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A New Shape Space for Second Order 3D-Variations

  • Per-Erik Danielsson
  • Qingfen Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2059)

Abstract

A common model of second degree variation is an ellipsoid spanned by the magnitudes of the Hessian eigenvalues. We find this model incomplete and often misleading. Here, we present a more complete representation of the information embedded in second degree derivatives. Using spherical harmonics as a basis set, the rotation invariant part of this information is portrayed as an orthonormal shape-space, which is non-redundant in the sense that any local second order variation can be rotated to match one and only one unique prototype in this space. A host of truly rotation invariant and shape discriminative shape factors is readily defined.

Keywords

Spherical Harmonic Shape Space Signal Space Response Vector Double Cone 
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.

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References

  1. 1.
    Lorenz, C., Carlsen, I.-C., Buzug, T.M., Fassnacht, C., Weese, J.: A Multi-Scale Line Filter with Automatic Scale Selection Based on the Hessian Matrix for Medical Image Segmentation. Lecture Notes in Computer Science, Vol. 1252, Springer (1997) 152–163Google Scholar
  2. 2.
    Sato, Y., Westin, C.F., Bhalero, A., Nakajima, S., Shiraga, N., Tamura, S., Kikinis, R.: Tissue Classification Based on 3D Local Intensity Structures. IEEE Trans. Visualization and Computer Graphics, 6 (2000) 160–180CrossRefGoogle Scholar
  3. 3.
    Frangi, A. Niessen, W., Vincken, K., Viergever, M.: Multi-Scale Vessel Enhancement Filtering. In: Wells, W., Colchester, A., Delp, S. (eds.): Medical Image Computing and Computer-Assisted Intervention-MICCAI’98. Lecture Notes in Computer Science, Vol. 1496. Springer (1998) 130–137Google Scholar
  4. 4.
    Kindlmann, G., Weinstein, D., Hart, D.: Strategies for Direct Volume Rendering of Diffusion Tensor Fields. IEEE Transactions on Visualization and Computer Graphics, 6 (2000) 124–138CrossRefGoogle Scholar
  5. 5.
    Knutsson, H., Representing Local Structure with Tensors. Proc. of 6th Scandinavian Conference on Image Analysis, Oulu, Finland (1989) 244–251Google Scholar
  6. 6.
    Basser, P.: Inferring Micro-Structural Features and the Physiological State of Tissues from Diffusion-Weighted Images. NMR in Biomedicine, Vol. 8 (1995) 333–344CrossRefGoogle Scholar
  7. 7.
    Andersson, L. E.: Fourier Transforms of RIO’s of Any Order. Appendix 1 in Report LiTHISY-1238, Dept of EE, Linköping Univ., SE-58183, Sweden (1991)Google Scholar
  8. 8.
    Danielsson, P.E., Lin, Q., Ye, Q.-Z.: Efficient Detection of Second Degree Variations in 2D and 3D Images. To appear in Journal of Visual Communications and Image Representation (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Per-Erik Danielsson
    • 1
  • Qingfen Lin
    • 1
  1. 1.Department of Electrical EngineeringLinkoping UniversitySweden

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