Image Description using Radial Associated Laguerre Moments

Bojun Pan, Yihong Li, Hongqing Zhu

Abstract


This study proposes a new set of moment functions for describing gray-level and color images based on the associated Laguerre polynomials, which are orthogonal over the whole right-half plane. Moreover, the mathematical frameworks of radial associated Laguerre moments (RALMs) and associated rotation invariants are introduced. The proposed radial Laguerre invariants retain the basic form of disc-based moments, such as Zernike moments (ZMs), pseudo-Zernike moments (PZMs), Fourier-Mellin moments (OFMMs), and so on. Therefore, the rotation invariants of RALMs can be easily obtained. In addition, the study extends the proposed moments and invariants defined in a gray-level image to a color image using the algebra of quaternion to avoid losing some significant color information. Finally, the paper verifies the feature description capacities of the proposed moment function in terms of image reconstruction and invariant pattern recognition accuracy. Experimental results confirmed that the associated Laguerre moments (ALMs) perform better than orthogonal OFMMs in both noise-free and noisy conditions.


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References


Zhang, H., Shu, H., Han, G.N., Coatrieux, G., Luo, L. & Coatrieux, J.L., Blurred Image Recognition by Legendre Moment Invariants, IEEE Transactions on Image Processing, 19(3), pp. 596-611, 2010.

Jain, S., Papadakis, M., Upadhyay, S. & Azencott, R., Rigid-motioninvariant Classification of 3-D textures, IEEE Transactions on Image Processing, 21(5), pp. 2449-2463, 2012.

Y. H. Lin & Chen, C.H., Template Matching Using the Parametric Template Vector with Translation, Rotation and Scale Invariance, Pattern Recognit., 41(7), pp. 2413-2421, 2008.

Yap, P.-T., Jiang, X. & Kot, A.C., Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation, IEEE Trans. Pattern Anal. & Mach. Intell., 32(7), pp. 1259-1270, 2010.

See, K.W., Loke, K.S., Lee, P. A. & Loe, K.F., Image Reconstruction Using Various Discrete Orthogonal Polynomials in Comparison with DCT, Applied Mathematics and Computation 193(2), pp. 346-359, 2007.

Teh, C.H. & Chin, R.T., On Image Analysis by the Methods of Moments, IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), pp. 496-513, 1988.

Teague, M.R., Image Analysis via the General Theory of Moments, Journal of the Optical Society of America, 70(8), pp. 920-930, 1980.

Mukundan, R. & Ramakrishnan, K.R., Moment Functions in Image Analysis-Theory and Applications, World Scientific, Singapore, 1998.

Sheng, Y. & Arsenault, H.H., Experiments on Pattern Recognition Using Invariant Fourier-Mellin Descriptors, J. Opt. Soc. Am. A, 3(6), pp. 771-776, 1986.

Mukundan, R., Ong, S.H. & Lee, P.A., Image analysis by Tchebichef moments, IEEE Transactions on Image Processing, 10(9), pp. 1357-1364, 2001.

Yap, P.T., Paramesran, R. & Ong, S.H., Image Analysis by Krawtchouk Moments, IEEE Transactions on Image Processing 12(11), pp. 1367-1377, 2003.

Zhu, H.Q. Shu, H.Z., Liang, J., Luo, L.M. & Coatrieux, J.L. Image Analysis by Discrete Orthogonal Racah Moments, Signal Processing 87(4), pp. 687-708, 2007.

Zhu, H.Q., Shu, H.Z., Zhou, J., Luo, L.M. & Coatrieux, J.L., Image Analysis by Discrete Orthogonal Dual Hahn Moments, Pattern Recognition Letters, 28(13), pp. 1688-1704, 2007.

Chen, B., Shu, H., Zhang, H., Coatrieux, G., Luo, L. & Coatrieux, J. L. Combined Invariants to Similarity Transformation and to Blur Using Orthogonal Zernike Moments, IEEE Trans. Image Process., 20(2), pp.345-360, 2011.

Yang, B. & Dai, M., Image analysis by Gaussian–Hermite moments, Signal Processing, 91(10), pp. 2290-2303, 2011.

Mukundan, R., A New Class of Rotation Invariants Using Discrete Orthogonal Moments, Honolulu, USA: Proceedings of the 6th IASTED International Conference, Signal and Image Processing, 2004.

Askey, R. & Wimp, J., Associated Laguerre and Hermite Polynomials,Proc. Roy. Soc. Edinburgh Sect. A., 96(1-2), pp. 15-37, 1984.

K. B. Howell, Fourier transforms, in Transforms and Applications Handbook, 3rd ed., A. D. Poularikas, Ed., ch.2, CRC Press, Boca Raton, FL, U.S.A, 2010.

Xiao, B., Ma, J.-F. & Cui, J.-T., Combined Blur, Translation, Scale and Rotation Invariant Image Recognition by Radon and Pseudo-Fourier–Mellin Transforms, Pattern Recognition, 45(1), pp. 314-321, 2012.

Zhu, H., Liu, M. &Li, Y. The RST Invariant Digital Image Watermarking Using Radon Transforms and Complex Moments, Digital Signal Processing, 20(6), pp. 1612-1628, 2010.

Nasir, I., Khelifi, F. Jiang, J. & Ipson, S., Robust Image Watermarking via Geometrically Invariant Feature Points and Image Normalization, IET Image Process., 6(4), pp. 354-363, 2012.

Hamilton, W.R., Elements of Quaternions, London, U.K.: Longmans, Green, 1866.

http://www1.cs.columbia.edu/CAVE/software/softlib/coil-20.php (24 May 2013).




DOI: http://dx.doi.org/10.5614%2Fitbj.ict.res.appl.2015.9.1.1

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