Elements Of Digital Geometry, Mathematical Morphology, And Discrete Optimization

This is a book on three distinct but related branches of science: digital geometry, mathematical morphology, and discrete optimization. They are united by a certain way of thinking as well as by the many applications where they can serve together. In addition to being useful, they are also intellectually challenging. The book contains a systematic study of inverses of mappings between ordered sets, and so offers a common foundation for various phenomena related to duality. To prepare the ground, there are chapters on convexity in real vector spaces, in anticipation of the many challenging problems of digital convexity. There is also a chapter on classical topology, preparing for the newer topologies introduced to serve in discrete spaces.