Embedding pyramids into 3D meshes

The pyramid architecture is a powerful topology in the area of computer vision. On the other hand, the 3D mesh architecture possesses rich topological features which make it suitable for building scalable parallel processor systems. The usefulness of these two architectures has led us to consider the problem of embedding pyramids into 3D meshes, for which we present two solutions. The first solution, termed natural embedding, maps a pyramid into a 3D mesh such that each level of the pyramid is mapped to a single level of the 3D mesh. The second solution, termed multiple embedding, allows simultaneous embedding of multiple pyramids into a single 3D mesh. The quality of both solutions is evaluated using dilation and expansion measures. Using the multiple embedding, we are able to obtain an average dilation of 1.26 and a near-optimal expansion of 1.12.