Partial 3D shape matching using large fat tetrahedrons

Abstract

We present a method of automatic alignment of two partially matching 3D shapes. The algorithm selects large fat tetrahedrons (LFT) composed of 4 vertices in one shape and exhaustively searches in the other shape for sets of 4 vertices being compatible with the tetrahedron. By selecting such salient tetrahedrons that are relatively wide and fat, although also being not too unlikely to be contained in the overlap region, the cost of search can be reduced. The method is relatively insensitive to noise and not depending on the existence of local shape features nor on feature correspondences. When implemented on a GPU in Cuda, two point sets of 40,000 each can be aligned within seconds. The method is intended to support interactive 3D scan registration applications.