[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

A fast and accurate computation of 2D and 3D generalized Laguerre moments for images analysis

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this paper, we will present a new set of 2D and 3D continuous orthogonal moments based on generalized Laguerre orthogonal polynomials (GLPs) for 2D and 3D image analysis. However, the computation of the generalized Laguerre orthogonal moments (GLMs) is limited by the problems of discretization of the continuous space of the polynomials, approximation of the integrals by finite sums and of too high computation time. To remedy these problems, we will propose a new method for the fast and the precise computation of 2D and 3D GLMs. This method is based on the development of an exact calculation of the double and triple integrals which define the 2D and 3D GLMs, and on the matrix calculation to accelerate the processing time of the images instead of the direct calculation. In addition to the theoretical results obtained, several experiments are carried out to validate the efficiency of the 2D and 3D GLMs descriptors in terms of computation precision and accuracy and in terms of acceleration of computation time and 2D/3D image reconstruction. The experimental results clearly show the advantages and the effectiveness of GLMs compared to the continuous orthogonal moments of Legendre, Chebyshev, Gegenbauer and Gaussian-Hermite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

The datasets generated in our experiments are available from McGill 3D Shape Benchmark images Database, URL link: http://www.cim.mcgill.ca/~shape/benchMark/airplane.html. (2017). Accessed 12 February 2020.

The datasets used or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

GLPs:

Generalized Laguerre polynomials

GLMs:

Generalized Laguerre moments

MSE:

mean squared error

ETIR:

execution-time improvement ratio

PSNR:

Peak Signal-To-Noise Ratio

CPU:

Computational time

References

  1. Abdulhussain SH, Ramli AR, Al-Haddad SAR, Mahmmod BM, Jassim WA (2018) Fast recursive computation of Krawtchouk polynomials. J Mathematic Imaging Vis 60(3):285–303

    Article  MathSciNet  Google Scholar 

  2. Abramowiz M, Stegun IA (1965) Hand book of mathematical functions. Dover Publications Inc., New York

    Google Scholar 

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

    Article  Google Scholar 

  4. Benouini R, Batioua I, Zenkouar K, Najah S, Qjidaa H (2018) Efficient 3D object classification by using direct Krawtchouk moment invariants. Multimed Tools Appl 1-26

  5. Buchanan JL, Turner PR (1992) Numerical methods and analysis. McGraw-Hill Inc., New York

    Google Scholar 

  6. Canterakis N (1999) “3D Zernike moments and Zernike affine invariants for 3D image analysis and recognition”. In In 11th Scandinavian Conf. on Image Analysis

  7. El Ogri O, Daoui A, Yamni M, Karmouni H, Sayyouri M, Qjidaa H (2020) New set of fractional-order generalized Laguerre moment invariants for pattern recognition. Multimed Tools Appl 79:23261–23294. https://doi.org/10.1007/s11042-020-09084-1

    Article  Google Scholar 

  8. Farokhi S, Sheikh UU, Flusser J, Yang B (2015) Near infrared face recognition using Zernike moments and Hermite kernels. Inf Sci 316:234–245

    Article  Google Scholar 

  9. Fu B, Zhou J-Z, Li Y-H, Peng B, Liu L-Y, Wen J-Q (2008) Novel recursive and symmetric algorithm of computing two kinds of orthogonal radial moments. Image Sci J 56(6):333–341

    Article  Google Scholar 

  10. Honarvar B, Paramesran R, Lim C-L (2013) The fast-recursive computation of Tchebichef moment and its inverse transform based on Z-transform. Digital Signal Process 23(5):1738–1746

    Article  Google Scholar 

  11. Hosny KM (2007) Exact and fast computation of geometric moments for gray level images. Appl Math Comput 189:1214–1222

    MathSciNet  MATH  Google Scholar 

  12. Hosny KM (2007) Exact Legendre moment computation for gray level images. Pattern Recogn 40(12):3597–3605

    Article  Google Scholar 

  13. Hosny KM (2008) Fast computation of accurate Zernike moments. J Real-Time Image Process 3(1–2):97–107

    Article  Google Scholar 

  14. Hosny KM (2010) A systematic method for efficient computation of full and subsets Zernike moments. Inf Sci 180(11):2299–2313

