Color image segmentation using nonparametric mixture models with multivariate orthogonal polynomials

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.