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Mathematical foundations of image processing and analysis. 2 /

Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overvie...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pinoli, Jean-Charles (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : ISTE, 2014.
Colección:Digital signal and image processing series.
Temas:
Acceso en línea:Texto completo

MARC

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245 1 0 |a Mathematical foundations of image processing and analysis.  |n 2 /  |c Jean-Charles Pinoli. 
264 1 |a London :  |b ISTE,  |c 2014. 
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588 0 |a Print version record. 
505 0 |a Cover; Title Page; Copyright; Contents; Preface; Introduction; PART 5: Twelve Main Geometrical Frameworks for Binary Images; Chapter 21: The Set-Theoretic Framework; 21.1. Paradigms; 21.2. Mathematical concepts and structures; 21.2.1. Mathematical disciplines; 21.3. Main notions and approaches for IPA; 21.3.1. Pixels and objects; 21.3.2. Pixel and object separation; 21.3.3. Local finiteness; 21.3.4. Set transformations; 21.4. Main applications for IPA; 21.4.1. Object partition and object components; 21.4.2. Set-theoretic separation of objects and object removal. 
505 8 |a 21.4.3. Counting of separate objects21.4.4. Spatial supports border effects; 21.5. Additional comments; Historical comments and references; Bibliographic notes and additional readings; Further topics and readings; Some references on applications to IPA; Chapter 22: The Topological Framework; 22.1. Paradigms; 22.2. Mathematical concepts and structures; 22.2.1. Mathematical disciplines; 22.2.2. Special classes of subsets of Rn; 22.2.3. Fell topology for closed subsets; 22.2.4. Hausdorff topology for compact subsets; 22.2.5. Continuity and semi-continuity of set transformations. 
505 8 |a 22.2.6. Continuity of basic set-theoretic and topological operations22.3. Main notions and approaches for IPA; 22.3.1. Topologies in the spatial domain Rn; 22.3.2. The Lebesgue-(Čech) dimension; 22.3.3. Interior and exterior boundaries; 22.3.3.1. Topologically regular objects; 22.3.4. Path-connectedness; 22.3.5. Homeomorphic objects; 22.4. Main applications to IPA; 22.4.1. Topological separation of objects and object removal; 22.4.1.1. (Path)-connected components; 22.4.2. Counting of separate objects; 22.4.3. Contours of objects; 22.4.4. Metric diameter; 22.4.5. Skeletons of proper objects. 
505 8 |a 22.4.6. Dirichlet-Voronoi's diagrams22.4.7. Distance maps; 22.4.8. Distance between objects; 22.4.9. Spatial support's border effects; 22.5. Additional comments; Historical comments and references; Bibliographic notes and additional readings; Further topics and readings; Some references on applications to IPA; Chapter 23: The Euclidean Geometric Framework; 23.1. Paradigms; 23.2. Mathematical concepts and structures; 23.2.1. Mathematical disciplines; 23.2.2. Euclidean dimension; 23.2.3. Matrices; 23.2.4. Determinants; 23.2.5. Eigenvalues, eigenvectors and trace of a matrix. 
505 8 |a 23.2.6. Matrix norms23.3. Main notions and approaches for IPA; 23.3.1. Affine transformations; 23.3.2. Special groups of affine transformations; 23.3.3. Linear and affine sub-spaces and Grassmannians; 23.3.4. Linear and affine spans; 23.4. Main applications to IPA; 23.4.1. Basic spatial transformations; 23.4.1.1. Reflected objects; 23.4.2. Hyperplanes; 23.4.3. Polytopes; 23.4.4. Minkowski addition and subtraction; 23.4.5. Continuity and semi-continuities of Euclidean transformations; 23.5. Additional comments; Historical comments and references; Commented bibliography and additional readings. 
520 |a Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes. 
504 |a Includes bibliographical references and index. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Image processing  |x Mathematics. 
650 0 |a Image analysis  |x Mathematics. 
650 6 |a Traitement d'images  |x Mathématiques. 
650 6 |a Analyse d'images  |x Mathématiques. 
650 7 |a COMPUTERS  |x General.  |2 bisacsh 
650 7 |a Image processing  |x Mathematics  |2 fast 
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830 0 |a Digital signal and image processing series. 
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