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_301468nas a2200169 4500008004100000245005600041210005600097260004600153300001100199520089100210100002501101700002801126700002001154700003101174700002601205856006701231 2013 eng d00aDirectional Convexity Measure for Binary Tomography0 aDirectional Convexity Measure for Binary Tomography aBerlin; HeidelbergbSpringer Verlagc2013 a9 - 163 aThere is an increasing demand for a new measure of convexity fordiscrete sets for various applications. For example, the well- known measures for h-, v-, and hv-convexity of discrete sets in binary tomography pose rigorous criteria to be satisfied. Currently, there is no commonly accepted, unified view on what type of discrete sets should be considered nearly hv-convex, or to what extent a given discrete set can be considered convex, in case it does not satisfy the strict conditions. We propose a novel directional convexity measure for discrete sets based on various properties of the configuration of 0s and 1s in the set. It can be supported by proper theory, is easy to compute, and according to our experiments, it behaves intuitively. We expect it to become a useful alternative to other convexity measures in situations where the classical definitions cannot be used.

1 aTasi, Tamás Sámuel1 aNyúl, László, Gábor1 aBalázs, Péter1 aSanniti di Baja, Gabriella1 aRuiz-Shulcloper, Jose uhttp://link.springer.com/chapter/10.1007%2F978-3-642-41827-3_200667nas a2200157 4500008004100000020002200041245009300063210006900156260005300225300001400278100002000292700002000312700002600332700003100358856012000389 2013 eng d a978-3-642-41821-100aReconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection0 aReconstruction and Enumeration of hvConvex Polyominoes with Give aHeidelberg; London; New YorkbSpringercNov 2013 a100 - 1071 aHantos, Norbert1 aBalázs, Péter1 aRuiz-Shulcloper, Jose1 aSanniti di Baja, Gabriella uhttps://sed.hu/publication/reconstruction-and-enumeration-of-hv-convex-polyominoes-with-given-horizontal-projection