rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Mathematical foundations of image processing and analysis
    part number: 2
  name:
    name part: Pinoli, Jean-Charles
    role:
      role term: creator
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (1 volume).
  abstract: 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.
  table of 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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  note: Jean-Charles Pinoli.
  note: Includes bibliographical references and index.
  subject:
    topic: Image processing
    topic: Mathematics
  subject:
    topic: Image analysis
    topic: Mathematics
  subject:
    topic: Convolutions (Mathematics)
  subject:
    topic: Image processing
    topic: Mathematical models
  subject:
    topic: Mathematics
  subject:
    topic: COMPUTERS
    topic: General
  classification: TA1637.5
  classification: 006.4/20151
  related item:
    title info:
      title: Mathematical foundations of image processing and analysis. 2
    name:
      name part: Pinoli, Jean-Charles, author.
    identifier: (OCoLC)884551293
  related item:
    title info:
      title: Digital signal and image processing series
  identifier: 9781118984567
  identifier: 1118984560
  identifier: 9781118984574
  identifier: 1118984579
  identifier: 9781848217485
  identifier: 184821748X
  identifier: https://doi.org/10.1002/9781118984574
  record info:
    record content source: N$T
    record creation date: 140814
    record change date: 20170124070216.7
    record identifier: ocn886880486
    language of cataloging:
      language term: eng