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Modelling Line and Edge Features Using Higher-Order Riesz Transforms

  • Ross Marchant
  • Paul Jackway
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8192)

Abstract

The 2D-complex Riesz transform is an extension of the Hilbert transform to images. It can be used to model local image structure as a superposition of sinusoids, and to construct 2D steerable wavelets. In this paper we propose to model local image structure as the superposition of a 2D steerable wavelet at multiple amplitudes and orientations. These parameters are estimated by applying recent developments in super-resolution theory. Using 2D steerable wavelets corresponding to line or edge segments then allows for the underlying structure of image features such as junctions and edges to be determined.

Keywords

Riesz transform 2D steerable filter super-resolution semi-definite program local feature analysis 

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References

  1. 1.
    Newell, A., Griffin, L.: Natural Image Character Recognition Using Oriented Basic Image Features. In: Proc. Int. Conf. Digital Image Computing Techniques and Applications, pp. 191–196 (December 2011)Google Scholar
  2. 2.
    Felsberg, M., Sommer, G.: The monogenic signal. IEEE Trans. Signal Process. 49(12), 3136–3144 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Zang, D., Sommer, G.: The Monogenic Curvature Scale-Space. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 320–332. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Wietzke, L., Sommer, G.: The Signal Multi-Vector. J. Math. Imaging and Vision 37(2), 132–150 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fleischmann, O., Wietzke, L., Sommer, G.: Image Analysis by Conformal Embedding. J. Math. Imaging and Vision 40(3), 305–325 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Unser, M., Van De Ville, D.: Wavelet steerability and the higher-order Riesz transform. IEEE Trans. Image Process. 19(3), 636–652 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Unser, M., Chenouard, N.: A unifying parametric framework for 2D steerable wavelet transforms. SIAM J. Imaging Sci. 6(1), 102–135 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Candes, E., Fernandez-Granda, C.: Towards a mathematical theory of super-resolution. arXiv preprint arXiv:1203.5871 (2012)Google Scholar
  9. 9.
    Candes, E., Fernandez-Granda, C.: Super-resolution from noisy data. arXiv preprint arXiv:1211.0290 (2012)Google Scholar
  10. 10.
    Marchant, R., Jackway, P.: Feature detection from the maximal response to a spherical quadrature filter set. In: Proc. Int. Conf. Digital Image Computing Techniques and Applications (December 2012)Google Scholar
  11. 11.
    Freeman, W.T., Adelson, E.H.: The design and use of steerable filters. IEEE Trans. Pattern Anal. Mach. Intell. 13(9), 891–906 (1991)CrossRefGoogle Scholar
  12. 12.
    Mühlich, M., Friedrich, D., Aach, T.: Design and Implementation of Multisteerable Matched Filters. IEEE Trans. Pattern Anal. Mach. Intell. 34(2), 279–291 (2012)CrossRefGoogle Scholar
  13. 13.
    Ward, J., Chaudhury, K., Unser, M.: Decay properties of Riesz transforms and steerable wavelets. arXiv preprint arXiv:1301.2525 (2013)Google Scholar
  14. 14.
    Boukerroui, D., Noble, J., Brady, M.: On the Choice of Band-Pass Quadrature Filters. J. Math. Imaging and Vision 21(1), 53–80 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ross Marchant
    • 1
    • 2
  • Paul Jackway
    • 2
  1. 1.James Cook UniversityAustralia
  2. 2.CSIRO Computational InformaticsAustralia

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