Multimedia Tools and Applications

, Volume 77, Issue 20, pp 27517–27542 | Cite as

Efficient 3D object classification by using direct Krawtchouk moment invariants

  • Rachid BenouiniEmail author
  • Imad Batioua
  • Khalid Zenkouar
  • Said Najah
  • Hassan Qjidaa


In this paper, we present an efficient set of moment invariants, named Direct Krawtchouk Moment Invariants (DKMI), for 3D objects recognition. This new set of invariants can be directly derived from the Krawtchouk moments, based on algebraic properties of Krawtchouk polynomials. The proposed computation approach is effectively compared with the classical method, which rely on the indirect computation of moment invariants by using the corresponding geometric moment invariants. Several experiments are carried out so as to evaluate the performance of the newly introduced invariants. Invariability property and noise robustness are firstly investigated. Secondly, the numerical stability is discussed. Then, the performance of the proposed moment invariants as pattern features for 3D object classification is compared with the existing Geometric, Krawtchouk, Tchebichef and Hahn Moment Invariants. Finally, a comparative analysis of computational time of these moment invariants is illustrated. The obtained results demonstrate the efficiency and the superiority of the proposed method.


Moment invariants Krawtchouk moments Direct method Indirect method 3D object classification Numerical stability 



Direct Krawtchouk Moment Invariants


Tchebichef Moment Invariants


Krawtchouk Moment Invariants


Hahn Moment Invariants


Geometric Moment Invariantsx


Time Reduction Rate


Region Of Interest


Rotation, Scaling and Translation



The authors thankfully acknowledge the Laboratory of Intelligent Systems and Applications (LSIA) for his support to achieve this work.

Funding Information

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Compliance with Ethical Standards

Conflict of interests

The authors declare no conflict of interest.


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Authors and Affiliations

  1. 1.Laboratory of Intelligent Systems and Application (LSIA), Faculty of Sciences and TechnologyUniversity Sidi Mohamed Ben AbdellahFezMorocco
  2. 2.LESSI, Faculty of Sciences Dhar el MehrazSidi Mohamed Ben Abdellah UniversityFezMorocco

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