Understanding the Shape Properties of Trihedral Polyhedra

This paper presents a general framework for the computation of projective invariants of arbitrary degree of freedom (dof) trihedral polyhedra. We show that high dof. figures can be broken down into sets of connected four dof. polyhedra, for which known invariants exist. Although the more general shapes do not possess projective properties as a whole (when viewed by a single camera), each subpart does yield a projective description which is based on the butterfly invariant. Furthermore, planar projective invariants can be measured which link together the subparts, and so we can develop a local-global description for general trihedral polyhedra. We demonstrate the recovery of polyhedral shape descriptions from images by exploiting the local-global nature of the invariants.