Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

On the fast computation of orthogonal Fourier–Mellin moments with improved numerical stability

  • Original Research Paper
  • Published:
Journal of Real-Time Image Processing Aims and scope Submit manuscript

Abstract

A fast and numerically stable recursive method for the computation of orthogonal Fourier–Mellin moments (OFMMs) is proposed. Fast recursive method is developed for the radial polynomials which occur in the kernel function of the OFMMs, thus enhancing the overall computation speed. The proposed method is free from any overflow situations as it does not consist of any factorial term. It is also free from underflow situations as no power terms are involved. The proposed recursive method is claimed to be fastest in comparison with the direct and other methods to compute OFMMs till date. The elimination of the computation of factorial terms makes the moments very stable even up to an order of 200, which become instable in conventional or in any other recursive methods proposed earlier wherein instability occurs at moment order ≥25. Experiments are performed on standard test images to prove the superiority of the proposed method on existing methods in terms of speed and numerical stability.

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

Similar content being viewed by others

References

  1. Kan, C., Srinath, M.D.: Invariant character recognition with Zernike and orthogonal Fourier–Mellin moments. Pattern Recogn. 35(1), 143–154 (2002)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Teh, C.-H., Chin, R.T.: On image analysis by the methods of moments. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 496–513 (1998)

    Article  Google Scholar 

  4. Sheng, Y., Shen, L.: Orthogonal Fourier-Mellin moments for invariant pattern recognition. J. Opt. Soc. Am. 11(6), 1748–1757 (1994)

    Article  Google Scholar 

  5. Andrew, T.B.J., David, N.C.L.: Integrated wavelet and Fourier–Mellin invariant feature in fingerprint verification system. In: Proceedings of the 2003 ACM SIGMM Workshop on Biometrics Methods and Applications, pp. 82–88 (2003)

  6. Wang, X., Xiao, B., Jian-Feng, M., Xiu-Li, B.: Scaling and rotation invariant analysis approach to object recognition based on Radon and Fourier–Mellin transforms. Pattern Recogn. 40(12), 3503–3508 (2007)

    Article  MATH  Google Scholar 

  7. Bin, T.J., Jiwen, C., Wenjing, K., Dandan, L.: Subpixel edge location based on orthogonal Fourier Mellin moments. Image Vis. Comput. 26, 563–569 (2008)

    Article  Google Scholar 

  8. Prata, A., Rusch, W.V.T.: Algorithm for computation of Zernike polynomials expansion coefficients. Appl. Opt. 28, 749–754 (1989)

    Article  Google Scholar 

  9. Belkasim, S.O., Ahmadi, M., Shridhar, M.: Efficient algorithm for fast computation of Zernike moments. In: Proceedings of IEEE 39th Midwest Symposium on Circuits and Systems, vol. 3, pp. 1401–1404 (1996)

  10. Kintner, E.C.: A recursive relation for calculating the Zernike polynomials. Opt. Acta 23(6), 499–500 (1976)

    Article  Google Scholar 

  11. Chong, C.-W., Paramesran, R., Mukundan, R.: A comparative analysis of algorithms for fast computation of Zernike moments. Pattern Recogn. 36, 731–742 (2003)

    Article  MATH  Google Scholar 

  12. Gu, J., Shu, H.Z., Toumoulin, C., Luo, L.M.: A novel algorithm for fast computation of Zernike moments. Pattern Recogn. 35(12), 2905–2911 (2002)

    Article  MATH  Google Scholar 

  13. Hwang, S.-K., Kim, W.-Y.: A novel approach to the fast computation of Zernike moments. Pattern Recogn. 39, 2065–2076 (2006)

    Article  MATH  Google Scholar 

  14. Chong, C.-W., Mukundan, R., Raveendran, P.: An efficient algorithm for fast computation of pseudo-Zernike moments. In: Proceedings of International Conference on Image and Vision Computing, pp. 237–242 (2001)

  15. Papakostas, G.A., Boutalis, Y.S., Karras, D.A., Mertzios, B.G.: Fast numerically stable computation of orthogonal Fourier–Mellin moments. IET Comput. Vis. 1(1), 11–16 (2007)

    Article  MathSciNet  Google Scholar 

  16. Papakostas, G.A., Boutalis, Y.S., Karras, D.A., Mertzios, B.G.: Fast computation of orthogonal Fourier–Mellin moments using modified direct method. In: Proceedings of 6th EURASIP Conference Focused on Speech and Image Processing, Multimedia Communications and the 14th International Workshop of Systems, Signals and Image Processing, pp. 153–156 (2007)

  17. Hosny, K.M., Shouman, M.A., Abdel Salam, H.M.: Fast computation of orthogonal Fourier-Mellin moments in polar coordinates. J. Real-Time Image Process. 5, 1–9 (2010)

    Article  Google Scholar 

  18. Fu, B., Zhou, J., Wen, J.: An efficient algorithm for fast computation of orthogonal Fourier Mellin moments. In: International Conference on Space Information Technology, Proceedings of SPIE, vol. 5985, 59853A (2005)

  19. Singh, C., Walia, E.: Computation of Zernike moments in improved polar configuration. IET Image Process. 3(4), 217–227 (2009)

    Article  Google Scholar 

  20. Papakostas, G.A., Boutalis, Y.S., Papaodysseus, C.N., Fragoutis, D.K.: Numerical error analysis in Zernike moments computation. Image Vis. Comput. 24, 960–969 (2006)

    Article  Google Scholar 

  21. Singh, C., Walia, E.: Fast and numerically stable methods for the computation of Zernike moments. Pattern Recogn. 43, 2497–2506 (2010)

    Article  MATH  Google Scholar 

  22. Wee, C.Y., Paramesran, R.: On the computational aspects of Zernike moments. Image Vis. Comput. 25, 967–980 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

The authors are thankful to the All India Council for Technical Education (AICTE), Govt. of India, New Delhi, for supporting the research work vide their file number 8023/RID/BOR/RPS-77/2005-06. Thanks are also due to the anonymous reviewers for their constructive comments to enhance the quality of this paper.

Author information

Authors and Affiliations

  1. Department of IT, MM University, Mullana, India

    Ekta Walia

  2. Department of Computer Science, Punjabi University, Patiala, India

    Chandan Singh

  3. Guru Nanak Institute of Management and Technology, Ludhiana, Punjab, India

    Anjali Goyal

Authors
  1. Ekta Walia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chandan Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anjali Goyal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ekta Walia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Walia, E., Singh, C. & Goyal, A. On the fast computation of orthogonal Fourier–Mellin moments with improved numerical stability. J Real-Time Image Proc 7, 247–256 (2012). https://doi.org/10.1007/s11554-010-0172-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11554-010-0172-7

Keywords

Search

Navigation