Continuous Lattices and Mathematical Morphology
Interim rept. Oct 96-Oct 97
ARMY RESEARCH LAB ADELPHI MD SENSORS AND ELECTRON DEVICES DIRECTORATE
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I generalize the topological structure of the concrete forms of mathematical morphology to the lattice-algebraical framework using the theory of continuous lattices. I show that when a complete lattice, fl, exhibits the dual of the property that defines a continuous lattice, then fl together with a certain intrinsic lattice topology, mfl, which is related by duality to the Lawson topology, has almost all the familiar properties, suitably generalized, of the topologized lattices that constitute the basic mathematical structure of the concrete forms of mathematical morphology for instance, the complete lattice of closed subsets of the Euclidean plane topologized with Matherons hit-miss topology.
- Operations Research