A reduction operator transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions may delete just one point at a time, while parallel reductions can alter a set of points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. This work lays a bridge between the parallel and the sequential strategies. A class of deletion rules are proposed that provide 2D parallel reductions being equivalent to sequential reductions. Some new sufficient conditions for topology-preserving parallel reductions are also reported.

}, isbn = {978-3-642-41821-1}, doi = {10.1007/978-3-642-41822-8_3}, url = {http://link.springer.com/chapter/10.1007\%2F978-3-642-41822-8_3}, author = {K{\'a}lm{\'a}n Pal{\'a}gyi}, editor = {Jose Ruiz-Shulcloper and Gabriella Sanniti di Baja} }