Multidimensional Systems and Signal Processing

, Volume 29, Issue 4, pp 1529–1552 | Cite as

Algebraic technique for computationally efficient Hahn moment invariants

  • Vishal Kumar Pandey
  • Jyotsna Singh
  • Harish Parthasarathy


In image processing applications such as scene analysis problems, moments are used as image descriptors of three dimensional objects. These moments may be sensitive to several transformations such as translation and scaling. Three-dimensional moment invariants are possible solution to such problems. Recently, Tchebichef and Krawtchouk moments and their invariants are proposed. These moment invariants are obtained using indirect method or image normalisation method. Perfect invariance cannot be achieved when moment invariants are not obtained from their corresponding polynomials. In this paper, the translation and scale invariance of Hahn moments for two and three dimensional symmetrical and non symmetrical images are derived directly from discrete orthogonal Hahn polynomials using algebraical method. This also enhances the computational efficiency in terms of processing time as compared to the method based on geometric moment invariants. The performance of proposed descriptor is evaluated using binary characters and 3D images. Hahn moment which is generalization of Tchebichef and Krawtchouk moment, give better results with translation and scale invariance and classification problems under clean and noisy image conditions.


Discrete orthogonal moment Hahn polynomial Scale invariant Translation invariant 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Vishal Kumar Pandey
    • 1
  • Jyotsna Singh
    • 1
  • Harish Parthasarathy
    • 1
  1. 1.Division of Electronics and Communication EngineeringNetaji Subhas Institute of TechnologyDwarkaIndia

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