Geometrical degeneracy removal by virtual disturbances

In surface reconstruction from slice samples (typical in medical imaging, coordinate measurement machines, stereolithography, etc.) the available methods attack the geometrical and topological properties of the surface. Topological methods classify the transitions occurred in the 2-manifold between two consecutive slices i and i+1. Geometrical methods synthesize the surface based on local proximity of the contours in consecutive slices. Superimposed 2D Voronoi Diagrams VDi and VDi+1 for slices i and i+1, respectively, present topological problems if, for example, a site of VDi lies on an site or an edge of VDi+1. The usual treatment of this problem in literature is to apply a geometrical disturbance to either VDi or VDi+1, thus eliminating the degeneracy. In contrast, this article presents the implementation of a method which identifies the degenerate situation, constructs un-instantiated topological constructs, choses a geometrical instantiation based on a virtual disturbance introduced to the actual configuration. The algorithm was successfully applied to remove non-manifold topologies produced by well known algorithms in surface reconstruction.