Mathematical foundations of image processing and analysis 2 / Jean-Charles Pinoli ; series editor, Jean-Pierre Goure.

Format:

Book

Author/Creator:

Pinoli, Jean-Charles, author.

Contributor:

Goure, J.-P., editor.

Series:

Digital signal and image processing series.

Digital Signal and Image Processing Series

Language:

English

Subjects (All):

Image processing--Mathematical models.

Image processing.

Convolutions (Mathematics).

Mathematics.

Physical Description:

1 online resource (492 p.)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : iSTE : Wiley, 2014.

Language Note:

English

Summary:

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 a bridge

Contents:

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

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

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

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

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

Further topics and readings

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781118984550

1118984552

9781118984574

1118984579

9781118984567

1118984560

OCLC:

885122545