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.

1 aPalágyi, Kálmán1 aRuiz-Shulcloper, Jose1 aSanniti di Baja, Gabriella uhttp://link.springer.com/chapter/10.1007%2F978-3-642-41822-8_3