Skip to main content

Advertisement

Springer Nature Link
Log in

Helmet-fourier orthogonal moments for image representation and recognition

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

The orthogonal moments have recently achieved outstanding predictive performance and become an indispensable tool in a wide range of imaging and pattern recognition applications, including image reconstruction, image classification and object detection. We present in this paper, a new set of orthogonal functions, called “Orthogonal helmet functions.” Using these functions we introduce three new sets of orthogonal moments and their invariants to scaling, rotation and translation for image representation and recognition, named, respectively, “the orthogonal helmet-Fourier moments” for the gray-level images, the multi-channel orthogonal helmet-Fourier moments and the quaternion orthogonal helmet-Fourier moments (QHFMs) for the color images. We introduce a series of experimental tests in image analysis and pattern recognition to validate the theoretical framework of our approach. The performance of these feature vectors is compared with the existing orthogonal invariant moments. The results of the comparative study show the efficiency and the superiority of our three orthogonal invariant moments. Thanks to our orthogonal moments QHFMs, we were able to lift the image recognition quality with rate can reach \(2.06\%.\)

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

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

taken from the Amsterdam Library of Objects Images database

Fig. 15
Fig. 16
Fig. 17
Fig. 18

References

  1. Hu M-K (1962) Visual pattern recognition by moment invariants. Inf Theory IRE Trans On 8:179–187

    MATH  Google Scholar 

  2. Teague MR (1980) Image analysis via the general theory of moments. J Opt Soc Am 70:920–930

    MathSciNet  Google Scholar 

  3. Zhang F, Liu SQ, Wang DB, Guan W (2009) Aircraft recognition in infrared image using wavelet moment invariants. Image Vis Comput 27:313–318

    Google Scholar 

  4. Hjouji A, Bouikhalene B, EL-Mekkaoui J et al (2021) New set of adapted Gegenbauer Chebyshev invariant moments for image recognition and classification. J Supercomput 77:5637–5667

    Google Scholar 

  5. Lahouli I, Karakasis E, Haelterman R, Chtourou Z, Cubber GD, Gasteratos A, Attia R (2018) Hot spot method for pedestrian detection using saliency maps, discrete Chebyshev moments and support vector machine. In: IET Image processing, Vol. 12, pp 1284–1291

  6. Hjouji A, Chakid R, El-Mekkaoui J et al (2021) Adapted jacobi orthogonal invariant moments for image representation and recognition. Circuits Syst Signal Process 40:2855–2882

    Google Scholar 

  7. Ji Z, Chen Q, Sun Q-S, Xia D-S (2009) A moment-based nonlocal-means algorithm for image denoising. Inf Process Lett 109:1238–1244

    MathSciNet  MATH  Google Scholar 

  8. Hjouji A, El-Mekkaoui J, Qjidaa H (2021) New set of non-separable 2D and 3D invariant moments for image representation and recognition. Multimed Tools Appl 80:12309–12333

    Google Scholar 

  9. Hosny KM, Darwish MM (2018) New set of quaternion moments for color images representation and recognition. J Math Imaging Vision 60:717–736

    MathSciNet  MATH  Google Scholar 

  10. Assefa D, Mansinha L, Tiampo KF, Rasmussen H, Abdella K (2010) Local quaternion Fourier transform and color image texture analysis. Signal Process 90:1825–1835

    MATH  Google Scholar 

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

    Google Scholar 

  12. Singh C, Pooja (2012) Local and global features based image retrieval system using orthogonal radial Moments. Opt Lasers Eng 50:655–667

    Google Scholar 

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

    MATH  Google Scholar 

  14. Chen B, Yu M, Su Q, Shim HJ, Shi YQ (2018) Fractional quaternion Zernike moments for robust color image copy-move forgery detection. IEEE Access 6:56637–56646

    Google Scholar 

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

    MATH  Google Scholar 

  16. Ansary TF, Daoudi M, Vandeborre J-P (2007) A Bayesian 3D search engine using adaptive views clustering. IEEE Trans Multimed 9:78–88

    Google Scholar 

  17. Lin YH, Chen CH (2008) Template matching using the parametric template vector with translation, rotation and scale invariance. Pattern Recognit 41:2413–2421

