Orientation Fields Filtering by Derivates of a Gaussian

  • Josef Bigun
  • Tomas Bigun
  • Kenneth Nilsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2749)


We suggest a set of complex differential operators, symmetry derivatives, that can be used for matching and pattern recognition. We present results on the invariance properties of these. These show that all orders of symmetry derivatives of Gaussians yield a remarkable invariance : they are obtained by replacing the original differential polynomial with the same polynomial but using ordinary scalars. Moreover, these functions are closed under convolution and they are invariant to the Fourier transform. The revealed properties have practical consequences for local orientation based feature extraction. This is shown by two applications: i) tracking markers in vehicle tests ii) alignment of fingerprints.


Pattern Recognition Computer Vision Feature Extraction Differential Operator Computer Graphic 
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.


  1. 1.
    Bigun, J., Granlund, G.H.: Optimal orientation detection of linear symmetry. In: First International Conference on Computer Vision, ICCV (London), Washington, DC, IEEE Computer Society Press (1987) 433–438Google Scholar
  2. 2.
    Kass, M., Witkin, A.: Analyzing oriented patterns. Computer Vision, Graphics, and Image Processing 37 (1987) 362–385CrossRefGoogle Scholar
  3. 3.
    Rao, A.R.: A taxonomy for texture description and identification. Springer (1990)Google Scholar
  4. 4.
    Forstner, W., Gulch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: intercommission conference on fast processing of photogrammetric data, interlaken. (1987) 281–305Google Scholar
  5. 5.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Proceedings of the 4’th Alvey Vision Conference, September. (1988) 147–151Google Scholar
  6. 6.
    Knutsson, H., Hedlund, M., Granlund, G.H.: Apparatus for determining the degree of consistency of a feature in a region of an image that is divided into discrete picture elements. In: US. patent, 4.747.152. (1988)Google Scholar
  7. 7.
    Bigun, J.: Recognition of local symmetries in gray value images by harmonic functions. In: Ninth International Conference on Pattern Recognition, Rome, IEEE Computer Society Press (1988) 345–347CrossRefGoogle Scholar
  8. 8.
    Johansson, B.: multiscale curvature detection in computer vision. Tekn. Lic. thesis, Linkoping University, Dep. Electrical Eng., SE-581 83 (2001)Google Scholar
  9. 9.
    Marr, D., Hildreth, E.: Theory of edge detection. Proc. Royal Society of London Bulletin 204 (1979) 301–328CrossRefGoogle Scholar
  10. 10.
    Wilson, R., Spann, M.: Finite prolate spheroidal sequences and their applications ii: Image feature description and segmentntation. IEEE-PAMI 10 (1988) 193–203Google Scholar
  11. 11.
    Freeman, W.T., Adelson, E.H.: The design and use of steerable filters. IEEE-PAMI 13 (1991) 891–906Google Scholar
  12. 12.
    Koenderink, J.J., van Doom, A.J.: The structure of images. Biological cybernetics 50 (1984) 363–370zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Bigun, J., Bigun, T.: Symmetry derivatives of gaussians illustrated by cross tracking. Technical Report HH-IDE-131, Halmstad University, S-30118 Halmstad (2001)Google Scholar
  14. 14.
    Danielsson, P.E., Ye, Q.Z.: Efficient detection of second-degree variations in 2d and 3d images. Visual Communication and Image Representation 12 (2001) 255–305CrossRefGoogle Scholar
  15. 15.
    Perona, P.: Steerable-scalable kernels for edge detection and junction analysis. In Sandini, G., ed.: Proceedings of Computer Vision (ECCV’ 92). Volume 588 of LNCS., Berlin, Germany, Springer (1992) 3–18Google Scholar
  16. 16.
    Black, M.J., Anandan, P.: A framework for the robust estimation of optical flow. In: ICCV-93, Berlin, IEEE Computer Society press (1993) 231–236CrossRefGoogle Scholar
  17. 17.
    Maio, D., Maltoni, D., Cappelli, R., Wayman, J., Jain, A.K.: Fvc 2000: Fingerprint verification competition. IEEE-PAMI 24 (2002) 402–412Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Josef Bigun
    • 1
  • Tomas Bigun
    • 2
  • Kenneth Nilsson
    • 1
  1. 1.Halmstad UniversityHalmstadSweden
  2. 2.TietoEnator ArosTechLinkpingSweden

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