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Elements of digital geometry, mathematical morphology, and discrete optimization / Christer Oscar Kiselman.

By: Material type: TextTextPublisher: New Jersey : World Scientific, [2022]Description: xxiii, 461 pages : illustrations (some color) ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9789811248290
Subject(s): DDC classification:
  • 006.6 23/eng/20220209
LOC classification:
  • TA1637.5 .K57 2022
Contents:
Sets, mappings, and order relations -- Morphological operations : Set-theoretical duality -- Complete lattices -- Inverses and quotients of mappings -- Structure theorems for mappings -- Digitization -- Digital straightness and digital convexity -- Convexity in vector spaces -- Discrete convexity -- Discrete convexity in two dimensions -- Three problems in discrete optimization -- Duality of convolution operators -- Topology -- The Khalimsky topology -- Distance transformations -- Skeletonizing -- Solutions.
Summary: "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"-- Provided by publisher.

Includes bibliographical references (pages 419-447) and indexes.

Sets, mappings, and order relations -- Morphological operations : Set-theoretical duality -- Complete lattices -- Inverses and quotients of mappings -- Structure theorems for mappings -- Digitization -- Digital straightness and digital convexity -- Convexity in vector spaces -- Discrete convexity -- Discrete convexity in two dimensions -- Three problems in discrete optimization -- Duality of convolution operators -- Topology -- The Khalimsky topology -- Distance transformations -- Skeletonizing -- Solutions.

"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"-- Provided by publisher.

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