||Firstly, we define the setup and the framework of connective segmentation. Then we start from a theorem that expresses segmentation in terms of connective criteria. As the theorem is established for the power set of an arbitrary set, and as the power set is an example of a complete lattice, we exhibit 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. We link this characterization to the first approach by means of a commutative diagram and, as a continuation of the work in the first part, we generalize the characterization to complete lattices as well.
This talk is based on the following joint publication with Jean Serra:
S. Alsaody, J. Serra. Connective Segmentation Generalized to Arbitrary Complete Lattices. In: P. Soille, M. Pesaresi, and G. K. Ouzounis (Eds.): ISMM 2011, LNCS 6671, pp. 61-72, 2011.