Connective segmentation generalized to arbitrary complete lattices.
2011 (English)In: Mathematical Morphology and Its Applications to Image and Signal Processing: 10th international symposium, ISMM 2011, Verbania-Intra, Italy, July 6–8, 2011. Proceedings, Berlin: Springer , 2011, 61-72 p.Chapter in book (Refereed)
Summary: We begin by defining the setup and the framework of connective segmentation. Then we start from a theorem based on connective criteria, established for the power set of an arbitrary set. As the power set is an example of a complete lattice, we formulate and prove an analogue of the theorem for general complete lattices. Secondly, we consider partial partitions and partial connections. We recall the definitions, and quote a result that gives a characterization of (partial) connections. As a continuation of the work in the first part, we generalize this characterization to complete lattices as well. Finally we link these two approaches by means of a commutative diagram, in two manners.
Place, publisher, year, edition, pages
Berlin: Springer , 2011. 61-72 p.
connective segmentation; complete lattice; partial partition; block-splitting opening; commutative diagram
Mathematics Computer and Information Science
IdentifiersURN: urn:nbn:se:uu:diva-175152DOI: 10.1007/978-3-642-21569-8_6OAI: oai:DiVA.org:uu-175152DiVA: diva2:530501