Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images

Finite Bivariate and Multivariate Beta Mixture Models Learning and Applications

Finite mixture models have been revealed to provide flexibility for data clustering. They have demonstrated high competence and potential to capture hidden structure in data. Modern technological progresses, growing volumes and varieties of generated data, revolutionized computers and other related factors are contributing to produce large scale data. This fact enhances the significance of finding reliable and adaptable models which can analyze bigger, more complex data to identify latent patterns, deliver faster and more accurate results and make decisions with minimal human interaction. Adopting the finest and most accurate distribution that appropriately represents the mixture components is critical. The most widely adopted generative model has been the Gaussian mixture. In numerous real-world applications, however, when the nature and structure of data are non-Gaussian, this modelling fails. One of the other crucial issues when using mixtures is determination of the model complexity or number of mixture components. Minimum message length (MML) is one of the main techniques in frequentist frameworks to tackle this challenging issue. In this work, we have designed and implemented a finite mixture model, using the bivariate and multivariate Beta distributions for cluster analysis and demonstrated its flexibility in describing the intrinsic characteristics of the observed data. In addition, we have applied our estimation and model selection algorithms to synthetic and real datasets. Most importantly, we considered interesting applications such as in image segmentation, software modules defect prediction, spam detection and occupancy estimation in smart buildings

Image Segmentation Based on Doubly Truncated Generalized Laplace Mixture Model and K Means Clustering

The present paper aims at performance evaluation of Doubly Truncated Generalized Laplace Mixture Model and K-Means clustering (DTGLMM-K) for image analysis concerned to various practical applications like security, surveillance, medical diagnostics and other areas. Among the many algorithms designed and developed for image segmentation the dominance of Gaussian Mixture Model (GMM) has been predominant which has the major drawback of suiting to a particular kind of data. Therefore the present work aims at development of DTGLMM-K algorithm which can be suitable for wide variety of applications and data. Performance evaluation of the developed algorithm has been donethrough various measures like Probabilistic Rand index (PRI), Global Consistency Error (GCE) and Variation of Information (VOI). During the current work case studies forvarious different images having pixel intensities has been carried out and the obtained results indicate the superiority of the developed algorithm for improved image segmentation

Unsupervised Selection and Estimation of Non-Gaussian Mixtures for High Dimensional Data Analysis

Lately, the enormous generation of databases in almost every aspect of life has created a great demand for new, powerful tools for turning data into useful information. Therefore, researchers were encouraged to explore and develop new machine learning ideas and methods. Mixture models are one of the machine learning techniques receiving considerable attention due to their ability to handle efficiently and effectively multidimensional data. Generally, four critical issues have to be addressed when adopting mixture models in high dimensional spaces: (1) choice of the probability density functions, (2) estimation of the mixture parameters, (3) automatic determination of the number of components M in the mixture, and (4) determination of what features best discriminate among the different components. The main goal of this thesis is to summarize all these challenging interrelated problems in one unified model. In most of the applications, the Gaussian density is used in mixture modeling of data. Although a Gaussian mixture may provide a reasonable approximation to many real-world distributions, it is certainly not always the best approximation especially in computer vision and image processing applications where we often deal with non-Gaussian data. Therefore, we propose to use three highly flexible distributions: the generalized Gaussian distribution (GGD), the asymmetric Gaussian distribution (AGD), and the asymmetric generalized Gaussian distribution (AGGD). We are motivated by the fact that these distributions are able to fit many distributional shapes and then can be considered as a useful class of flexible models to address several problems and applications involving measurements and features having well-known marked deviation from the Gaussian shape. Recently, researches have shown that model selection and parameter learning are highly dependent and should be performed simultaneously. For this purpose, many approaches have been suggested. The vast majority of these approaches can be classified, from a computational point of view, into two classes: deterministic and stochastic methods. Deterministic methods estimate the model parameters for a set of candidate models using the Expectation-Maximization (EM) framework, then choose the model that maximizes a model selection criterion. Stochastic methods such as Markov chain Monte Carlo (MCMC) can be used in order to sample from the full a posteriori distribution with M considered unknown. Hence, in this thesis, we propose three learning techniques capable of automatically determining model complexity while learning its parameters. First, we incorporate a Minimum Message Length (MML) penalty in the model learning step performed using the EM algorithm. Our second approach employs the Rival Penalized EM (RPEM) algorithm which is able to select an appropriate number of densities by fading out the redundant densities from a density mixture. Last but not least, we incorporate the nonparametric aspect of mixture models by assuming a countably infinite number of components and using Markov Chain Monte Carlo (MCMC) simulations for the estimation of the posterior distributions. Hence, the difficulty of choosing the appropriate number of clusters is sidestepped by assuming that there are an infinite number of mixture components. Another essential issue in the case of statistical modeling in general and finite mixtures in particular is feature selection (i.e. identification of the relevant or discriminative features describing the data) especially in the case of high-dimensional data. Indeed, feature selection has been shown to be a crucial step in several image processing, computer vision and pattern recognition applications not only because it speeds up learning but also because it improves model accuracy and generalization. Moreover, the learning of the mixture parameters ( i.e. both model selection and parameters estimation) is greatly affected by the quality of the features used. Hence, in this thesis, we are trying to solve the feature selection problem in unsupervised learning by casting it as an estimation problem, thus avoiding any combinatorial search. Finally, the effectiveness of our approaches is evaluated by applying them to different computer vision and image processing applications

Statistical Models for Co-occurrence Data

Modeling and predicting co-occurrences of events is a fundamental problem of unsupervised learning. In this contribution we develop a statistical framework for analyzing co-occurrence data in a general setting where elementary observations are joint occurrences of pairs of abstract objects from two finite sets. The main challenge for statistical models in this context is to overcome the inherent data sparseness and to estimate the probabilities for pairs which were rarely observed or even unobserved in a given sample set. Moreover, it is often of considerable interest to extract grouping structure or to find a hierarchical data organization. A novel family of mixture models is proposed which explain the observed data by a finite number of shared aspects or clusters. This provides a common framework for statistical inference and structure discovery and also includes several recently proposed models as special cases. Adopting the maximum likelihood principle, EM algorithms are derived to fit the model parameters. We develop improved versions of EM which largely avoid overfitting problems and overcome the inherent locality of EM--based optimization. Among the broad variety of possible applications, e.g., in information retrieval, natural language processing, data mining, and computer vision, we have chosen document retrieval, the statistical analysis of noun/adjective co-occurrence and the unsupervised segmentation of textured images to test and evaluate the proposed algorithms