Sufficient Conditions for Topology-Preserving Parallel Reductions on the Face-Centered Cubic Grid (30APR, 10.1007/s10851-024-01177-y, 2024)

Topology preservation is a crucial issue in parallel reductions that transform binary pictures by changing only a set of black points to white at a time. In this paper, we present sufficient conditions for topology-preserving parallel reductions on the three types of pictures of the unconventional 3D face-centered cubic (FCC) grid. Some conditions provide methods of verifying that a given parallel reduction always preserves the topology, and the remaining ones directly provide deletion rules of topology-preserving parallel reductions, and make us possible to generate topologically correct thinning algorithms. We give local characterizations of P-simple points, whose simultaneous deletion preserves the topology, and the relationships among the existing universal sufficient conditions for arbitrary types of binary pictures and our new FCC-specific results are also established. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. corrected publication 2024.