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

  • Max Langbein
  • Hans Hagen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5876)


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.


Scale Invariance Structure Tensor Gravity Center Invariant Moment Integral Invariant 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schlemmer, M., Heringer, M., Morr, F., Hotz, I., Hering-Bertram, M., Garth, C., Kollmann, W., Hamann, B., Hagen, H.: Moment invariants for the analysis of 2d flow fields. IEEE Transactions on Visualization and Computer Graphics 13, 1743–1750 (2007)CrossRefGoogle Scholar
  2. 2.
    Keren, D.: Using symbolic computation to find algebraic invariants. IEEE Trans. Pattern Anal. Mach. Intell. 16, 1143–1149 (1994)CrossRefGoogle Scholar
  3. 3.
    Pottmann, H., Wallner, J., Huang, Q.X., Yang, Y.L.: Integral invariants for robust geometry processing. Computer Aided Geometric Design 26, 37–59 (2009)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Schultz, T., Weickert, J., Seidel, H.P.: A higher-order structure tensor. Research Report MPI-I-2007-4-005, Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany (2007)Google Scholar
  5. 5.
    Özarslan, E., Vemuri, B.C., Mareci, T.H.: Generalized scalar measures for diffusion mri using trace, variance, and entropy. Magnetic resonance in Medicine 53, 866–867 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Max Langbein
    • 1
  • Hans Hagen
    • 1
  1. 1.TU Kaiserslautern 

Personalised recommendations