On the space requirements of indexing 3D models from 2D perspective images

The space requirements for indexing under perspective projections are addressed. It is known that the surface representing the set of possible images of a model point set within the index space must be three-dimensional (Jacobs, 1996). Under affine projections, the representing surface can be factorized as the cartesian product of lower-dimensional surfaces: these are obtained by projecting the representing surface onto orthogonal subspaces of the index space (Jacobs, 1992; Weinshall, 1993). This paper shows that, under perspective, such a factorization does not exist, yielding a negative answer to a question left open in (Jacobs, 1996). However, it is shown that there exist subspaces of the index space, onto which the representing surface projection is two-dimensional.