Salvador Botello

An accurate and efficient Bayesian method for automatic segmentation of brain MRI

Automatic three-dimensional (3-D) segmentation of the brain from magnetic resonance (MR) scans is a challenging problem that has received an enormous amount of attention lately. Of the techniques reported in the literature, very few are fully automatic. In this paper, we present an efficient and accurate, fully automatic 3-D segmentation procedure for brain MR scans. It has several salient features; namely, the following. 1) Instead of a single multiplicative bias field that affects all tissue intensities, separate parametric smooth models are used for the intensity of each class. 2) A brain atlas is used in conjunction with a robust registration procedure to find a nonrigid transformation that maps the standard brain to the specimen to be segmented. This transformation is then used to: segment the brain from nonbrain tissue; compute prior probabilities for each class at each voxel location and find an appropriate automatic initialization. 3) Finally, a novel algorithm is presented which is a variant of the expectation-maximization procedure, that incorporates a fast and accurate way to find optimal segmentations, given the intensity models along with the spatial coherence assumption. Experimental results with both synthetic and real data are included, as well as comparisons of the performance of our algorithm with that of other published methods.

Hidden Markov measure field models for image segmentation

Parametric image segmentation consists of finding a label field that defines a partition of an image into a set of nonoverlapping regions and the parameters of the models that describe the variation of some property within each region. A new Bayesian formulation for the solution of this problem is presented, based on the key idea of using a doubly stochastic prior model for the label field, which allows one to find exact optimal estimators for both this field and the model parameters by the minimization of a differentiable function. An efficient minimization algorithm and comparisons with existing methods on synthetic images are presented, as well as examples of realistic applications to the segmentation of Magnetic Resonance volumes and to motion segmentation.

A Boltzmann based estimation of distribution algorithm

This paper introduces a new approach for estimation of distribution algorithms called the Boltzmann Univariate Marginal Distribution Algorithm (BUMDA). It uses a Normal-Gaussian model to approximate the Boltzmann distribution, hence, formulae for computing the mean and variance parameters of the Gaussian model are derived from the analytical minimization of the Kullback-Leibler divergence. The resulting formulae explicitly introduces information about the fitness landscape for the Gaussian parameters computation, in consequence, the Gaussian distribution obtains a better bias to sample intensively the most promising regions than simply using the maximum likelihood estimator of the selected set. In addition, the BUMDA formulae needs only one user parameter. Accordingly to the experimental results, the BUMDA excels in its niche of application. We provide theoretical, graphical and statistical analysis to show the BUMDA performance contrasted with state of the art EDAs.

An Accurate and Efficient Bayesian Method for Automatic Segmentation of Brain MRI

Automatic 3D segmentation of the brain from MR scans is a challenging problem that has received enormous amount of attention lately. Of the techniques reported in literature, very few are fully automatic. In this paper, we present an efficient and accurate, fully automatic 3D segmentation procedure for brain MR scans. It has several salient features namely, (1) instead of a single multiplicative bias field that affects all tissue intensities, separate parametric smooth models are used for the intensity of each class. This may be a more realistic model and avoids the need for a logarithmic transformation. (2) A brain atlas is used in conjunction with a robust registration procedure to find a non-rigid transformation that maps the standard brain to the specimen to be segmented. This transformation is then used to: segment the brain from non-brain tissue; compute prior probabilities for each class at each voxel location and find an appropriate automatic initialization. (3) Finally, a novel algorithm is presented which is a variant of the EM procedure, that incorporates a fast and accurate way to find optimal segmentations, given the intensity models along with the spatial coherence assumption. Experimental results with both synthetic and real data are included, as well as comparisons of the performance of our algorithm with that of other published methods.

Regularization methods for processing fringe-pattern images

A powerful technique for processing fringe-pattern images is based on Bayesian estimation theory with prior Markov random-field models. In this approach the solution of a processing problem is characterized as the minimizer of a cost function with terms that specify that the solution should be compatible with the available observations and terms that impose certain (prior) constraints on the solution. We show that, by the appropriate choice of these terms, one can use this approach in almost every processing step for accurate and robust interferogram demodulation and phase unwrapping.

Multigrid algorithms for processing fringe-pattern images

We present a modification of the multigrid method for the minimization of quadratic cost functions that result from the formulation of several problems in the digital processing of fringe-pattern images by using the Bayesian estimation-theory framework. With this modification the method can be applied to irregular domains and results in substantial savings in computational cost. We compare it with other state-of-the-art numerical techniques and present examples of its application to image smoothing without edge effects, robust quadrature filtering for the phase demodulation of spatial-carrier fringe patterns, and robust phase unwrapping.

A Set of Test Cases for Performance Measures in Multiobjective Optimization

Comparing the performance of different evolutive multiobjective algorithms is an open problem. With time, many performance measures have been proposed. Unfortunately, the evaluations of many of these performance measures disagree with the common sense of when a multiobjective algorithm is performing better than another. In this work we present a benchmark that is helpful to check if a performance measure actually has a good behavior. Some of the most popular performance measures in literature are tested. The results are valuable for a better understanding of what performance measures are better.

The MPM-MAP algorithm for image segmentation

We present a new algorithm for the efficient estimation of piecewise parametric models for image segmentation. This algorithm permits the simultaneous estimation of: the number of models; the parameters for each model and the regions where each model is applicable. It is based on Bayesian estimation theory, and is theoretically justified by the use of a specific cost function that decreases at every iteration and by a new model for the posterior marginal distributions which is amenable to the use of fast computational methods.

The MPM-MAP algorithm for motion segmentation

We present an MPM-MAP application for the efficient estimation of piecewise parametric models for motion segmentation. This algorithm permits the simultaneous estimation of: the number of models, the parameters for each model and the regions where each model is applicable. It is based on Bayesian estimation theory, and is theoretically justified by the use of a specific cost function whose expected value decreases at every iteration and by a new model for the posterior marginal distributions which is amenable to the use of fast computational methods. We compare the performance of this method with the most similar segmentation algorithm, the well known Expectation-Maximization algorithm. We present a comparison of the performance of both algorithms using synthetic and real image sequences.

On Modeling Flow in Fractal Media form Fractional Continuum Mechanics and Fractal Geometry

In this work we present a model for radial flow in highly heterogenous porous media. Heterogeneity is modeled by means of fractal geometry, a heterogeneous medium is regarded as fractal if its Hausdorff dimension is non-integral. Our purpose is to present a derivation of the model consistent with continuum mechanics, capable to describe anomalous diffusion as observed in some naturally fractured reservoirs. Consequently, we introduce fractional mass and a generalized Gauss theorem to obtain a continuity equation in fractal media. A generalized Darcy law for flux completes the model. Then we develop the basic equation for Well test analysis as is applied in petroleum engineering. Finally, the equation is solved by Laplace transform and inverted numerically to illustrate anomalous diffusion. In this case by showing that the flow rate from fractal systems is smaller than that from the Euclidean system.