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Generalized Analytic Signals in Image Processing: Comparison, Theory and Applications

  • Swanhild Bernstein
  • Jean-Luc Bouchot
  • Martin Reinhardt
  • Bettina Heise
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

This article is intended as a mathematical overview of the generalizations of analytic signals to higher-dimensional problems, as well as of their applications to and of their comparison on artificial and real-world image samples.

We first start by reviewing the basic concepts behind analytic signal theory and derive its mathematical background based on boundary value problems of one-dimensional analytic functions. Following that, two generalizations are motivated by means of higher-dimensional complex analysis or Clifford analysis. Both approaches are proven to be valid generalizations of the known analytic signal concept.

In the last part we experimentally motivate the choice of such higherdimensional analytic or monogenic signal representations in the context of image analysis. We see how one can take advantage of one or the other representation depending on the application.

Keywords

Monogenic signal monogenic functional theory image processing texture Riesz transform. 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Swanhild Bernstein
    • 1
  • Jean-Luc Bouchot
    • 2
  • Martin Reinhardt
    • 1
  • Bettina Heise
    • 3
    • 4
  1. 1.Fakultät für Mathematik und Informatik Institut für Angewandte AnalysisTechnische Universität Bergakademie FreibergFreibergGermany
  2. 2.Department of Knowledge-Based Mathematical Systems, FLLLJohannes Kepler UniversityLinzAustria
  3. 3.Department of Knowledge-Based Mathematical Systems, FLLLJohannes Kepler UniversityLinzAustria
  4. 4.Christian Doppler Laboratory MS-MACH Center for Surface- and Nanoanalytics, ZONALinzAustria

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