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A Generalization of Moment Invariants on 2D Vector Fields to Tensor Fields of Arbitrary Order and Dimension

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Book cover Advances in Visual Computing (ISVC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5876))

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Abstract

For object recognition in tensorfields and in pointclouds, the recognition of features in the object irrespective of their rotation is an important task. Rotationally invariant features exist for 2d scalar fields and for 3d scalar fields as moments of a second order structure tensor. For higher order structure tensors iterative algorithms for computing something similar to an eigenvector-decomposition exist. In this paper, we introduce a method to compute a basis for analytical rotationally invariant moments of tensorfields of – in principle – any order and dimension and give an example using up to 4th-order structure tensors in 3d.

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References

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Author information

Authors and Affiliations

  1. TU Kaiserslautern,  

    Max Langbein & Hans Hagen

Authors
  1. Max Langbein
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  2. Hans Hagen
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama-shi, 338-8570, 338-8570, Japan

    Yoshinori Kuno

  6. Microsoft Research, Redmond, WA, USA

    Junxian Wang

  7. Univ. of Zurich, Department of Informatics, Winterthurerstr. 190, P.O. Box, 8057, Zurich, Switzerland

    Renato Pajarola

  8. Lawrence Livermore National Laboratory, 94550, Livermore, CA, USA

    Peter Lindstrom

  9. University of Applied Sciences Bonn-Rhein-Sieg, 53754, Sankt Augustin, Germany

    André Hinkenjann

  10.  ,  

    Miguel L. Encarnação

  11. SCI Institute & School of Computing, University of Utah, 84112, Salt Lake City, UT, USA

    Cláudio T. Silva

  12. Desert Research Institute, 89512, Reno, NV, USA

    Daniel Coming

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© 2009 Springer-Verlag Berlin Heidelberg

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Langbein, M., Hagen, H. (2009). A Generalization of Moment Invariants on 2D Vector Fields to Tensor Fields of Arbitrary Order and Dimension. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2009. Lecture Notes in Computer Science, vol 5876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10520-3_110

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  • DOI: https://doi.org/10.1007/978-3-642-10520-3_110

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10519-7

  • Online ISBN: 978-3-642-10520-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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