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Fast computation of orthogonal Fourier–Mellin moments in polar coordinates

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Abstract

Fast, accurate and memory-efficient method is proposed for computing orthogonal Fourier–Mellin moments. Since the basis polynomials are continuous orthogonal polynomials defined in polar coordinates over a unit disk, the proposed method is applied to polar coordinates where the unit disk is divided into a number of non-overlapping circular rings that are divided into circular sectors of the same area. Each sector is represented by one point in its center. The implementation of this method completely removes both approximation and geometrical errors produced by the conventional methods. Based on the symmetry property, a fast and memory-efficient algorithm is proposed to accelerate the moment’s computations. A comparison to conventional methods is performed. Numerical experiments are performed to ensure the efficiency of the proposed method.

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References

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

    Article  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. Terrillon, J.C., McReynolds, D., Sadek, M., Sheng, Y., Akamatsu, S.: Invariant neural-network based face detection with orthogonal Fourier–Mellin moments. In: Proceedings of the 15th IEEE International Conference on Pattern Recognition, vol. 2, pp. 993–1000 (2000)

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

    Article  MATH  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 Recognit. 40(12), 3503–3508 (2007)

    Article  MATH  Google Scholar 

  7. Jiu-bin, T., Lei, A., Ji-wen, C., Wen-jing, K., Dan-dan, L.: Subpixel edge location based on orthogonal Fourier–Mellin moments. Image Vis. Comput. 26(4), 563–569 (2008)

    Article  Google Scholar 

  8. 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 

  9. 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)

  10. Xin, Y., Pawlak, M., Liao, S.: Accurate computation of Zernike moments in polar coordinates. IEEE Trans. Image Process. 16(2), 581–587 (2007)

    Article  MathSciNet  Google Scholar 

  11. Hosny, K.M.: Exact and fast computation of geometric moments for gray-level images. Appl. Math. Comput. 189(2), 1214–1222 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  13. Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Prentice-Hall, Englewood Cliffs (2002)

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Correspondence to Khalid Mohamed Hosny.

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Hosny, K.M., Shouman, M.A. & Abdel Salam, H.M. Fast computation of orthogonal Fourier–Mellin moments in polar coordinates. J Real-Time Image Proc 6, 73–80 (2011). https://doi.org/10.1007/s11554-009-0135-z

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  • DOI: https://doi.org/10.1007/s11554-009-0135-z

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