Abstract: To solve the problem of over reliance on priori assumptions of the parameter methods for finite mixture mo dcls and the problem that monk 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 pa- per. First, the multivariate Chebyshev orthogonal polynomials was derived by the Fourier analysis and the tensor pro- duct theory, and the nonparametric mixture model of multivariate orthogonal polynomials was proposed. And the mean integrated squared error(MISE) was used to estimate the smoothing parameter for each model. Second, the expectation maximum(EM) algorithm was used to estimate the orthogonal polynomial coefficients and the model of the weight. hhis method does not require any prior assumptions on the model, and it can effectively overcome the "model mismatch" problem. hhe experimental results with the images show that this method can achieve better segmentation results than the mean-shift method.

Key words: Non-parametric mixture models, Image segmentation, Smoothing parameter, Multivariate orthogonal polynomial