This paper presents a new method based on the Expectation-Maximization (EM) algorithm that we apply for color image segmentation. Since this algorithm partitions the data based on an initial set of mixtures, the color segmentation provided by the EM algorithm is highly dependent on the starting condition (initialization stage). Usually the initialization procedure selects the color seeds random...

The expectation−maximization (EM) algorithm for maximum likelihood image recovery converges very slowly. Thus, the ordered subsets EM (OS−EM) algorithm has been widely used in image reconstruction for tomography due to an order−of−magnitude acceleration over the EM algorithm [1]. However, OS− EM is not guaranteed to converge. The recently proposed ordered subsets, separable paraboloidal surroga...

This paper proposes the first model-based clustering algorithm for multivariate functional data. After introducing multivariate functional principal components analysis (MFPCA), a parametric mixture model, based on the assumption of normality of the principal components, is defined and estimated by an EM-like algorithm. The main advantage of the proposed model is its ability to take into accoun...

Quantitative and qualitative description of particles is one of the most important tasks in the Electron Microscopy (EM) analysis. In this paper, we present an algorithm for identifying ball-like nanostructures of gahnite in the Transmission Electron Microscopy (TEM) images. Our solution is based on the cross-entropy clustering which allows to count and measure disk-like objects which are not n...

The Expectation Maximization (EM) algorithm [1, 2] is one of the most widely used algorithms in statistics. Suppose we are given some observed data X and a model family parametrized by θ, and would like to find the θ which maximizes p(X |θ), i.e. the maximum likelihood estimator. The basic idea of EM is actually quite simple: when direct maximization of p(X |θ) is complicated we can augment the...

In this article, an on-line EM algorithm is derived for general Exponential Family models with Hidden variables (EFH models). It is proven that the on-line EM algorithm is equivalent to a stochastic gradient method with the inverse of the Fisher information matrix as a coeecient matrix. As a result, the stochastic approximation theory guarantees the convergence to a local maximum of the likelih...

Mixture models have been widely used in cluster analysis. Traditional mixture densities-based clustering algorithms usually predefine the number of clusters via random selection or contend based knowledge. An improper pre-selection of the number of clusters may easily lead to bad clustering outcome. Expectation-maximization (EM) algorithm is a common approach to estimate the parameters of mixtu...

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown tha...

In the field of statistical data mining, the Expectation Maximization (EM) algorithm is one of the most popular methods used for solving parameter estimation problems in the maximum likelihood (ML) framework. Compared to traditional methods such as steepest descent, conjugate gradient, or Newton-Raphson, which are often too complicated to use in solving these problems, EM has become a popular m...

Model-based clustering using a family of Gaussian mixture models, with parsimonious factor analysis-like covariance structure, is described and an efficient algorithm for its implementation is presented. This algorithm uses the alternating expectationconditional maximization (AECM) variant of the expectation-maximization (EM) algorithm. Two central issues around the implementation of this famil...