3D Object Digitization: Majority Interpolation and Marching Cubes

In a previous paper we showed that a 3D object can be digitized without changing the topology if the object is r-regular and if the reconstruction method fulfills certain requirements. In this paper we give two important examples for such reconstruction methods. First, we introduce Majority Interpolation, an algorithm to interpolate sampling points at doubled resolution such that topological ambiguities are resolved. Second, we show how the well-known Marching Cubes algorithm has to be modified such that it is topology preserving. This is the first approach of digitizing 3D objects which guarantees topology preservation for voxel-based or polygonal surface-based reconstructions.