Inferring the shape of the real object from the object reconstructed by volume intersection

The volume intersection approach to the reconstruction of 3-D objects consists in intersecting the volumes obtained by back-projecting a number of silhouettes of an unknown object O. The problem of inferring, as far as possible, the shape of the unknown object O from the reconstructed object R is addressed. The points of the surface of R are divided 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. Two cases are considered: in the first case R is the closest approximation of O which can be obtained with volume intersection techniques, i.e., its visual hull; in the second case, R is a generic reconstructed object. In both cases necessary and sufficient conditions are supplied for a point to be hard. Rules are given for computing the hard surfaces