Overlap of convex polytopes under rigid motion (Q390361)

The authors study a problem of maximizing the overlap of two convex polytopes under rigid motion. The polytopes are specified by a set of distinct bounding hyperplanes. The overlap as a robust similarity measure for two convex shapes is defined as the volume of their intersection. A new algorithm to approximate the maximum overlap of two convex polytopes in three-dimensional space under rigid motion is presented. The presented algorithm is based on a decomposition of the rigid motion of convex polytopes into a set of rotations followed by a translation. The obtained results can be used in many applications, e.g., geometric shape matching, where a transformation of one shape in order to maximize some similarity measure with another shape has to be determined, object recognition problems, etc.