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} }