AMS Mathematical Review of the book" Géométrie discrète et images numériques"(French)

Abstract:

This is the AMS Mathematical Review for the book: Géométrie discrète et images numériques [Discrete geometry and numerical images] Edited by David Coeurjolly, Annick Montanvert and Jean-Marc Chassery. Traité IC2. Série Signal et Image.[IC2 Treatise. Series Signal and Image] Hermes Science Publications/Lavoisier, Paris, 2007. 401+ xii pp. ISBN: 978-2-7462-1643-3 65D18 (51N99 68U10 94A08) This is a collective book stemming from the French colloquium on Discrete Geometry in Imaging created in 1991, which became international in 1996 under the name of “Discrete Geometry in Computer Science”. The book is structured in five parts. The first part (chapters 2 through 4) presents the general mathematical foundations of discrete geometry and topology: arithmetic (chapter 2, which is later referred to in chapters 6, 7 and 11), topology (chapter 3, which is referred to in chapter 8) and combinatorics (chapter 4, the foundation of chapter 12). The second part (chapters 5 to 8) introduces discrete geometry and discrete topology, which are the foundations of the next part. The third part (chapters 9 through 12) presents the different representations and their mappings: the medial axis (chapter 9), representations by projections obtained by accumulation (and in particular the Mojette transform, chapter 10), polygonization and polyhedrization (chapter 11) and approximation of surfaces by triangulation (chapter 12). The medial axis and the Mojette transform are key representations, whose applications are further described in the fifth part. The fourth part (chapters 13 and 14) focuses on image analysis from either original images or their …

Año de publicación:

2010

Keywords:

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