred to as volume intersection. This correspondence addresses the problem of inferring the shape of the unknown object O from the reconstructed object R. For doing this, we divide the points of the surface of R into hard points, which belong to the surface of any possible object originating R, and soft points, which may or may not belong to O. We consider two cases: In the first case R is the closest approximation of O which can be obtained from its silhouettes, i.e., its visual hull; in the second case, R is a generic reconstructed object. In both cases we supply necessary and sufficient conditions for a point to be hard and give rules for computing the hard surfaces.