    Article  MathSciNet  Google Scholar 

  15. Hosny KM (2011) Image representation using accurate orthogonal Gegenbauer moments. Pattern Recogn Lett 32(6):795–804

    Article  Google Scholar 

  16. Hosny KM (2011) Fast and low-complexity method for exact computation of 3D Legendre moments. Pattern Recogn Lett 32(9):1305–1314

    Article  Google Scholar 

  17. Hosny KM (2012) Fast computation of accurate Gaussian-Hermite moments for image processing applications. Digital Signal Process 22(3):476–485

    Article  MathSciNet  Google Scholar 

  18. http://www.cim.mcgill.ca/~shape/benchMark/airplane.html. (2017). Accessed 12 Feb 2017

  19. Jahid T, Hmimid A, Karmouni H, Sayyouri M, Qjidaa H, Rezzouk A (2017) Image analysis by Meixner moments and a digital filter. Multimed Tools Appl 1–21

  20. T. Jahid, H. Karmouni, M. Sayyouri, A. Hmimid, & H. Qjidaa (2018) Fast algorithm of 3D discrete image orthogonal moments computation based on 3D cuboid. Journal of Mathematical Imaging and Vision, 1-21

  21. Jahid T, Karmouni H, Hmimid A, Sayyouri M, Qjidaa H (2018) Fast computation of Charlier moments and its inverses using Clenshaw’s recurrence formula for image analysis. Multimed Tools Appl 1-19

  22. Karmouni H, Jahid T, Sayyouri M, Hmimid A, El affar A, Qjidaa H (2018) Fast and Stable Computation of the Tchebichef’s Moments Using Image Block Representation and Clenshaw’s Formula. In: International Conference on Advanced Intelligent Systems for Sustainable Development. Springer, Cham, p. 261–273

  23. Karmouni H, Jahid T, Sayyouri M, Hmimid A, El affar A, Qjidaa H (2018) Image Analysis by Hahn Moments and a Digital Filter. In: Ezziyyani M. (eds) Advanced Intelligent Systems for Sustainable Development (AI2SD’2018). AI2SD 2018. Advances in Intelligent Systems and Computing, vol 915. Springer, Cham

  24. Karmouni H, Jahid T, Sayyouri M et al. (2019) Fast 3D image reconstruction by cuboids and 3D Charlier’s moments. J Real-Time Image Proc, 1–17

  25. Karmouni H, Jahid T, Sayyouri M, Hmimid A, Qjidaa H (2019) Fast Reconstruction of 3D Images Using Charlier Discrete Orthogonal Moments. Circuits Syst Signal Process 38(8):3715–3742. https://doi.org/10.1007/s00034-019-01025-0

    Article  MATH  Google Scholar 

  26. R. Koekoek, P.A. Lesky and R.F. Swarttouw (2010) Hypergeometric orthogonal polynomials and their q-analogues. Springer Monographs in Mathematics. Library of Congress Control Number: 923797

  27. Long M, Peng F, Zhu Y (2019) Identifying natural images and computer generated graphics based on binary similarity measures of PRNU. Multimed Tools Appl 78(1):489–506

    Article  Google Scholar 

  28. Mesbah A, Berrahou A, El Mallahi M, Qjidaa H (2016) Fast and efficient computation of three-dimensional Hahn moments. J Electron Imaging 25(6):061621

    Article  Google Scholar 

  29. Papakostas GA, Karakasis EG, Koulourisotis DE (2008) Efficient and accurate computation of geometric moments on gray-scale images. Pattern Recogn 41(6):1895–1904

    Article  Google Scholar 

  30. Sayyouri M, Hmimid A, Qjidaa H (2013) Improving the performance of image classification by Hahn moment invariants. Optic Soc Am JOSA A 30(11):2381–2394

    Article  Google Scholar 

  31. Sayyouri M, Hmimid A, Qjidaa H (2015) A fast computation of novel set of Meixner invariant moments for image analysis. Circuits Systems Signal Process 34(3):875–900

    Article  Google Scholar 

  32. Spiliotis IM, Karampasis ND, Boutalis YS (2020) Fast computation of Hahn moments on gray images using block representation. J Electron Imaging 29(1):013020

