The author presents three distinct but related branches of science
in this book: digital geometry, mathematical morphology, and
discrete optimization. They are united by a common mindset as well
as by the many applications where they are useful. In addition to
being useful, each of these relatively new branches of science is
also intellectually challenging.The book contains a systematic
study of inverses of mappings between ordered sets, and so offers a
uniquely helpful organization in the approach to several phenomena
related to duality.To prepare the ground for discrete convexity,
there are chapters on convexity in real vector spaces in
anticipation of the many challenging problems coming up in digital
geometry. To prepare for the study of new topologies introduced to
serve in discrete spaces, there is also a chapter on classical
topology.The book is intended for general readers with a modest
background in mathematics and for advanced undergraduate students
as well as beginning graduate students.
General
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