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A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition

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Abstract

Orthogonal moments are the projections of image functions on particular functions of the kernel. They play an essential role in image extraction: rotation, scaling, translation invariance, object recognition, image classification, image noise robustness, and low information redundancy. These moments are derived from orthogonal polynomials that can be continuous or discrete. This paper focuses on the fractional-order modified generalized Laguerre moment invariants (FMGLMIs), which is a generalization of the traditional integer order one. In this research, we have developed a new algorithm to compute the 3D invariant moments of FMGLMIs based on the 3D image cuboid representation, our proposed calculation method can improve the efficiency of 3D invariant moment calculation to maintain numerical stability and significantly reduce calculation time with very satisfactory accuracy. To check this new algorithm, the calculation of 3D invariant moments gives very encouraging results for the invariability property of the proposed method with respect to different geometric transformations and noise degradations of 3D images, classification and recognition of 3D images and the calculation time of fractional-order invariants proposed. Finally, the experimental results show that the proposed method makes it possible to construct fractional-order modified generalized Laguerre invariant moments offering better performances for image analysis and pattern recognition.

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Abbreviations

CGLM:

Classical generalized Laguerre moments

FMGLPs:

Fractional-order modified generalized Laguerre polynomials

FGLM:

Fractional-order modified generalized Laguerre moments

FGGMI:

Fractional-order generalized geometric moment invariants

FMGLMI:

Fractional-order modified generalized Laguerre moment invariants

RST:

Rotation, scaling and translation

ICR:

Images cuboid representation

FDE:

Fractional differential equations

GMI:

Geometric moment invariants

CMI:

Chebychev moment invariants

GegMI:

Gegenbauer moment invariants

JMI:

Jacobi moment invariants

GHMI:

Gauss–Hermite moment invariants

FC-FMGLMI-ICR:

Fast computation of the fractional-order modified generalized Laguerre moment invariants by images cuboid representation

References

  • Baleanu, D., Bhrawy, A. H., & Taha, T. M. (2013). A modified generalized Laguerre spectral method for fractional differential equations on the half line. Abstract and Applied Analysis, 2013, 1–12. https://doi.org/10.1155/2013/413529.

    Article  MathSciNet  MATH  Google Scholar 

  • Batioua, I., Benouini, R., Zenkouar, K., & Zahi, A. (2017). 3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials. Pattern Recognition, 71, 264–277.

    Article  Google Scholar 

  • Bharathi, V. S., & Ganesan, L. (2008). Orthogonal moments based texture analysis of CT liver images. Pattern Recognition Letters, 29(13), 1868–1872.

    Article  Google Scholar 

  • Bhrawy, A. H., Alghamdi, M. M., & Taha, T. M. (2012). A new modified generalized Laguerre operational matrix of fractional integration for solving fractional differential equations on the half line. Advances in Difference Equations, 2012(1), 179. https://doi.org/10.1186/1687-1847-2012-179.

    Article  MathSciNet  MATH  Google Scholar 

  • Bhrawy, A., Alhamed, Y., Baleanu, D., & Al-Zahrani, A. (2014). New spectral techniques for systems of fractional differential equations using fractional-order generalized Laguerre orthogonal functions. Fractional Calculus and Applied Analysis, 17(4), 1137–1157. https://doi.org/10.2478/s13540-014-0218-9.

    Article  MathSciNet  MATH  Google Scholar 

  • Camacho-Bello, C., Toxqui-Quitl, C., Padilla-Vivanco, A., & Báez-Rojas, J. J. (2014). High-precision and fast computation of Jacobi–Fourier moments for image description. JOSA A, 31(1), 124–134.

    Article  Google Scholar 

  • Dai, X. B., Shu, H. Z., Luo, L. M., Han, G. N., & Coatrieux, J. L. (2010). Reconstruction of tomographic images from limited range projections using discrete Radon transform and Tchebichef moments. Pattern Recognition, 43(3), 1152–1164.

