2D Image Analysis by Generalized Hilbert Transforms in Conformal Space

  • Lennart Wietzke
  • Oliver Fleischmann
  • Gerald Sommer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5303)


This work presents a novel rotational invariant quadrature filter approach - called the conformal monogenic signal - for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase, direction/orientation, energy and curvature in one unified algebraic framework. The conformal monogenic signal will be theoretically illustrated and motivated in detail by the relation of the 3D Radon transform and the generalized Hilbert transform on the sphere. The main idea is to lift up 2D signals to the higher dimensional conformal space where the signal features can be analyzed with more degrees of freedom. Results of this work are the low computational time complexity, the easy implementation into existing Computer Vision applications and the numerical robustness of determining curvature without the need of any derivatives.


Conformal Space Poisson Kernel Conformal Curvature Monogenic Signal Radon Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lennart Wietzke
    • 1
  • Oliver Fleischmann
    • 1
  • Gerald Sommer
    • 1
  1. 1.Department of Computer ScienceKiel UniversityKielGermany

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