Why Mathematical Morphology Needs Quantales
John G. Stell · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · 2009
The importance of complete lattices in mathematical morphology is well-known. There are some aspects of the subject that can, however, be clarified by using complete lattices equipped with the additional structure of a binary operation subject to conditions making them quantales. This extended abstract shows how quantales, and more generally quantale modules, can be used to capture a number of constructions for dilations in a uniform way. The treatment is partly an exposition of material that is not technically novel, but which provides a valuable conceptual perspective on mathematical morphology.