    Article  Google Scholar 

  • Daoui, A., Yamni, M., Karmouni, H., Sayyouri, M., & Qjidaa, H. (2019). 2D and 3D medical image analysis by discrete orthogonal moments. Procedia Computer Science, 148, 428–437.

    Article  Google Scholar 

  • Flusser, J., & Suk, T. (1993). Pattern recognition by affine moment invariants. Pattern Recognition, 26(1), 167–174.

    Article  MathSciNet  Google Scholar 

  • Flusser, J., Suk, T., & Zitová, B. (2016). 2D and 3D image analysis by moments. New York: Wiley.

    Book  Google Scholar 

  • Heywood, M. I., & Noakes, P. D. (1995). Fractional central moment method for movement-invariant object classification. IEE Proceedings-Vision, Image and Signal Processing, 142(4), 213–219.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Höschl, C., IV, & Flusser, J. (2016). Robust histogram-based image retrieval. Pattern Recognition Letters, 69, 72–81.

    Article  Google Scholar 

  • Hosny, K. M. (2012). Fast computation of accurate Gaussian-Hermite moments for image processing applications. Digital Signal Processing, 22(3), 476–485.

    Article  MathSciNet  Google Scholar 

  • Hosny, K. M. (2014). New set of Gegenbauer moment invariants for pattern recognition applications. Arabian Journal for Science and Engineering, 39(10), 7097–7107.

    Article  Google Scholar 

  • Hosny, K. M., Darwish, M. M., & Eltoukhy, M. M. (2020). New fractional-order shifted Gegenbauer moments for image analysis and recognition. Journal of Advanced Research, 25, 57–66. https://doi.org/10.1016/j.jare.2020.05.024.

    Article  Google Scholar 

  • Hu, M.-K. (1962). Visual pattern recognition by moment invariants. IRE Transactions on Information Theory, 8(2), 179–187.

    Article  Google Scholar 

  • Jahid, T., Karmouni, H., Sayyouri, M., Hmimid, A., & Qjidaa, H. (2019). Fast algorithm of 3D discrete image orthogonal moments computation based on 3D cuboid. Journal of Mathematical Imaging and Vision, 61(4), 534–554.

    Article  MathSciNet  Google Scholar 

  • Karakasis, E. G., Amanatiadis, A., Gasteratos, A., & Chatzichristofis, S. A. (2015). Image moment invariants as local features for content based image retrieval using the bag-of-visual-words model. Pattern Recognition Letters, 55, 22–27.

    Article  Google Scholar 

  • Karmouni, H., Jahid, T., Hmimid, A., Sayyouri, M., & Qjidaa, H. (2019a). Fast computation of inverse Meixner moments transform using Clenshaw’s formula. Multimedia Tools and Applications, 78(22), 31245–31265.

    Article  Google Scholar 

  • Karmouni, H., Jahid, T., Sayyouri, M., Hmimid, A., & Qjidaa, H. (2019b). Fast reconstruction of 3D images using Charlier discrete orthogonal moments. Circuits, Systems, and Signal Processing, 38(8), 3715–3742.

    Article  Google Scholar 

  • Khotanzad, A., & Hong, Y. H. (1990). Invariant image recognition by Zernike moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5), 489–497.

    Article  Google Scholar 

  • Koekoek, R., Lesky, P. A., & Swarttouw, R. F. (2010). Hypergeometric orthogonal polynomials and their q-analogues. New York: Springer.

    Book  Google Scholar 

  • Koekoek, R., & Meijer, H. G. (1993). A generalization of Laguerre polynomials. SIAM Journal on Mathematical Analysis, 24(3), 768–782.

    Article  MathSciNet  Google Scholar 

  • Liao, S., Chiang, A., Lu, Q., & Pawlak, M. (2002). Chinese character recognition via Gegenbauer moments. In Object recognition supported by user interaction for service robots (Vol. 3, pp. 485–488). IEEE.

