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: Nonlinear Eigenproblems in Image Processing and Computer Vision
  name:
    name part: Gilboa, Guy.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 172 p. 41 illus., 39 illus. in color. online resource.
  abstract: This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: Introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case Reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms Describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals Provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion Proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions Examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms Presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis Discusses relations to other branches of image processing, such as wavelets and dictionary based methods This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great inte…
  table of contents: Introduction and Motivation.- Variational Methods in Image Processing -- Total Variation and its Properties -- Eigenfunctions of One-Homogeneous Functionals -- Spectral One-Homogeneous Framework -- Applications Using Nonlinear Spectral Processing -- Numerical Methods for Finding Eigenfunctions -- Graph and Nonlocal Framework -- Beyond Convex Analysis: Decompositions with Nonlinear Flows -- Relations to Other Decomposition Methods -- Future Directions -- Appendix: Numerical Schemes.
  note: by Guy Gilboa.
  subject:
    topic: Optical data processing
  subject:
    topic: Signal processing
  subject:
    topic: Image processing
  subject:
    topic: Speech processing systems
  subject:
    topic: Calculus of variations
  subject:
    topic: Computer science-Mathematics
  subject:
    topic: Computer mathematics
  subject:
    topic: Image Processing and Computer Vision
  subject:
    topic: Signal, Image and Speech Processing
  subject:
    topic: Calculus of Variations and Optimal Control; Optimization
  subject:
    topic: Math Applications in Computer Science
  subject:
    topic: Mathematical Applications in Computer Science
  classification: TA1630-1650
  classification: 006.6
  classification: 006.37
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Advances in Computer Vision and Pattern Recognition
  identifier: 9783319758473
  identifier: https://doi.org/10.1007/978-3-319-75847-3
  record info:
    record creation date: 180329
    record change date: 20191026161958.0
    record identifier: 978-3-319-75847-3