Moment Invariants for Multi-Dimensional Data

  • Roxana BujackEmail author
  • Hans Hagen
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Moment invariants have long been successfully used for pattern matching in scalar fields. By their means, features can be detected in a data set independent of their exact orientation, position, and scale. Their recent extension to vector fields was the first step towards rotation invariant pattern detection in multi-dimensional data.

In this paper, we propose an algorithm that extends the normalization approach to tensor fields of arbitrary rank in two and three dimensions.



We would like to thank the FAnToM development group from Leipzig University for providing the environment for the visualization of the presented work. Further, we thank Professor Mario Hlawitschka for providing the dataset used in this publication and Terece Turton for help with the writing. This work was partly funded by the German Research Foundation (DFG) as part of the IRTG 2057 “Physical Modeling for Virtual Manufacturing Systems and Processes”.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Technical University KaiserslauternKaiserslauternGermany

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