    MATH  Google Scholar 

  18. Kim WY, Kim YS (2000) A region-based shape descriptor using Zernike moments. Signal Process: Image Commun 16:95–102

    Google Scholar 

  19. Kanaya N, Liguni Y, Maeda H (2002) 2-D DOA estimation method using Zernike moments. Signal Process 82:521–526

    MATH  Google Scholar 

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

    Google Scholar 

  21. Bailey R, Srinath M (1996) Orthogonal moment features for use with parametric and non- parametric classifiers. IEEE Trans Pattern Anal Mach Intell 18:389–399

    Google Scholar 

  22. Ping ZL, Wu R, Sheng YL (2002) Image description with Chebyshev-Fourier moments. J Opt Soc Am A 19:1748–1754

    MathSciNet  Google Scholar 

  23. Sheng Y, Shen L (1994) Orthogonal Fourier-Mellin moments for invariant pattern recognition. J Opt Soc Am A 11:1748–1757

    Google Scholar 

  24. Ren H, Ping Z, Bo W, Wu W, Sheng Y (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A 20:631–637

    MathSciNet  Google Scholar 

  25. Xiao B, Ma J, Wang X (2010) Image analysis by Bessel-Fourier moments. Pattern Recognit 43:2620–2629

    MATH  Google Scholar 

  26. Yap P-T, Jiang X, Kot AC (2010) Two-dimensional polar harmonic transforms for invariant image representation. IEEE Trans PAMI 32(6):1259–1270

    Google Scholar 

  27. Hu H-T, Zhang Y-D, Shao C, Ju Q (2014) Orthogonal moments based on exponent functions: exponent-Fourier moments. Pattern Recognit 47:2596–2606

    MATH  Google Scholar 

  28. Wang C, Wang X, Xia Z, Ma B, Shi Y-Q (2019) Image description with polar harmonic fourier moments. IEEE Trans Circuits Syst Video Technol 30(12):4440–52

    Google Scholar 

  29. Wanga C, Wang X, Li Y, Xiac Z, Zhang C (2018) Quaternion polar harmonic Fourier moments for color images. Inf Sci 450:141–156

    MathSciNet  Google Scholar 

  30. Chen BJ, Shu HZ, Zhang H, Chen G, Luo LM (2012) Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process 92:308–318

    Google Scholar 

  31. Hosny KM, Darwish MM (2019) New set of multi-channel orthogonal moments for color image representation and recognition. Pattern Recognit 88:153–173

    Google Scholar 

  32. Singh C, Singh J (2018) Multi-channel versus quaternion orthogonal rotation invariant moments for color image representation. Digital Signal Processing 78:376–392

    MathSciNet  Google Scholar 

  33. Chen BJ, Sun XM, Wang DC, Zhao XP (2012) Color face recognition using quaternion representation of color image. ACTA Automatica Sinica 8:1815–1823

    MathSciNet  MATH  Google Scholar 

  34. Guo L, Zhu M (2011) Quaternion Fourier-Mellin moments for color images. Pattern Recogn 44:187–195

    MATH  Google Scholar 

  35. Singh C, Singh J (2018) Quaternion generalized Chebyshev-Fourier and pseudo Jacobi-Fourier moments. Opt Laser Technol 106:234–250

    Google Scholar 

  36. Xin Y, Pawlak M, Liao S (2007) Accurate computation of Zernike moments in polar coordinates. IEEE Trans Image Process 16:581–587

    MathSciNet  Google Scholar 

  37. Hosny KM, Shouman MA, Abdel Salam HM (2011) Fast computation of orthogonal Fourier-Mellin moments in polar coordinates. J Real-Time Image Proc 6:73–80

    Google Scholar 

  38. Wang X, Li W, Yang H, Wang P, Li Y (2015) Quaternion polar complex exponential transform for invariant color image description. Appl Math Comput 256:951–967

    MathSciNet  MATH  Google Scholar 

  39. Suk T, Flusser J (2009) Affine moment invariants of color images. In: The 13th International Conference on Computer Analysis of Images and Patterns, Lecture Notes Computer Science, 5702, Münste, Germany, pp 334–341

