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Junction Characterization Using Polar Pyramid

  • Weichuan Yu
  • Kostas Daniilidis
  • Gerald Sommer
Part of the Informatik aktuell book series (INFORMAT)

Abstract

In this paper we present a new approach in characterizing gray-value junctions. Due to the multiple intrinsic orientations present in junctions the response of a filter is needed at every orientation. As a rotation of the filter would considerably increase the computational burden alternative techniques like filter steerability have been proposed. Steerability relies in interpolating the response at an arbitrary orientation from the responses of some basis filters. Unfortunately, current steerability approaches suffer from the consequences of the uncertainty principle: In order to achieve high selectivity in orientation they need a huge number of basis filters increasing, thus, the computational complexity.

The new approach presented here achieves a higher orientational selectivity with a lower complexity. We consider the local polar map of the neighborhood of a junction where the new coordinates are the radius and the angle. Finding the gray-value transitions of a junction can be interpreted as ID edge detection. Hence, the orientational selectivity problem can be attacked by applying a pyramidal scheme. It is well known that it is always possible to reconstruct a signal using the sampling kernel as an interpolation function. Therefore, our approach can also steer the response of a Gaussian derivative to every orientation. The total algorithmic complexity encompasses the small support 2D-filtering for polar mapping and radial smoothing plus an ID-differentiation.

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References

  1. 1.
    D. H. Ballard and L. E. Wixson. Object recognition using steerable filters at multiple scales. In IEEE Workshop on Qualitative Vision, pages 2–10, 1993.CrossRefGoogle Scholar
  2. 2.
    J. Babaud, A. P. Witkin, M. Baudin and R. O. Duda. Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Trans. Pattern Analysis and Machine Intelligence, 8: 26–33, 1986.zbMATHCrossRefGoogle Scholar
  3. 3.
    P. J. Burt and E. H. Adelson. The Laplacian pyramid as a compact image code. IEEE Transactions on Communications, 31: 532–540, 1983.CrossRefGoogle Scholar
  4. 4.
    W. Yu, K. Daniilidis and G. Sommer. Rotated wedge averaging method for junction characterization. In the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’98), Santa Barbara, June 23–25, 1998.Google Scholar
  5. 5.
    W. Foerstner. A framework for low level feature extraction. In European Conf. on Computer Vision, volume II, pages 383–394, Stockholm, Sweden, May 2–6, J.O. Eklundh (Ed.), Springer LNCS 801, 1994.Google Scholar
  6. 6.
    W.T. Freeman and E.H. Adelson. The design and use of steerable filters. IEEE Trans. Pattern Analysis and Machine Intelligence, 13: 891–906, 1991.CrossRefGoogle Scholar
  7. 7.
    M. Michaelis and G. Sommer. Junction classification by multiple orientation detection. In European Conf. on Computer Vision, volume I, pages 101–108, Stockholm, Sweden, May 2–6, J.O. Eklundh (Ed.), Springer LNCS 800, 1994.Google Scholar
  8. 8.
    M. Michaelis and G. Sommer. A Lie group approach to steerable filters. Pattern Recognition Letters, 16: 1165–1174, 1995.CrossRefGoogle Scholar
  9. 9.
    P. Perona. Deformable kernels for early vision. IEEE Trans. Pattern Analysis and Machine Intelligence, 17 (5): 488–499, 1995.CrossRefGoogle Scholar
  10. 10.
    K. Rohr. Recognizing corners by fitting parametric models. International Journal of Computer Vision, 9 (3): 213–230, 1992.CrossRefGoogle Scholar
  11. 11.
    K. Rohr. On the precision in estimating the location of edges and corners. Journal of Mathematical Imaging and Vision, 7: 7–22, 1997.MathSciNetCrossRefGoogle Scholar
  12. 12.
    E. P. Simoncelli and H. Farid. Steerable wedge filters for local orientation analysis. IEEE Trans. Image Processing, 5 (9): 1377–1382, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Weichuan Yu
    • 1
  • Kostas Daniilidis
    • 1
  • Gerald Sommer
    • 1
  1. 1.Lehrstuhl für Kognitive SystemeChristian-Albrechts-UniversitätKielGermany

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