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Color image segmentation using nonparametric mixture models with multivariate orthogonal polynomials

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Abstract

To solve the problem of over-reliance on a priori assumptions of the parametric methods for finite mixture models and the problem that monic Chebyshev orthogonal polynomials can only process the gray images, a segmentation method of mixture models of multivariate Chebyshev orthogonal polynomials for color image was proposed in this paper. First, the multivariate Chebyshev orthogonal polynomials are derived by the Fourier analysis and tensor product theory, and the nonparametric mixture models of multivariate orthogonal polynomials are proposed. And the mean integrated squared error is used to estimate the smoothing parameter for each model. Second, to resolve the problem of the estimation of the number of density mixture components, the stochastic nonparametric expectation maximum algorithm is used to estimate the orthogonal polynomial coefficient and weight of each model. This method does not require any prior assumptions on the models, and it can effectively overcome the problem of model mismatch. Experimental performance on real benchmark images shows that the proposed method performs well in a wide variety of empirical situations.

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Acknowledgments

The authors would like to thank Prof. Sun Jiachang and the referees for their helpful comments and suggestions to improve the presentation of this paper. This work was supported by the National Science Foundation of China under Grant No. 60841003, the Special Fund of Software and Integrated Circuit Foundation of Jiangsu Information Industry of China (2009[100]) and the Innovation Fund of PhD candidate in Jiangsu Province of China(CX10B_274Z).

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Authors and Affiliations

  1. School of Computer Science and Telecommunication, Jiangsu University, Room 522, Zhenjiang, Jiangsu Province, People’s Republic of China

    Zhe Liu, Yu-Qing Song, Jian-Mei Chen, Cong-Hua Xie & Feng Zhu

  2. School of Computer Science, Jilin Normal University, Siping, Jilin Province, People’s Republic of China

    Zhe Liu

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  1. Zhe Liu
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  2. Yu-Qing Song
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  3. Jian-Mei Chen
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  4. Cong-Hua Xie
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  5. Feng Zhu
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Correspondence to Yu-Qing Song.

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Liu, Z., Song, YQ., Chen, JM. et al. Color image segmentation using nonparametric mixture models with multivariate orthogonal polynomials. Neural Comput & Applic 21, 801–811 (2012). https://doi.org/10.1007/s00521-011-0538-1

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