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} } @inbook {1163, title = {Directional Convexity Measure for Binary Tomography}, booktitle = {Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications}, year = {2013}, note = {ScopusID: 84893169866doi: 10.1007/978-3-642-41827-3_2}, month = {2013}, pages = {9 - 16}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Berlin; Heidelberg}, abstract = {There 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.

}, doi = {10.1007/978-3-642-41827-3_2}, url = {http://link.springer.com/chapter/10.1007\%2F978-3-642-41827-3_2}, author = {Tam{\'a}s S{\'a}muel Tasi and L{\'a}szl{\'o} G{\'a}bor Ny{\'u}l and P{\'e}ter Bal{\'a}zs}, editor = {Gabriella Sanniti di Baja and Jose Ruiz-Shulcloper} } @inbook {1167, title = {Reconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection}, booktitle = {Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications (CIARP)}, series = {Lecture Notes in Computer Science}, number = {8258}, year = {2013}, note = {ScopusID: 84893181366doi: 10.1007/978-3-642-41822-8_13}, month = {Nov 2013}, pages = {100 - 107}, publisher = {Springer}, organization = {Springer}, type = {Conference paper}, address = {Heidelberg; London; New York}, isbn = {978-3-642-41821-1}, doi = {10.1007/978-3-642-41822-8_13}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs}, editor = {Jose Ruiz-Shulcloper and Gabriella Sanniti di Baja} } @inbook {1108, title = {A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets}, booktitle = {Discrete Geometry for Computer Imagery}, year = {2003}, note = {UT: 000187499600037ScopusID: 0242460250}, month = {2003///}, pages = {388 - 397}, publisher = {Springer Verlag}, organization = {Springer Verlag}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo}, author = {P{\'e}ter Bal{\'a}zs and Emese Balogh and Attila Kuba}, editor = {Ingela Nystr{\"o}m and Gabriella Sanniti di Baja and Stina Svensson} }