caa a22 4500 44581392X CHVBK 20180317145220.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11083-010-9190-0 doi (NATIONALLICENCE)springer-10.1007/s11083-010-9190-0 Ronse Christian LSIIT UMR 7005 CNRS-UdS, Parc d'Innovation, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cedex, France aut Idempotent Block Splitting on Partial Partitions, II: Non-isotone Operators [Elektronische Daten] [Christian Ronse] Our first paper introduced block splitting operators on the complete lattice of partial partitions, studied their algebraic properties and characterized block splitting openings (kernel operators) in terms of partial connections. In this second paper we study non-isotone idempotent block splitting operators on partial partitions. In particular we analyse the following two constructions: the residual combination of block splitting openings, where the (n + 1)-th opening is applied to the "residue” of the n-th one; a supremum of operators obtained by composition of a block splitting opening followed by a block selection operator guided by a predicate on sets. These operators belong to two families of idempotent operators generalizing openings that the author studied previously. In the same way as the openings analysed in the first paper, these two types of idempotent operators underlie recent image segmentation approaches due to Serra and Soille. 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), 307-339 0167-8094 28:2<307 2011 28 11083 https://doi.org/10.1007/s11083-010-9190-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9190-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ronse Christian LSIIT UMR 7005 CNRS-UdS, Parc d'Innovation, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cedex, France aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/2(2011-07-01), 307-339 0167-8094 28:2<307 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445813873 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer