Yuqing Song

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.

A new clustering method of gene expression data based on multivariate Gaussian mixture models

Clustering gene expression data are an important problem in bioinformatics because understanding which genes behave similarly can lead to the discovery of important biological information. Many clustering methods have been used in the field of gene clustering. This paper proposed a new method for gene expression data clustering based on an improved expectation maximization(EM) method of multivariate Gaussian mixture models. To solve the problem of over-reliance on the initialization, we propose a remove and add initialization for the classical EM, and make a random perturbation on the solution before continuing EM iterations. The number of clusters is estimated with the Quasi Akaike’s information criterion in this paper. The improved EM method is tested and compared with some other clustering methods; the performance of our clustering algorithm has been extensively compared over several simulated and real gene expression data sets. Our results indicated that improved EM clustering method is superior than other clustering algorithms and can be widely used for gene clustering.

Brain MR image segmentation based on Gaussian mixture model with spatial information

As magnetic resonance imaging (MRI) is an important technology of radiological evaluation and computer-aided diagnosis, the accuracy of the MR image segmentation directly influences the validity of following processing. In general, the Gaussian mixture model (GMM) is highly effective for MR image segmentation. But for the conventional GMM appling in image segmentation, cluster assignment is based solely on the distribution of pixel attributes in the feature space, and the spatial distribution of pixels in an image is not taken into consideration. In this paper, we present a novel GMM scheme by utilizing local contextual information and the high inter-pixel correlation inherent for the segmentation of brain MR image. Firstly, a local spatial function is established, and the class probabilities of very pixels according to bayesian rules are determined adaptively based on local spatial function. Secondly, Expectation Maximization algorithm as an optimization method is used to obtain iterative formula of E-step and M-step for the proposed model Finally, the segmentation experiments by synthetic image and real image demonstrate that the proposed method can get a better classification result.

Fractal descriptors based on quaternion Fourier transform for color texture analysis

Abstract. Texture and color are important features in analyzing images of natural scenes. Fractal descriptors based on quaternion Fourier transform and local polynomial regression are proposed for color texture image analysis. First, considering the relation between the power spectrum and frequency in the quaternion Fourier transform domain, we proposed fractal dimensions of a color image using a fast quaternion Fourier transform. Second, local polynomial regression is applied to estimate log(spectrum)–log(frequency) curve, which is not usually linear in a natural texture image. Finally, a local polynomial regression curve is defined as fractal descriptors for the color image classification problem with multiclasses. The experimental results show that our proposed approach is more effective than other color texture analysis methods both in the correct classification rate and the duration.

Medical Image Clustering Based on Improved Particle Swarm Optimization and Expectation Maximization Algorithm

We proposed a hybrid clustering algorithm based on the improved particle swarm optimization algorithm and EM clustering algorithm to overcome the shortcomings of EM algorithm, which is sensitive to initial value and easy to sink into local minimum. First, get the optimal clustering number of any dataset to obtain the initial parameter of mixed model with the improved PSO algorithm, whose inertia weight increased and decreased along the fold line automatically. Then build the mixed density model of image data by multiple iterations of the EM algorithm. Finally divide all the pixel value of the image into corresponding branch of hybrid model with the Bayesian criterion to get the classification of image data. The proposed algorithm can increase the diversity of EM clustering algorithm initialization and promote optimization search in the global scope. Experimental results of simulation prove its accuracy and validity.

Medical image segmentation based on non-parametric mixture models with spatial information

Because of too much dependence on prior assumptions, parametric estimation methods using finite mixture models are sensitive to noise in image segmentation. In this study, we developed a new medical image segmentation method based on non-parametric mixture models with spatial information. First, we designed the non-parametric image mixture models based on the cosine orthogonal sequence and defined the spatial information functions to obtain the spatial neighborhood information. Second, we calculated the orthogonal polynomial coefficients and the mixing ratio of the models using expectation-maximization (EM) algorithm, to classify the images by Bayesian Principle. 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 appears to have a better performance in the segmentation of simulated brain images and computed tomography (CT) images.

An Improved Brain MRI Segmentation Method Based on Scale-Space Theory and Expectation Maximization Algorithm

Expectation Maximization EM algorithm is an unsupervised clustering algorithm, but initialization information especially the number of clusters is crucial to its performance. In this paper, a new MRI segmentation method based on scale-space theory and EM algorithm has been proposed. Firstly, gray level density of a brain MRI is estimated; secondly, the corresponding fingerprints which include initialization information for EM using scale-space theory are obtained; lastly, segmentation results are achieved by the initialized EM. During the initialization phase, restrictions of clustering component weights decrease the influence of noise or singular points. Brain MRI segmentation results indicate that our method can determine more reliable initialization information and achieve more accurate segmented tissues than other initialization methods.

Noised image segmentation based on rough set and orthogonal polynomial density model

Abstract. In order to segment a noised image, a method is proposed based on the rough set and orthogonal polynomial density model, in which the nonparametric mixture model can accurately fit the image gray distribution and the rough set can deal with the inaccuracy and uncertainty problems. First, the nonparametric mixture density model is constructed based on the upper and lower approximations of the rough set which can address the problem of over-relying on the prior presumption. Second, the nonparametric expectation-maximization is used to estimate the mixture model parameters. Finally, image pixels are classified according to Bayesian criterion. Experiments on different datasets show that our method is effective in solving the problem of model mismatch, restraining the noise, and preserving the boundary for the noised image segmentation.

A method of wavelet-based dual thresholding de-noising for ECG signal

ECG (Electrocardiography) signal is one of important means of clinical diagnosis for heart disease which has great significance in clinical medicine. De-noising is a critical task in the preprocess of ECG signal. This paper proposed a dual thresholding function and a level-dependent threshold estimator by the different thresholds estimated based on wavelet coefficients in different layers. Experiments were carried out and the results suggest that the proposed new threshold algorithm is suitable to remove the ECG signal noise and has potential in ECG signal processing field.

Image segmentation based on finite mixture models of nonparametric Hermite orthogonal sequence

To solve the problem of over-reliance on priori assumptions of the parameter methods for finite mixture models, a nonparametric Hermite orthogonal sequence of mixture model for image segmentation method is proposed in this paper. First, the Hermite orthogonal sequence base on the image nonparametric mixture model is designed, and the mean integrated squared error(MISE) is used to estimate the smoothing parameter for each model; Second, the Expectation Maximum(EM) algorithm is used to estimate the orthogonal polynomial coefficients and the model of the weight. This method does not require any prior assumptions on the model, and it can effectively overcome the “model mismatch” problem. The experimental results with the images show that this method can achieve better segmentation results than the Gaussian Mixture Models method.