Correspondence-Free Alignment of 3D Object Models

In this work, we present a pose-invariant shape matching methodology for complete 3D object models. Our approach is based on first describing the objects with shape descriptors and then minimizing the distance between descriptors over an appropriate set of geometric transformations. Our chosen shape description methodology is the density-based framework (DBF), which is experimentally shown to be very effective in 3D object retrieval [1]. In our earlier work, we showed that density-based descriptors exhibit a permutation property that greatly reduces the equivocation of the eigenvalue-based axis labeling and moments-based polarity assignment in a computationally very efficient manner. In the present work, we show that this interesting permutation property is a consequence of the symmetry properties of regular polyhedra. Furthermore, we extend the invariance scheme to arbitrary 3D rotations by a discretization of the infinite space of 3D rotations followed by a nearest neighbor based approximate procedure employed to generate the necessary permutations.