Harmonic Filters for Generic Feature Detection in 3D

  • Marco Reisert
  • Hans Burkhardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5748)


This paper proposes a concept for SE(3)-equivariant non-linear filters for multiple purposes, especially in the context of feature and object detection. The idea of the approach is to compute local descriptors as projections onto a local harmonic basis. These descriptors are mapped in a non-linear way onto new local harmonic representations, which then contribute to the filter output in a linear way. This approach may be interpreted as a kind of voting procedure in the spirit of the generalized Hough transform, where the local harmonic representations are interpreted as a voting function. On the other hand, the filter has similarities with classical low-level feature detectors (like corner/blob/line detectors), just extended to the generic feature/object detection problem. The proposed approach fills the gap between low-level feature detectors and high-level object detection systems based on the generalized Hough transform. We will apply the proposed filter to a feature detection task on confocal microscopical images of airborne pollen and compare the results to a 3D-extension of a popular GHT-based approach and to a classification per voxel solution.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Reisert, M., Burkhardt, H.: Equivariant holomorphic filters for contour denoising and rapid object detection. IEEE Trans. on Image Processing 17(2) (2008)Google Scholar
  2. 2.
    Reisert, M., Burkhardt, H.: Complex derivative filters. IEEE Trans. Image Processing 17(12), 2265–2274 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Reisert, M., Burkhardt, H.: Spherical tensor calculus for local adaptive filtering. In: Tensors in Image Processing and Computer Vision (2009)Google Scholar
  4. 4.
    Thurnhofer, S., Mitra, S.: A general framework for quadratic volterra filters for edge enhancment. IEEE Trans. Image Processing, 950–963 (1996)Google Scholar
  5. 5.
    Mathews, V.J., Sicuranza, G.: Polynomial Signal Processing. J.Wiley, New York (2000)Google Scholar
  6. 6.
    Freeman, W.T., Adelson, E.H.: The design and use of steerable filters. IEEE Trans. Pattern Anal. Machine Intell. 13(9), 891–906 (1991)CrossRefGoogle Scholar
  7. 7.
    Perona, P.: Deformable kernels for early vision. IEEE Trans. Pattern Anal. Machine Intell. 17(5), 488–499 (1995)CrossRefGoogle Scholar
  8. 8.
    Ballard, D.: Generalizing the hough transform to detect arbitrary shapes. Pattern Recognition 13(2), 111–122 (1981)CrossRefMATHGoogle Scholar
  9. 9.
    Lowe, D.: Distinct image features from scale-invariant keypoints. International Journal of Computer Vision 60, 91–110 (2004)CrossRefGoogle Scholar
  10. 10.
    Leibe, B., Leonardis, A., Schiele, B.: Combined object categorization and segmentation with an implicit shape model. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS. Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Mordohai, P.: Tensor Voting: A Perceptual Organization Approach to Computer Vision and Machine Learning. Morgan and Claypool, San Francisco (2006)Google Scholar
  12. 12.
    Rose, M.: Elementary Theory of Angular Momentum. Dover Publications (1995)Google Scholar
  13. 13.
    Miller, W., Blahut, R., Wilcox, C.: Topics in harmonic analysis with applications to radar and sonar. In: IMA Volumes in Mathematics and its Applications. Springer, New York (1991)Google Scholar
  14. 14.
    Lenz, R.: Group theoretical methods in Image Processing. Lecture Notes. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  15. 15.
    Ronneberger, O., Burkhardt, H., Schultz, E.: General-purpose Object Recognition in 3D Volume Data Sets using Gray-Scale Invariants. In: Proceedings of the International Conference on Pattern Recognition, Quebec, Canada. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  16. 16.
    Reisert, M.: Harmonic filters in 3d - theory and applications. Technical Report 1/09, IIF-LMB, Computer Science Department, University of Freiburg (2009)Google Scholar
  17. 17.
    Staal, J., Ginneken, B., Niemeijer, M., Viegever, A., Abramoff, M.: Ridge based vessel segmentation in color images of the retina. IEEE Trans. Med. Imaging 23(4), 501–509 (2004)CrossRefGoogle Scholar
  18. 18.
    Fehr, J., Ronneberger, O., Kurz, H., Burkhardt, H.: Self-learning segmentation and classification of cell-nuclei in 3D volumetric data using voxel-wise gray scale invariants. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds.) DAGM 2005. LNCS, vol. 3663, pp. 377–384. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Marco Reisert
    • 1
  • Hans Burkhardt
    • 2
    • 3
  1. 1.Dept. of Diagnostic Radiology, Medical PhysicsUniversity Medical CenterGermany
  2. 2.Computer Science DepartmentUniversity of FreiburgGermany
  3. 3.Centre for Biological Signaling Studies (bioss)University of FreiburgGermany

Personalised recommendations