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Mathematical Foundations of Image Processing and Analysis, Volume 1

Book Description

Image processing and image analysis are typically important fields in information science and technology. By "image processing", we generally understand all kinds of operation performed on images (or sequences of images) in order to increase their quality, restore their original content, emphasize some particular aspect of the information or optimize their transmission, or to perform radiometric and/or spatial analysis. By "image analysis" we understand, however, all kinds of operation performed on images (or sequences of images) in order to extract qualitative or quantitative data, perform measurements and apply statistical analysis. Whereas there are nowadays many books dealing with image processing, only a small number deal with image analysis. The methods and techniques involved in these fields of course have a wide range of applications in our daily world: industrial vision, material imaging, medical imaging, biological imaging, multimedia applications, satellite imaging, quality control, traffic control, and so on

Table of Contents

  1. Cover
  2. Contents
  3. Dedication Page
  4. Title Page
  5. Copyright Page
  6. Preface
  7. Introduction
  8. Elements of Mathematical Terminology
  9. PART 1: An Overview of Image Processing and Analysis (Ipa)
    1. 1 Gray-Tone Images
      1. 1.1. Intensity images, pixels and gray tones
      2. 1.2. Scene, objects, context, foreground and background
      3. 1.3. Simple intensity image formation process models
      4. 1.4. The five main requirements for a relevant imaging approach
      5. 1.5. Additional comments
    2. 2 Gray-Tone Image Processing and Analysis
      1. 2.1. Image processing
      2. 2.2. Image analysis
      3. 2.3. Image comparison
      4. 2.4. Importance of Human Vision
      5. 2.5. Additional comments
    3. 3 Binary Images
      1. 3.1. Scene, objects and context
      2. 3.2. Binary and multinary images
      3. 3.3. Additional comments
    4. 4 Binary Image Processing and Analysis
      1. 4.1. Binary image processing
      2. 4.2. Binary image analysis
      3. 4.3. Binary image and object description
      4. 4.4. Object comparison
      5. 4.5. Object analysis, recognition and formation
      6. 4.6. Additional comments
    5. 5 Key Concepts and Notions for Ipa
      1. 5.1. Dimensionality
      2. 5.2. Continuity and discreteness
      3. 5.3. Scale, resolution and definition
      4. 5.4. Domains
      5. 5.5. Ranges
      6. 5.6. Additional comments
    6. 6 Mathematical Imaging Frameworks
      1. 6.1. Mathematical imaging frameworks
      2. 6.2. Image representation and image modeling
      3. 6.3. A mathematical imaging methodology
      4. 6.4. Additional comments
  10. PART 2: Basic Mathematical Reminders for Gray-tone and Binary Image Processing and Analysis
    1. 7 Basic Reminders in Set Theory
      1. 7.1. Mathematical disciplines
      2. 7.2. Sets and elements
      3. 7.3. Order and equivalence relations on sets
      4. 7.4. Mappings between sets
      5. 7.5. Mapping composition, involutions, and idempotent mappings
      6. 7.6. Cardinality
      7. 7.7. Cover
      8. 7.8. Additional comments
    2. 8 Basic Reminders in Topology and Functional Analysis
      1. 8.1. Mathematical disciplines
      2. 8.2. Topological spaces
      3. 8.3. Metric spaces
      4. 8.4. Some particular kinds of points in topological and metric spaces
      5. 8.5. Some particular kinds of subsets in topological and metric spaces
      6. 8.6. Some particular topological spaces
      7. 8.7. Lipschitz and Gromov–Hausdorff distances
      8. 8.8. Topological vector spaces
      9. 8.9. Additional comments
  11. PART 3: The Main Mathematical Notions for the Spatial and Tonal Domains
    1. 9 The Spatial Domain
      1. 9.1. Paradigms
      2. 9.2. Mathematical structures
      3. 9.3. Main approaches for IPA
      4. 9.4. Main applications to IPA
      5. 9.5. Additional comments
    2. 10 The Tonal Domain
      1. 10.1. Paradigms
      2. 10.2. Mathematical concepts and structures
      3. 10.3. Main approaches for IPA
      4. 10.4. Main applications for IPA
      5. 10.5. Additional comments
  12. PART 4: Ten Main Functional Frameworks for Gray Tone Images
    1. 11 The Algebraic and Order Functional Framework
      1. 11.1. Paradigms
      2. 11.2. Mathematical structures and notions for IPA
      3. 11.3. Main approaches for IPA
      4. 11.4. Main applications for IPA
      5. 11.5. Additional comments
    2. 12 The Morphological Functional Framework
      1. 12.1. Paradigms
      2. 12.2. Mathematical concepts and structures
      3. 12.3. Main approaches for IPA
      4. 12.4. Main applications for IPA
      5. 12.5. Additional comments
    3. 13 The Integral Functional Framework
      1. 13.1. Paradigms
      2. 13.2. Mathematical structures
      3. 13.3. Main approaches for IPA
      4. 13.4. Main applications for IPA
      5. 13.5. Additional comments
    4. 14 The Convolutional Functional Framework
      1. 14.1. Paradigms
      2. 14.2. Mathematical concepts and structures
      3. 14.3. Main approaches for IPA
      4. 14.4. Main applications for IPA
      5. 14.5. Additional comments
    5. 15 The Differential Functional Framework
      1. 15.1. Paradigms
      2. 15.2. Mathematical concepts and structures
      3. 15.3. Main approaches for IPA
      4. 15.4. Main applications for IPA
      5. 15.5. Additional comments
    6. 16 The Generalized Functional Framework
      1. 16.1. Paradigms
      2. 16.2. Mathematical concepts and structures
      3. 16.3. Main approaches for IPA
      4. 16.4. Main applications for IPA
      5. 16.5. Additional comments
    7. 17 The Frequential Functional Framework
      1. 17.1. Paradigms
      2. 17.2. Mathematical concepts and structures
      3. 17.3. Main approaches for IPA
      4. 17.4. Main applications to IPA
      5. 17.5. Additional comments
    8. 18 The Multiscale Functional Framework
      1. 18.1. Paradigms
      2. 18.2. Mathematical concepts and structures
      3. 18.3. Main approaches for IPA
      4. 18.4. Main applications for IPA
      5. 18.5. Additional comments
    9. 19 The Variational Functional Framework
      1. 19.1. Paradigms
      2. 19.2. Mathematical structures
      3. 19.3. Main approaches for IPA
      4. 19.4. Main applications for IPA
      5. 19.5. Additional comments
    10. 20 The Probabilistic Functional Framework
      1. 20.1. Paradigms
      2. 20.2. Mathematical concepts and structures
      3. 20.3. Main approaches for IPA
      4. 20.4. Main applications for IPA
      5. 20.5. Additional comments
  13. Appendices
  14. Tables of Notations and Symbols
  15. Table of Acronyms
  16. Table of Latin Phrases
  17. Bibliography
  18. Index of Authors
  19. Index of Subjects