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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 1 — Jan. 1, 2014
  • pp: 124–134

High-precision and fast computation of Jacobi–Fourier moments for image description

C. Camacho-Bello, C. Toxqui-Quitl, A. Padilla-Vivanco, and J. J. Báez-Rojas  »View Author Affiliations


JOSA A, Vol. 31, Issue 1, pp. 124-134 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000124


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Abstract

A high-precision and fast algorithm for computation of Jacobi–Fourier moments (JFMs) is presented. A fast recursive method is developed for the radial polynomials that occur in the kernel function of the JFMs. The proposed method is numerically stable and very fast in comparison with the conventional direct method. Moreover, the algorithm is suitable for computation of the JFMs of the highest orders. The JFMs are generic expressions to generate orthogonal moments changing the parameters α and β of Jacobi polynomials. The quality of the description of the proposed method with α and β parameters known is studied. Also, a search is performed of the best parameters, α and β, which significantly improves the quality of the reconstructed image and recognition. Experiments are performed on standard test images with various sets of JFMs to prove the superiority of the proposed method in comparison with the direct method. Furthermore, the proposed method is compared with other existing methods in terms of speed and accuracy.

© 2013 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.2960) Image processing : Image analysis
(100.5760) Image processing : Rotation-invariant pattern recognition
(150.0150) Machine vision : Machine vision
(100.4994) Image processing : Pattern recognition, image transforms

ToC Category:
Image Processing

History
Original Manuscript: June 13, 2013
Revised Manuscript: November 21, 2013
Manuscript Accepted: November 26, 2013
Published: December 16, 2013

Citation
C. Camacho-Bello, C. Toxqui-Quitl, A. Padilla-Vivanco, and J. J. Báez-Rojas, "High-precision and fast computation of Jacobi–Fourier moments for image description," J. Opt. Soc. Am. A 31, 124-134 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-1-124


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References

  1. Z. Ping, H. Ren, J. Zou, Y. Sheng, and W. Bo, “Generic orthogonal moments: Jacobi–Fourier moments for invariant image description,” Pattern Recogn. 40, 1245–1254 (2007). [CrossRef]
  2. N. V. S. Sree Rathna Lakshmi and C. Manoharan, “An automated system for classification of micro calcification in mammogram based on Jacobi moments,” IJCTE 3, 431–434 (2011). [CrossRef]
  3. C. Toxqui-Quitl, A. Padilla-Vivanco, and J. Baez-Rojas, “Classification of mechanical parts using an optical-digital system and the Jacobi–Fourier moments,” Proc. SPIE 7389, 738934 (2009). [CrossRef]
  4. C. Camacho-Bello, C. Toxqui-Quitl, and A. Padilla-Vivanco, “Gait recognition by Jacobi–Fourier moments,” in Frontiers in Optics/Laser Science XXVII, OSA Technical Digest (Optical Society of America, 2011), paper JTuA19.
  5. M. R. Teague, “Image analysis via the general theory of moments,” J. Opt. Soc. Am. 70, 920–930 (1980). [CrossRef]
  6. Y. L. Sheng and L. X. Shen, “Orthogonal Fourier–Mellin moments for invariant pattern recognition,” J. Opt. Soc. Am. A 11, 1748–1757 (1994). [CrossRef]
  7. G. Amu, S. Hasi, X. Yang, and Z. Ping, “Image analysis by pseudo-Jacobi (p=4, q=3)-Fourier moments,” Appl. Opt. 43, 2093–2101 (2004). [CrossRef]
  8. Z. L. Ping, R. G. Wu, and Y. L. Sheng, “Image description with Chebyshev–Fourier moments,” J. Opt. Soc. Am. A 19, 1748–1754 (2002). [CrossRef]
  9. B. Xiao, J. F. Ma, and X. Wang, “Image analysis by Bessel–Fourier moments,” Pattern Recogn. 43, 2620–2629 (2010). [CrossRef]
  10. H. Ren, Z. Ping, W. Bo, W. Wu, and Y. Sheng, “Multi-distorted invariant image recognition with radial-harmonic-Fourier moments,” J. Opt. Soc. Am. A 20, 631–637 (2003). [CrossRef]
  11. H. Hu and P. Zi-liang, “Computation of orthogonal Fourier–Mellin moments in two coordinate systems,” J. Opt. Soc. Am. A 26, 1080–1084 (2009). [CrossRef]
  12. A. Padilla-Vivanco, G. Urcid-Serrano, F. Granados-Agustín, and A. Cornejo-Rodríguez, “Comparative analysis of pattern reconstruction using orthogonal moments,” Opt. Eng. 46, 017002 (2007). [CrossRef]
  13. S. X. Liao and M. Pawlak, “On the accuracy of Zernike moments for image analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 1358–1364 (1998). [CrossRef]
  14. Y. Xin, M. Pawlak, and S. Liao, “Accurate computation of Zernike moments in polar coordinates,” IEEE Trans. Image Process. 16, 581–587 (2007). [CrossRef]
  15. C. Y. Wee and R. Paramesran, “On the computational aspects of Zernike moments,” Image Vis. Comput. 25, 967–980 (2007). [CrossRef]
  16. R. Biswas and S. Biswas, “Polar Zernike moments and rotational invariance,” Opt. Eng. 51, 087204 (2012). [CrossRef]
  17. R. Mukundan and K. R. Ramakrishnan, “Fast computation of Legendre and Zernike moments,” Pattern Recogn. 28, 1433–1442 (1995). [CrossRef]
  18. G. A. Papakostas, Y. S. Boutalis, D. A. Karras, and B. G. Mertzios, “Fast numerically stable computation of orthogonal Fourier–Mellin moments,” IET Comput. Vis. 1, 11–16 (2007). [CrossRef]
  19. K. M. Hosny, M. A. Shouman, and H. M. Abdel Salam, “Fast computation of orthogonal Fourier–Mellin moments in polar coordinates,” J. Real-Time Image Process. 6, 73–80 (2011). [CrossRef]
  20. E. Walia, C. Singh, and A. Goyal, “On the fast computation of orthogonal Fourier–Mellin moments with improved numerical stability,” J. Real-Time Image Process. 7, 247–256 (2012). [CrossRef]
  21. M. Abramowitz and I. A. Stegun, Handbook of Functions with Formulas, Graphs and Mathematical Tables (Dover, 1964).
  22. T. Hoang and S. Tabbone, “Errata and comments on ‘generic orthogonal moments: Jacobi–Fourier moments for invariant image description,” Pattern Recogn. 46, 3148–3155 (2013). [CrossRef]
  23. C. Singh and R. Upneja, “Accurate computation of orthogonal Fourier–Mellin moments,” J. Math. Imaging Vision 44, 411–431 (2012). [CrossRef]
  24. C. Singh, E. Walia, and R. Upneja, “Accurate calculation of Zernike moments,” Inf. Sci. 233, 255–275 (2013). [CrossRef]
  25. R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 29, 1153–1160 (1981). [CrossRef]
  26. C. Toxqui-Quitl, L. Gutierrez-Lazcano, A. Padilla-Vivanco, and C. Camacho-Bello, “Gray-level image reconstruction using Bessel–Fourier moments,” Proc. SPIE 8011, 80112T (2011). [CrossRef]
  27. A. B. Bhatia and E. Wolf, “On the circular polynomials of Zernike and related orthogonal sets,” Proc. Cambridge Philos. Soc. 50, 40–48 (1954). [CrossRef]
  28. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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