Thinning is an iterative layer-by-layer erosion until only the skeleton-like shape features of the objects are left. This paper presents a family of new 3D parallel thinning algorithms that are based on our new sufficient conditions for 3D parallel reduction operators to preserve topology. The strategy which is used is called subiteration-based: each iteration step is composed of six parallel reduction operators according to the six main directions in 3D. The major contributions of this paper are: 1) Some new sufficient conditions for topology preserving parallel reductions are introduced. 2) A new 6-subiteration thinning scheme is proposed. Its topological correctness is guaranteed, since its deletion rules are derived from our sufficient conditions for topology preservation. 3) The proposed thinning scheme with different characterizations of endpoints yields various new algorithms for extracting centerlines and medial surfaces from 3D binary pictures. {\textcopyright} 2011 Springer-Verlag Berlin Heidelberg.

}, isbn = {978-3-642-21072-3}, doi = {10.1007/978-3-642-21073-0_5}, author = {G{\'a}bor N{\'e}meth and P{\'e}ter Kardos and K{\'a}lm{\'a}n Pal{\'a}gyi}, editor = {Jake K Aggarwal and Reneta P Barneva and Valentin E Brimkov and Kostadin N Koroutchev and Elka R Korutcheva} } @inbook {935, title = {On topology preservation for hexagonal parallel thinning algorithms}, booktitle = {Combinatorial Image Analysis (IWCIA)}, series = {Lecture Notes in Computer Science}, number = {6636}, year = {2011}, note = {ScopusID: 79957628214doi: 10.1007/978-3-642-21073-0_6}, month = {May 2011}, pages = {31 - 42}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Madrid, Spain}, abstract = {Topology preservation is the key concept in parallel thinning algorithms on any sampling schemes. This paper establishes some sufficient conditions for parallel thinning algorithms working on hexagonal grids (or triangular lattices) to preserve topology. By these results, various thinning (and shrinking to a residue) algorithms can be verified. To illustrate the usefulness of our sufficient conditions, we propose a new parallel thinning algorithm and prove its topological correctness. {\textcopyright} 2011 Springer-Verlag Berlin Heidelberg.

}, isbn = {978-3-642-21072-3}, doi = {10.1007/978-3-642-21073-0_6}, author = {P{\'e}ter Kardos and K{\'a}lm{\'a}n Pal{\'a}gyi}, editor = {Jake K Aggarwal and Reneta P Barneva and Valentin E Brimkov and Kostadin N Koroutchev and Elka R Korutcheva} }