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Local Structure Analysis by Isotropic Hilbert Transforms

  • Lennart Wietzke
  • Oliver Fleischmann
  • Anne Sedlazeck
  • Gerald Sommer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6376)

Abstract

This work presents the isotropic and orthogonal decomposition of 2D signals into local geometrical and structural components. We will present the solution for 2D image signals in four steps: signal modeling in scale space, signal extension by higher order generalized Hilbert transforms, signal representation in classical matrix form, followed by the most important step, in which the matrix-valued signal will be mapped to a so called multivector. We will show that this novel multivector-valued signal representation is an interesting space for complete geometrical and structural signal analysis. In practical computer vision applications lines, edges, corners, and junctions as well as local texture patterns can be analyzed in one unified algebraic framework. Our novel approach will be applied to parameter-free multilayer decomposition.

Keywords

Scale Space Geometric Algebra Convolution Kernel Signal Extension Inverse Radon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Lennart Wietzke
    • 1
  • Oliver Fleischmann
    • 2
  • Anne Sedlazeck
    • 2
  • Gerald Sommer
    • 2
  1. 1.Raytrix GmbHGermany
  2. 2.Cognitive Systems Group, Department of Computer ScienceKiel University 

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