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Mathematical Foundations of Image Processing and Analysis, Volume 2

Mathematical Foundations of Image Processing and Analysis, Volume 2

          
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About the Book

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 between the pure and applied mathematical disciplines, and the processing and analysis of gray-tone and binary images. It is accessible to readers who have neither extensive mathematical training, nor peer knowledge in Image Processing and Analysis. It is a self-contained book focusing on the mathematical notions, concepts, operations, structures, and frameworks that are beyond or involved in Image Processing and Analysis. The notations are simplified as far as possible in order to be more explicative and consistent throughout the book and the mathematical aspects are systematically discussed in the image processing and analysis context, through practical examples or concrete illustrations. Conversely, the discussed applicative issues allow the role of mathematics to be highlighted. Written for a broad audience – students, mathematicians, image processing and analysis specialists, as well as other scientists and practitioners – the author hopes that readers will find their own way of using the book, thus providing a mathematical companion that can help mathematicians become more familiar with image processing and analysis, and likewise, image processing and image analysis scientists, researchers and engineers gain a deeper understanding of mathematical notions and concepts.

Table of Contents:
Preface xvii Introduction xxv Part 5 Twelve Main Geometrical Frameworks for Binary Images 1 Chapter 21 The Set-Theoretic Framework 3 Chapter 22 The Topological Framework 9 Chapter 23 The Euclidean Geometric Framework 23 Chapter 24 The Convex Geometric Framework 37 Chapter 25 the Morphological Geometric Framework 47 Chapter 26 The Geometric and Topological Framework 57 Chapter 27 The Measure-Theoretic Geometric Framework 71 Chapter 28 The Integral Geometric Framework 89 Chapter 29 The Differential Geometric Framework 111 Chapter 30 The Variational Geometric Framework 129 Chapter 31 The Stochastic Geometric Framework 135 Chapter 32 The Stereological Framework 159 Part 6 Four Specific Geometrical Framework for Binary Images 177 Chapter 33 The Granulometric Geometric Framework 179 Chapter 34 The Morphometric Geometric Framework 189 Chapter 35 The Fractal Geometric Framework 211 Chapter 36 The Textural Geometric Framework 229 Part 7 Four 'Hybrid' Framework for Gray-Tone and Binary Images 241 Chapter 37 The Interpolative Framework 243 Chapter 38 The Bounded-Variation Framework 253 Chapter 39 The Level Set Framework 269 Chapter 40 The Distance-Map Framework 281 Concluding Discussion and Perspectives 295 Appendices 301 Tables of Notations and Symbols 303 Table of Acronyms 341 Table of Latin Phrases 347 Bibliography 349 Index of Authors 435 Index of Subjects 445


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Product Details
  • ISBN-13: 9781848217485
  • Publisher: ISTE Ltd and John Wiley & Sons Inc
  • Publisher Imprint: ISTE Ltd and John Wiley & Sons Inc
  • Depth: 32
  • Language: English
  • Returnable: N
  • Spine Width: 32 mm
  • Weight: 871 gr
  • ISBN-10: 184821748X
  • Publisher Date: 04 Jul 2014
  • Binding: Hardback
  • Height: 241 mm
  • No of Pages: 496
  • Series Title: Iste
  • Volume: 2
  • Width: 163 mm


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