  • McGill 3D Shape Benchmark. http://www.cim.mcgill.ca/~shape/benchMark/ (consulté le mai 15, 2020).

  • Mukundan, R., & Ramakrishnan, K. R. (1998). Moment functions in image analysis: Theory and applications. Singapore: World Scientific.

    Book  Google Scholar 

  • Pandey, V. K., Singh, J., & Parthasarathy, H. (2018). Fractional order tchebichef moment and its invariants. In 2018 2nd IEEE international conference on power electronics, intelligent control and energy systems (ICPEICES) (pp. 1078–1082). IEEE.

  • Pee, C. Y., Ong, S. H., & Raveendran, P. (2017). Numerically efficient algorithms for anisotropic scale and translation Tchebichef moment invariants. Pattern Recognition Letters, 92, 68–74.

    Article  Google Scholar 

  • Ping, Z., Ren, H., Zou, J., Sheng, Y., & Bo, W. (2007). Generic orthogonal moments: Jacobi-Fourier moments for invariant image description. Pattern Recognition, 40(4), 1245–1254.

    Article  Google Scholar 

  • Qader, H. A., Ramli, A. R., & Al-Haddad, S. A. R. (2007). Fingerprint recognition using Zernike moments. The International Arab Journal of Information Technology, 4(4), 372–376.

    Google Scholar 

  • Rao, C., Kumar, S. S., & Mohan, B. C. (2010). Content based image retrieval using exact legendre moments and support vector machine. ArXiv Prepr. ArXiv10055437.

  • Sayyouri, M., Hmimid, A., Karmouni, H., Qjidaa, H., & Rezzouk, A. (2015). Image classification using separable invariant moments of Krawtchouk-Tchebichef. In 2015 IEEE/ACS 12th international conference of computer systems and applications (AICCSA) (pp. 1–6). IEEE.

  • Sayyouri, M., Hmimid, A., & Qjidaa, H. (2013). Improving the performance of image classification by Hahn moment invariants. JOSA A, 30(11), 2381–2394. https://doi.org/10.1364/josaa.30.002381.

    Article  MATH  Google Scholar 

  • Sayyouri, M., Hmimid, A., & Qjidaa, H. (2015b). A fast computation of novel set of Meixner invariant moments for image analysis. Circuits, Systems, and Signal Processing, 34(3), 875–900. https://doi.org/10.1007/s00034-014-9881-7.

    Article  MATH  Google Scholar 

  • Sayyouri, M., Hmimid, A., & Qjidaa, H. (2016). Image analysis using separable discrete moments of Charlier–Hahn. Multimedia Tools and Applications, 75(1), 547–571. https://doi.org/10.1007/s11042-014-2307-5.

    Article  MATH  Google Scholar 

  • Shao, Z., Shang, Y., Zhang, Y., Liu, X., & Guo, G. (2016). Robust watermarking using orthogonal Fourier–Mellin moments and chaotic map for double images. Signal Processing, 120, 522–531.

    Article  Google Scholar 

  • Shu, H. Z., Luo, L. M., Yu, W. X., & Fu, Y. (2000). A new fast method for computing Legendre moments. Pattern Recognition, 33(2), 341–348.

    Article  Google Scholar 

  • Tabbone, S., Terrades, O. R., & Barrat, S. (2008). Histogram of Radon Transform. A useful descriptor for shape retrieval. In 2008 19th International conference on pattern recognition (pp. 1–4). IEEE.

  • Teague, M. R. (1980). Image analysis via the general theory of moments. JOSA, 70(8), 920–930.

    Article  MathSciNet  Google Scholar 

  • Teh, C. H., & Chin, R. T. (1988). On image analysis by the methods of moments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), 496–513.

    Article  Google Scholar 

  • Xiao, B., Cui, J. T., Qin, H. X., Li, W. S., & Wang, G. Y. (2015). Moments and moment invariants in the Radon space. Pattern Recognition, 48(9), 2772–2784.

