Journal of Mathematical Imaging and Vision

, Volume 44, Issue 3, pp 223–235 | Cite as

Geometric Moments and Their Invariants

  • Mark S. Hickman


Moments and their invariants have been extensively used in computer vision and pattern recognition. There is an extensive and sometimes confusing literature on the computation of a basis of functionally independent moments up to a given order. Many approaches have been used to solve this problem albeit not entirely successfully. In this paper we present a (purely) matrix algebra approach to compute both orthogonal and affine invariants for planar objects that is ideally suited to both symbolic and numerical computation of the invariants. Furthermore we generate bases for both systems of invariants and, in addition, our approach generalises to higher dimensional cases.


Orthogonal and affine transformations Moments Invariants Covariants Image recognition 



I would like to thank the Galaad group at INRIA Sophia Antipolis for hosting me while this work was completed. In particular, I would like to thank Evelyne Hubert for fruitful discussions on this material and for running her code and comparing its output with the basis given in this paper.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of CanterburyChristchurchNew Zealand

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