Journal of Mathematical Imaging and Vision

, Volume 49, Issue 1, pp 251–271 | Cite as

Error Analysis in the Computation of Orthogonal Rotation Invariant Moments

  • Chandan Singh
  • Rahul Upneja


Orthogonal rotation invariant moments (ORIMs) are among the best region based shape descriptors. Being orthogonal and complete, they possess minimum information redundancy. The magnitude of moments is invariant to rotation and reflection and with some geometric transformation, they can be made translation and scale invariant. Apart from these characteristics, they are robust to image noise. These characteristics of ORIMs make them suitable for many pattern recognition and image processing applications. Despite these characteristics, the ORIMs suffer from many digitization errors, thus they are incapable of representing subtle details in image, especially at high orders of moments. Among the various errors, the image discretization error, geometric and numerical integration errors are the most prominent ones. This paper investigates the contribution and effects of these errors on the characteristics of ORIMs and performs a comparative analysis of these errors on the accurate computation of the three major ORIMs: Zernike moments (ZMs), Pseudo Zernike moments (PZMs) and orthogonal Fourier-Mellin moments (OFMMs). Detailed experimental analysis reveals some interesting results on the performance of these moments.


Orthogonal rotation invariant moments Zernike moments Pseudo Zernike moments Orthogonal Fourier Mellin moments Numerical integration Image reconstruction 



The useful comments and suggestions of the anonymous reviewers to raise the standard of the paper are highly appreciated. The research fellowship awarded to one of the authors (Rahul Upneja) by the Council of Scientific and Industrial Research (C.S.I.R.), Govt. of India, is also highly acknowledged.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Computer SciencePunjabi UniversityPatialaIndia
  2. 2.Department of MathematicsSri Guru Granth Sahib World UniversityFatehgarh SahibIndia

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