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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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