  40. Hamilton WR (1866) Elements of Quaternions. Longmans Green, London, U.K.

    Google Scholar 

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

  42. Geusebroek JM, Burghouts GJ, Smeulders AWM (2005) The Amsterdam library of object images. Int J Comput Vis 61:103–112

    Google Scholar 

  43. Nene SA, Nayar SK, Murase H (1996) Columbia object image library (COIL-100), Technical Report CUCS-006–96

  44. Wang JZ, Li J, Wiederhold G (2001) Simplicity: semantics-sensitive integrated matching for picture libraries. IEEE Trans Pattern Anal Mach Intell 23(9):947–963

    Google Scholar 

  45. Oliva A, Torralba A (2001) Modeling the shape of the scene: a holistic representation of the spatial envelope. Int J Comput Vis 42:145–175

    MATH  Google Scholar 

  46. Hosny KM, Darwish MM (2017) Comments on "Robust circularly orthogonal moment based on Chebyshev rational function. Digit Signal Process 62:249–258

    Google Scholar 

  47. Benouini R, Batioua I, Zenkouar K, Zahi A, Najah S, Qjidaa H (2019) Fractional-order orthogonal Chebyshev Moments and Moment Invariants for image representation and pattern recognition. Pattern Recogn 86:332–343

    Google Scholar 

  48. Xiao B, Luo J, Bi X, Li W, Chen B (2020) Fractional discrete Tchebyshev moments and their applications in image encryption and watermarking. Inf Sci 516:545–559

    MathSciNet  MATH  Google Scholar 

  49. Yamni M, Daoui A, El ogri O, Karmouni H, Sayyouri M, Qjidaaa H, Flusser J (2020) Fractional Charlier moments for image reconstruction and image watermarking. Signal Process. https://doi.org/10.1016/j.sigpro.2020.107509

    Article  MATH  Google Scholar 

  50. Hosny KM, Darwish MM, Aboelenen T (2020) Novel fractional-order polar harmonic transforms for gray-scale and color image analysis. J Frankl Inst 357(4):2533–2560

    MathSciNet  MATH  Google Scholar 

  51. Hosny KM, Darwish MM, Aboelenan T (2020) Novel fractional-order generic jacobi-fourier moments for image analysis. Signal Process 172:107545

    Google Scholar 

  52. Hosny KM, Darwish MM, Aboelenan T (2020) New fractional-order legendre-fourier moments for pattern recognition applications. Pattern Recognit 103(107324):1–19

    Google Scholar 

  53. Hosny KM, Darwish MM, Eltoukhy MM (2020) Novel multi-channel fractional-order radial harmonic fourier moments for color image analysis. IEEE ACCESS 8:40732–40743

    Google Scholar 

  54. Naveen P, Sivakumar P (2021) A deep convolution neural network for facial expression recognition. J Current Sci Technol 11(3):402–410

    Google Scholar 

  55. Naveen P, Sivakumar P (2021) Adaptive morphological and bilateral filtering with ensemble convolutional neural network for pose-invariant face recognition. J Ambient Intell Human Comput 12:10023–10033. https://doi.org/10.1007/s12652-020-02753-x

    Article  Google Scholar 

  56. Naveen P, Sivakumar P (2021) Human emotions detection using kernel nonlinear collaborative discriminant regression classifier : human emotions detection using KNCDRC. In: 2021 2nd International Conference on Smart Electronics and Communication (ICOSEC), 1807–1812, doi: https://doi.org/10.1109/ICOSEC51865.2021.9591878

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computer Science, Signals, Automation and Cognitivism, Faculty of Sciences Dhar El, Mahrez, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Amal Hjouji

  2. LTI, Laboratory, EST, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Jaouad EL-Mekkaoui

Authors
  1. Amal Hjouji
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Jaouad EL-Mekkaoui
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Amal Hjouji.

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

Hjouji, A., EL-Mekkaoui, J. Helmet-fourier orthogonal moments for image representation and recognition. J Supercomput 78, 13583–13623 (2022). https://doi.org/10.1007/s11227-022-04414-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-022-04414-6

Keywords