On the space requirements of indexing 3D models from 2D perspective images
Vincenzo Caglioti · 2002
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.