    Article  Google Scholar 

  • Xiao, B., Li, L., Li, Y., Li, W., & Wang, G. (2017). Image analysis by fractional-order orthogonal moments. Information Sciences, 382, 135–149. https://doi.org/10.1016/j.ins.2016.12.011.

    Article  MATH  Google Scholar 

  • Xiao, B., Luo, J., Bi, X., Li, W., & Chen, B. (2020). Fractional discrete Tchebyshev moments and their applications in image encryption and watermarking. Information Sciences, 516, 545–559.

    Article  MathSciNet  Google Scholar 

  • Xiao, B., Ma, J. F., & Wang, X. (2010). Image analysis by Bessel–Fourier moments. Pattern Recognition, 43(8), 2620–2629.

    Article  Google Scholar 

  • Xiao, B., Zhang, Y., Li, L., Li, W., & Wang, G. (2016). Explicit Krawtchouk moment invariants for invariant image recognition. Journal of Electronic Imaging, 25(2), 023002.

    Article  Google Scholar 

  • Yamni, M., et al. (2020). Fractional Charlier moments for image reconstruction and image watermarking. Signal Processing, 171, 107509.

    Article  Google Scholar 

  • Yan, J. P., & Guo, B. Y. (2011). A collocation method for initial value problems of second-order ODEs by using Laguerre functions. Numerical Mathematics: Theory, Methods and Applications, 4(2), 283–295.

    MathSciNet  MATH  Google Scholar 

  • Yang, M., Bian, Y., Yang, J., & Liu, G. (2018). Combustion state recognition of flame images using radial Chebyshev moment invariants coupled with an IFA-WSVM model. Applied Sciences, 8(11), 2331.

    Article  Google Scholar 

  • Yang, B., Flusser, J., & Suk, T. (2015). 3D rotation invariants of Gaussian-Hermite moments. Pattern Recognition Letters, 54, 18–26.

    Article  Google Scholar 

  • Yap, P. T., Raveendran, P., & Ong, S. H. (2001). Chebyshev moments as a new set of moments for image reconstruction. In IJCNN’01. International joint conference on neural networks. Proceedings (Cat. No. 01CH37222) (Vol. 4, pp. 2856–2860). IEEE.

  • Yuan, X. C., Pun, C. M., & Chen, C. L. P. (2013). Geometric invariant watermarking by local Zernike moments of binary image patches. Signal Processing, 93(7), 2087–2095.

    Article  Google Scholar 

  • Zhang, H., Li, Z., & Liu, Y. (2016). Fractional orthogonal Fourier-Mellin moments for pattern recognition. In Chinese conference on pattern recognition (pp. 766–778). Singapore: Springer.

  • Zhu, H., Liu, M., Shu, H., Zhang, H., & Luo, L. (2010). General form for obtaining discrete orthogonal moments. IET Image Processing, 4(5), 335–352.

    Article  MathSciNet  Google Scholar 

  • Zhu, H., Shu, H., Liang, J., Luo, L., & Coatrieux, J. L. (2007). Image analysis by discrete orthogonal Racah moments. Signal Processing, 87(4), 687–708.

    Article  Google Scholar 

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Authors and Affiliations

  1. CED-ST, STIC, Laboratory of Electronic Signals and Systems of Information LESSI, Faculty of Science Dhar El Mahrez, University Sidi Mohamed Ben Abdellah, Fez, Morocco

    O. El ogri, M. Yamni, A. Daoui & H. Qjidaa

  2. Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, BP 72, My Abdallah Avenue Km. 5 Imouzzer Road, Fez, Morocco

    H. Karmouni & M. Sayyouri

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  1. O. El ogri
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  2. H. Karmouni
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El ogri, O., Karmouni, H., Yamni, M. et al. A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition. Multidim Syst Sign Process 32, 431–464 (2021). https://doi.org/10.1007/s11045-020-00745-w

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