Image Segmentation And Fusion Based On Nonparametric Orthogonal Polynomial Density Model

On the theory of density estimation, they were proposed that nonparametric orthogonal polynomials density model and mixture model were used in image segmentation and fusion. Based on the model, image segmentation and fusion mehods were proposed. The main contributions were contained following several aspects:1. To solve the problem of "model mismatch" for image fitting, we proposed the univariate and multivariate orthogonal polynomial density model for image gray information. It is difficulty to fit the complicated image precisely with single parameter distribution. We proposed a mixture model of the non-parametric second Chebyshev orthogonal polynomials for image data. For the multivariate Chebyshev orthogonal polynomials, deriving by the Fourier analysis and Tensor product theory, We proposed a nonparametric mixture model of the multivariate orthogonal polynomials2. A novel Particle Swarm Optimization method based on nonparametric orthogonal polynomials density model is proposed. In order to resolve the multi-modal function optimization problem, we presented an improved particle swarms optimization algorithm which decreased the global factors of the PSO and increased the local factors as most as possible, meanwhile a variable step is used to enhance variety of the particles and to change the parameter in order to speed up the algorithm convergence speed. On the basis of the heuristic optimization search, the novel method was successful in multi-modal function optimization.3. For the univariate orthogonal polynomial mixture model, an A image segmentation method was proposed on the basis of the Nonparametric Stochastic Nonparametric Estimation Maximization(SNEM) and Bayesian criterion. And the Mean Integrated Squared Error(MISE) is used to estimate the smooth parameter for each model, the SNEM algorithm is used to estimate the orthogonal polynomial coefficient and weight of each model, and the Bayesian principle is used to classify the images. Meanwhile, we developed a new image segmentation method based on non-parametric mixture models with spatial information, This method can effectively overcome the problem of "model mismatch", restrain noise and keep the edge property well. In comparison with other methods, our method has a better segmentation performance.4. To address the problem that univariate orthogonal polynomials can only use the gray feature, a new segmentation method with mixture models of multivariate orthogonal polynomials was proposed in this thesis. The multivariate orthogonal polynomials were derived by the Fourier analysis and tensor product theory, and the nonparametric mixture models of multivariate orthogonal polynomials were proposed. The parameters of the nonparametric mixture models of multivariate orthogonal polynomials algorithm was estimated by the method of Multivariate Orthogonal Polynomials Stochastic Nonparametric Expectation Maximum(MOP-SNEM). The experimental results with the images show that this method can achieve better segmentation results than the methods of mean-shift.5. Image fusion algorithms based on estimation theory assumed that all distortions should follow Gaussian distribution, which caused the problems of the model mismatch, of lossing local details, and of time-consuming. Therefore, this thesis proposed a new medical image fusion method based on multi-resolution and nonparametric orthogonal polynomials. First, decompose the source images into high frequency and low frequency band coefficients with multi-resolution decomposition. Then, the NEM algorithm is used to estimate the parameters of the image information model and the non-parametric orthogonal polynomials image mixture model. By which, the fusion result for low frequency band image is got. For the high frequency band image, selecting the maximum absolute value of the coefficient is applied to get the fusion result; finally, the fused image is obtained by reconstructing the inverse transformation of the results of high and low frequency images. Experimental results show that the proposed algorithm achieves better performance than other fusion methods and the fusion time is reduced considerably.