Image Segmentation Based on Non-Parametric Mixture Models of Chebyshev Orthogonal Polynomials of the Second Kind

To solve the problem of over-reliance on priori assumptions of the parameter methods for finite mixture models, a nonparametric mixture model of Chebyshev orthogonal polynomials of the second kind for image segmentation method is proposed in this paper. Firstly, an image nonparametric misture model based on Chebyshev orthogonal polynomials of the second kind is designed. The mixture identification step based on the maximisation of the likelihood can be realised without hypothesis on the distribution of the conditional probability density function(PDF). In this paper, we intend to give some simulation results for the determination of the smoothing parameter, and use mean integrated squared error (MISE) estimation of the smoothing parameter for each model. Secondly, the stochastic expectation maximum (SEM) algorithm is used to estimate the Chebyshev orthogonal polynomial coefficients and the model of the weight. This method does not require any priori assumptions on the model, and it can effectively overcome the “model mismatch” problem. The algorithm finds the most likely number of classes and their associated model parameters and generates a segmentation of the image by classifying the pixels into these classes. Compared with the segmentation methods of other orthogonal polynomials, this new method is much more fast in speed and better segmentation quality. The experimental results about the image segmentation show that this method is better than the Gaussian mixture model segmentation results.