Connectivity Preservation of 3D 6-Subiteration Thinning Algorithms

Thinning is a process which erodes an object layer by layer until only a skeleton is left. A thinning algorithm should preserve connectivity; i.e., any object and its skeleton should maintain the same connectivity structure. This paper concerns the connectivity preservation of 3D 6-subiteration thinning algorithms. The first objective of this paper is to propose sufficient conditions so that any 3D 6-subiteration parallel thinning algorithm satisfying these conditions is guaranteed to preserve connectivity. Even with these sufficient conditions, it is still not very easy to prove the connectivity soundness of a 3D 6-subiteration thinning algorithm. Thus, the second objective of this paper is to propose an approach to computerize the above sufficient conditions. Any 3D 6-subiteration thinning algorithm passing the computerized tests is guaranteed to preserve connectivity.