Topology preservation on the BCC grid

A frequently investigated problem in various applications of binary image processing is to ensure the topology preservation of image operators. Although the literature primarily focuses on 2D and 3D pictures that are sampled on the conventional square and cubic grids, respectively, some alternate structures such as the body-centered cubic grid and the face-centered cubic grid have also attracted remarkable scientific interest. This work examines the topology preservation on the 3D body-centered cubic grid. A simple object point in a binary picture has the property that the deletion of that single point preserves the topology. As the first result of this paper, some easily visualized characterizations of simple points are presented. It is well-known that the simultaneous deletion of a set of simple points may not preserve the topology. The author also managed to state a sufficient condition for topology preserving operators that deletes a number of object points at a time. In addition, two examples for so-called subfield-based reductions are presented, and their topological correctness is verified with the help of the new sufficient condition.