Abstract
This paper presents a fast and accurate approach to the computation of Zernike moments from a digital image. Exact Zernike moments are computed with these fixed exact coefficients. The digital image is transformed to be inside the unit circle, where the transformed image is divided into eight parts. Based on the specific symmetry or anti-symmetry about the x-axis, the y-axis, the origin, and the straight line y = x, we can generate the Zernike basis functions by only computing one eighth of the image. Inside the unit circle, the image information is not lost. Experimental results show that the proposed method can reduce significantly the computation operations, so the time can be reduced to just one eighth of the original computation methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Teague, M.R.: Image analysis via the general theory of moments. J. Opt. Soc. Amer. 70, 920–930 (1980)
Khotanzad, A., Hong, Y.H.: Invariant image recognition by Zernike moments. IEEE Trans. Pattern Anal. Mach. Intell. 12(5), 489–497 (1990)
Kim, W.Y., Yuan, P.: A practical pattern recognition system for translation, scale and rotation invariance. In: Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, pp. 391–396 (June 1994)
Khotanzad, A., Hong, Y.H.: Invariant image recognition by Zernike moments. IEEE Trans. Pattern Anal. Machine Intell. 12, 489–497 (1990)
Kim, Y.S., Kim, W.Y.: Content-based trademark retrieval system using visually salient feature. J. Image Vision Comput. 16, 931–939 (1998)
Wang, L., Healey, G.: Using Zernike moments for the illumination and geometry invariant classification of multispectral texture. IEEE Trans. Image Process. 7(2), 196–203 (1998)
Kim, W.Y., Kim, Y.S.: Robust rotation angle estimator. IEEE Trans. Pattern Anal. Mach. Intell. 21(8), 768–773 (1999)
Mukundan, R., Ramakrishnan, K.R.: Fast computation of Legendre and Zernike moments. Pattern Recognition 28(9), 1433–1442 (1995)
Gu, J., Shu, H.Z., Toumoulin, C., Luo, L.M.: A novel algorithm for fast computation of Zernike moments. Pattern Recognition 35(12), 2905–2911 (2002)
Prata, A., Rusche, W.V.T.: Algorithm for computation of Zernike polynomials expansion coefficients. Appl. Opt. 28, 749–754 (1989)
Kintner, E.C.: On the mathematical properties of the Zernike polynomials. Opt. Acta. 23(8), 679–680 (1976)
Belkasim, S.O.: Efficient algorithm for fast computation of Zernike moments. In: IEEE 39th Midwest Symposium on Circuits and Systems, vol. 3, pp. 1401–1404 (1996)
Brlksdim, S.O., Shridhar, M., Ahmadi, M.: Pattern recognition with moment invariants: a comparative study and new results. Pattern Recognition 24(12), 1117–1138 (1991)
Nukundan, R., Ramakrishnan, K.R.: Moment Functions in Image Analysis. World Scientific Publishing, Singapore (1998)
Chong, C.-W.: A formulation of a new class of continuous orthogonal moment invariants, and the analysis of their computational aspects, PhD thesis, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia (May 2003)
Bin, Y., Jia-Xiong, P.: Invariance analysis of improved Zernike moments. J. Opt. A: Pure Appl. Opt. 4, 606–614
Hwang, S.-K., Kim, W.-Y.: A novel approach to the fast computation of Zernike moments. Pattern Recognition 39, 2065–2076 (2006)
Papakostas, G.A., Boutalis, Y.S.: Numerical error analysis in Zernike moments computation. Image and Vision Computing 24, 960–969 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tian, H., Yan, H., Zhao, H. (2011). A Fast and Accurate Approach to the Computation of Zernike Moments. In: Zhang, J. (eds) Applied Informatics and Communication. ICAIC 2011. Communications in Computer and Information Science, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23223-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-23223-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23222-0
Online ISBN: 978-3-642-23223-7
eBook Packages: Computer ScienceComputer Science (R0)