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Adapted Jacobi Orthogonal Invariant Moments for Image Representation and Recognition

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Abstract

Images recognition and classification require an extraction technique of feature vectors of these images. These vectors must be invariant to the three geometric transformations: rotation, translation and scaling. Several authors used the theory of orthogonal moments to extract the feature vectors of images. Jacobi moments are orthogonal moments, which have been widely applied in imaging and pattern recognition. However, the invariance to rotation of Cartesian Jacobi moments is very difficult to obtain. In this paper, we obtain at first a set of transformed orthogonal Jacobi polynomials, called “Adapted Jacobi polynomials”. Based on these polynomials, a set of orthogonal moments is presented, named adapted Jacobi moments (AJMs). These moments are orthogonal on the rectangle \(\left[ {0, N\left] { \times } \right[0, M} \right],\) where \(N \times M\) is the size of the described image. We also provide a new series of feature vectors of images based on adapted Jacobi orthogonal invariants moments, which are a linear combination of geometric moment invariants, where the latest ones are invariant under rotation, translation and scaling of the described image. Based on k-NN algorithm, we apply a new 2D image classification system. We introduce a set of experimental tests in pattern recognition. The obtained results express the efficiency of our method. The performance of these feature vectors is compared with someones extracted from Hu, Legendre and Tchebichef invariant moments using three different 2D image databases: MPEG7-CE shape database, Columbia Object Image Library (COIL-20) database and ORL database. The results of the comparative study show the performance and superiority of our orthogonal invariant moments.

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Data Availability

The data used to support the findings of this study are available in [3, 13, 15].

References

  1. I. Batioua, R. Benouini, K. Zenkouar, A. Zahia, E. Hakim, 3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials. Pattern Recognit. 71, 264–277 (2017)

    Article  Google Scholar 

  2. H. Cheng, S.M. Chung, Action recognition from point cloud patches using discrete orthogonal moments. Multimed Tools Appl 77(7), 8213–8236 (2018)

    Article  Google Scholar 

  3. Coil-20: http://www.cs.columbia.edu/cave/software/softlib/coil- 20.php.

  4. M. El Mallahi, J. El Mekkaoui, A. Zouhri, H. Amakdouf, H. Qjidaa, Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments. Int. J. Autom. Comput. 15(2), 169–180 (2018)

    Article  Google Scholar 

  5. M. El Mallahi, A. Zouhri, J. El-Mekkaoui, H. Qjidaa, Three dimensional radial Tchebichef moment invariants for volumetric image recognition. Pattern Recognit. Image Anal. 27, 810–824 (2017)

    Article  Google Scholar 

  6. Gábor Szegő, Orthogonal Polynomials, AMS Colloquium Publications Vol. 23, Providence, Rhode Island 2000

  7. A. Hjouji, M. Jourhmane, J. EL-Mekkaoui, H. Qjidaa, A. EL Khalfi, Image clustering based on hermetian positive definite matrix and radial Jacobi moments. In: International Conference on Intelligent Systems and Computer Vision (ISCV), pp. 17751499 (2018)

  8. A. Hmimid, M. Sayyouri, H. Qjidaa, Fast computation of separable two-dimensional discrete invariant moments for image classification. Pattern Recognit. 48(2), 509–521 (2015)

    Article  Google Scholar 

  9. K.M. Hosny, Image representation using accurate orthogonal Gegenbauer moments. Pattern Recognit. Lett. 32(6), 795–804 (2011)

    Article  Google Scholar 

  10. K.M. Hosny, New set of Gegenbauer moment invariants for pattern recognition applications. Arab J Sci Eng 3, 7097–7107 (2014)

    Article  Google Scholar 

  11. M.K. Hu, Visual pattern recognition by moment invariants. IRE Trans. Inform. Theory 8(2), 179–187 (1962)

    Article  Google Scholar 

  12. J.M. Keller, R.G. Michael, J.A. Givens, A fuzzy K-nearest neighbor algorithm. IEEE Trans. Syst. Man Cybern. 15(4), 580–585 (1985)

    Article  Google Scholar 

  13. MPEG-7-CE: http://www.dabi.temple.edu/shape/mpeg7/dataset.html

  14. R. Mukundan, S.H. Ong, P.A. Lee, Image analysis by Tchebichef moments. IEEE Trans. Image Process 10(9), 1357–1364 (2001)

    Article  MathSciNet  Google Scholar 

  15. ORL: http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase. Html

  16. G.A. Papakostas, E.G. Karakasis, D.E. Koulouriotis, Novel moment invariants for improved classification performance in computer vision applications. Pattern Recognit. 43(1), 58–68 (2010)

    Article  Google Scholar 

  17. S. Tan, Neighbour-weighted K-nearest neighbour for unbalanced text corpus. Expert Syst. Appl. 8(4), 667–671 (2005)

    Article  Google Scholar 

  18. M.R. Teague, Image analysis via the general theory of moments. J. Opt. Soc. Am. 70(8), 920–930 (1980)

    Article  MathSciNet  Google Scholar 

  19. C.H. Teh, R.T. Chin, On digital approximation of moment in invariants. Comput. Vision Graph. Image Process. 33(3), 318–326 (1986)

    Article  Google Scholar 

  20. C.H. Teh, R.T. Chin, On image analysis by the methods of moments. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 496–513 (1988)

    Article  Google Scholar 

  21. B. Xiao, L. Li, Y. Li, W. Li, G. Wang, Image analysis by fractional-order orthogonal moments. Inf. Sci. 382–383, 135–149 (2017)

    Article  Google Scholar 

  22. B. Xiao, G. Wang, W. Li, Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis. Comput. 32(12), 994–1006 (2014)

    Article  Google Scholar 

  23. J. Yang, L. Zhang, T.Y. Yan, Mellin polar coordinate moment and its affine invariance. Pattern Recognit. 85, 37–49 (2019)

    Article  Google Scholar 

  24. P.T. Yap, R. Paramesran, S.H. Ong, Image analysis by Krawtchouk moments. IEEE Trans. Image Process. 12(1), 1367–1377 (2003)

    MathSciNet  Google Scholar 

  25. H. Zhang, H.Z. Shu, G.N. Han, G. Coatrieu, L. Luo, J.L. Coatrieux, Blurred image recognition by Legendre moment invariants. Image Process. IEEE Trans. Image Process. 19(3), 596–611 (2010)

    Article  MathSciNet  Google Scholar 

  26. H. Zhu, Image representation using separable two-dimensional continuous and discrete orthogonal moments. Pattern Recognit. 45(4), 1540–1558 (2012)

    Article  Google Scholar 

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Acknowledgements

The essay’s authors express their deepest gratitude to the Editor-in-Chief and other reviewers and acknowledge their valuable comments and contributions.

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The authors received no specific funding for this work.

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Authors and Affiliations

  1. TIAD Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Amal Hjouji & Rachid Chakid

  2. Transmission and Information Processing Laboratory, EST, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Jaouad El-Mekkaoui

  3. CED-ST, LESSI, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Hassan Qjidaa

Authors
  1. Amal Hjouji
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  2. Rachid Chakid
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  3. Jaouad El-Mekkaoui
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  4. Hassan Qjidaa
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Correspondence to Amal Hjouji.

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Hjouji, A., Chakid, R., El-Mekkaoui, J. et al. Adapted Jacobi Orthogonal Invariant Moments for Image Representation and Recognition. Circuits Syst Signal Process 40, 2855–2882 (2021). https://doi.org/10.1007/s00034-020-01600-w

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