    Article  Google Scholar 

  33. Spiliotis IM, Bekakos MP, Boutalis YS (2020) Parallel implementation of the image block representation using OpenMP. J Parallel Distrib Comput 137:134–147

    Article  Google Scholar 

  34. Upneja R, Singh C (2015) Fast computation of Jacobi-Fourier moments for invariant image recognition. Pattern Recogn 48(5):1836–1843

    Article  Google Scholar 

  35. Wee CY, Paramesran R (2007) Derivation of blur-invariant features using orthogonal Legendre moments. IET Comput Vis 1(2):66–77

    Article  MathSciNet  Google Scholar 

  36. Wu G, Xu L (2019) Shape description and recognition by implicit Chebyshev moments. Pattern Recogn Lett 128:137–145

    Article  Google Scholar 

  37. Wu CH, Horng SJ, Lee PZ (2001) A new computation of shape moments via quadtree decomposition. Pattern Recogn 34(7):1319–1330

    Article  Google Scholar 

  38. Wu H, Coatrieux JL, Shu H (2013) New algorithm for constructing and computing scale invariants of 3D Tchebichef moments. Math Probl Eng 813606:2013

    MathSciNet  Google Scholar 

  39. Xia T, Zhu H, Shu H, Haigron P, Luo L (2007) Image description with generalized pseudo-Zernike moments. JOSA A 24(1):50–59

    Article  Google Scholar 

  40. Yang L, Albregtsen F (1996) Fast and exact computation of Cartesian geometric moments using discrete Green’s theorem. Pattern Recogn 29(7):1069–1073

    Article  Google Scholar 

  41. Zhang H, Shu H, Han G-N, Coatrieux G, Luo L, Coatrieux JL (2010) Blurred image recognition by Legendre moment invariants. IEEE Trans Image Process 19(3):596–611

    Article  MathSciNet  Google Scholar 

  42. Zhang D, Li Q, Yang G, Li L, Sun X (2017) Detection of image seam carving by using weber local descriptor and local binary patterns. J Info Secur Appl 36:135–144

    Google Scholar 

  43. Zhang D, Yin T, Yang G, Xia M, Li L, Sun X (2017) Detecting image seam carving with low scaling ratio using multi-scale spatial and spectral entropies. J Vis Commun Image Represent 48:281–291

    Article  Google Scholar 

  44. Zhang LB, Peng F, Qin L, Long M (2018) Face spoofing detection based on color texture Markov feature and support vector machine recursive feature elimination. J Vis Commun Image Represent 51:56–69

    Article  Google Scholar 

  45. Zhang X, Peng F, Long M (2018) Robust coverless image steganography based on DCT and LDA topic classification. IEEE Trans Multimed 20(12):3223–3238

    Article  Google Scholar 

  46. Zhu H, Liu M, Ji H, Li Y (2010) Combined invariants to blur and rotation using Zernike moment descriptors. Pattern Anal Applic 3(13):309–319

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

Author information

Authors and Affiliations

  1. 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

    Mhamed Sayyouri

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

    Hicham Karmouni, Abdeslam Hmimid & Hassan Qjidaa

  3. Finance, Entrepreneurship and Development laboratory, Faculty of Juridical, Economic and Social Sciences of Sale, Mohammed 5 University, Rabat, Morocco

    Ayoub Azzayani

Authors
  1. Mhamed Sayyouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hicham Karmouni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdeslam Hmimid
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ayoub Azzayani
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hassan Qjidaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Mhamed Sayyouri developed the idea of the study of Laguerre’s generalized moments and contributed to the central idea of our manuscript. Hicham Karmouni analyzed the properties of the moments of the proposed image and analyzed most of the data. Abedslam Hmimid wrote the first draft of the document, and the other authors helped refine the ideas, conduct additional analysis, and finalize the document. All the authors participated in the writing of the manuscript.

Corresponding author

Correspondence to Mhamed Sayyouri.

Ethics declarations

Competing interests

The authors declare that we have no competing interests in the submission of this manuscript.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sayyouri, M., Karmouni, H., Hmimid, A. et al. A fast and accurate computation of 2D and 3D generalized Laguerre moments for images analysis. Multimed Tools Appl 80, 7887–7910 (2021). https://doi.org/10.1007/s11042-020-09921-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09921-3

Keywords

Search

Navigation