caa a22 4500 445813873 CHVBK 20180317145220.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11083-010-9171-3 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9171-3 Ronse Christian LSIIT UMR 7005 CNRS, Université de Strasbourg, Parc d'Innovation, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cedex, France aut Idempotent Block Splitting on Partial Partitions, I: Isotone Operators [Elektronische Daten] [Christian Ronse] Image segmentation algorithms can be modelled as image-guided operators (maps) on the complete lattice of partitions of space, or on the one of partial partitions (i.e., partitions of subsets of the space). In particular region-splitting segmentation algorithms correspond to block splitting operators on the lattice of partial partitions, in other words anti-extensive operators that act by splitting each block independently. This first paper studies in detail block splitting operators and their lattice-theoretical and monoid properties; in particular we consider their idempotence (a requirement in image segmentation). We characterize block splitting openings (kernel operators) as operators splitting each block into its connected components according to a partial connection; furthermore, block splitting openings constitute a complete sublattice of the complete lattice of all openings on partial partitions. Our results underlie the connective approach to image segmentation introduced by Serra. The second paper will study two classes of non-isotone idempotent block splitting operators, that are also relevant to image segmentation. Springer Science+Business Media B.V., 2010 Partial partitions nationallicence Complete lattice nationallicence Block splitting nationallicence Idempotence nationallicence Image segmentation nationallicence Order Springer Netherlands 28/2(2011-07-01), 273-306 0167-8094 28:2<273 2011 28 11083 https://doi.org/10.1007/s11083-010-9171-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9171-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ronse Christian LSIIT UMR 7005 CNRS, Université de Strasbourg, Parc d'Innovation, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cedex, France aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/2(2011-07-01), 273-306 0167-8094 28:2<273 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445813873 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer