The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform

Ayman Elbaz - One of the best experts on this subject based on the ideXlab platform.

  • modified akaike information criterion for estimating the number of components in a Probability mixture model
    International Conference on Image Processing, 2012
    Co-Authors: Ahmed Elnakib, Georgy Gimelfarb, Tamer Inanc, Ayman Elbaz
    Abstract:

    To estimate the number of unimodal components in a mixture model of a Marginal Probability Distribution of signals while learning the model with a conventional Expectation-Maximization (EM) algorithm, a modification of the well-known Akaike information criterion (AIC) called the modified AIC (mAIC), is proposed. Embedding the mAIC into the EM algorithm allows us to exclude sequentially, one-by-one, the least informative components from their initially excessive, or over-fitting set. Experiments on modeling empirical Marginal signal Distributions with mixtures of continuous or discrete Gaussians in order to describe the visual appearance of synthetic phantoms and real medical 3D images (lung CT and brain MRI) demonstrate a marked and monotone increase of the mAIC towards its maximum at the proper number that is known for the synthetic phantom or practically justified for the real image. These results confirm the accuracy and robustness of the proposed automated mAIC-EM based learning.

  • accurate modeling of tagged cmr 3d image appearance characteristics to improve cardiac cycle strain estimation
    International Conference on Image Processing, 2012
    Co-Authors: Matthew Nitzken, Georgy Gimelfarb, Ahmed Elnakib, Fahmi Khalifa, Garth M Beache, Ayman Elbaz
    Abstract:

    To reduce noise within a tag line, unsharpen the tag edges in spatial domain, and amplify the tag-to-background contrast, a 3D energy minimization framework for the enhancement of tagged Cardiac Magnetic Resonance (CMR) image sequences, based on learning first- and second-order visual appearance models, is proposed. The first-order appearance modeling uses adaptive Linear Combinations of Discrete Gaussians (LCDG) to accurately approximate the empirical Marginal Probability Distribution of CMR signals for a given sequence, and separates tag and background submodels. It is also used to classify the tag lines and the background. The second-order model considers image sequences as samples of a translation- and rotation-invariant 3D Markov-Gibbs Random Field (MGRF) with multiple pairwise voxel interactions. A 3D energy function for this model is built by using the analytical estimation of the spatio-temporal geometry and Gibbs potentials of interaction. To improve the strain estimation, by enhancing the tag and background homogeneity and contrast, the given sequence is adjusted using comparisons to the energy minimizer. Special 3D geometric phantoms, motivated by statistical analysis of the tagged CMR data, have been designed to validate the accuracy of our approach. Experiments with the phantoms and eight real data sets have confirmed the high accuracy of the functional parameters that are estimated for the enhanced tagged sequences when using popular spectral techniques, such as spectral Harmonic Phase (HARP).

  • improving full cardiac cycle strain estimation from tagged cmr by accurate modeling of 3d image appearance characteristics
    International Symposium on Biomedical Imaging, 2012
    Co-Authors: Matthew Nitzken, Georgy Gimelfarb, Ahmed Elnakib, Fahmi Khalifa, Garth M Beache, Ayman Elbaz
    Abstract:

    To reduce noise within a tag line, unsharpen tag edges in the spatial domain, and amplify the tag-to-background contrast, a 3D energy minimization framework for the enhancement of tagged Cardiac Magnetic Resonance (CMR) images, that is based on first- and second-order learned visual appearance models, is proposed. The first-order appearance modeling uses an adaptive Linear Combination of Discrete Gaussians (LCDG) to accurately approximate the empirical Marginal Probability Distribution of CMR signals for a given sequence, and to separate the tag and background submodels. It is also used to classify the tag lines and the background. The second-order model considers image sequences as samples of a translation- and rotation-invariant 3D Markov-Gibbs Random Field (MGRF), with multiple pairwise voxel interactions. A 3D energy function for this model is built by using the analytical estimation of the spatiotemporal geometry and the Gibbs potentials of interaction. To improve the strain estimation, through enhancement of the tag and background homogeneity and contrast, the given sequence is adjusted using comparisons to the energy minimizer. Special 3D geometric phantoms, motivated by the statistical analysis of the tagged CMR data, have been designed to validate the accuracy of our approach. Experiments with the phantoms and eight in-vivo data sets have confirmed the high accuracy of functional parameter estimation for the enhanced CMR images when using popular spectral techniques, such as spectral Harmonic Phase (HARP).

  • precise segmentation of 3 d magnetic resonance angiography
    IEEE Transactions on Biomedical Engineering, 2012
    Co-Authors: Ayman Elbaz, Ahmed Elnakib, Fahmi Khalifa, Mohamed Abou Elghar, Patrick Mcclure, Ahmed Soliman, G Gimelrfarb
    Abstract:

    Accurate automatic extraction of a 3-D cerebrovascular system from images obtained by time-of-flight (TOF) or phase contrast (PC) magnetic resonance angiography (MRA) is a challenging segmentation problem due to the small size objects of interest (blood vessels) in each 2-D MRA slice and complex surrounding anatomical structures (e.g., fat, bones, or gray and white brain matter). We show that due to the multimodal nature of MRA data, blood vessels can be accurately separated from the background in each slice using a voxel-wise classification based on precisely identified Probability models of voxel intensities. To identify the models, an empirical Marginal Probability Distribution of intensities is closely approximated with a linear combination of discrete Gaussians (LCDG) with alternate signs, using our previous EM-based techniques for precise linear combination of Gaussian-approximation adapted to deal with the LCDGs. The high accuracy of the proposed approach is experimentally validated on 85 real MRA datasets (50 TOF and 35 PC) as well as on synthetic MRA data for special 3-D geometrical phantoms of known shapes.

German Drazer - One of the best experts on this subject based on the ideXlab platform.

  • Transport of Brownian particles confined to a weakly corrugated channel
    Physics of Fluids, 2010
    Co-Authors: Xinli Wang, German Drazer
    Abstract:

    We investigate the average velocity of Brownian particles driven by a constant external force when constrained to move in two-dimensional, weakly-corrugated channels. We consider both the geometric confinement of the particles between solid walls as well as the soft confinement induced by a periodic potential. Using perturbation methods we show that the leading order correction to the Marginal Probability Distribution of particles in the case of soft confinement is equal to that obtained in the case of geometric confinement, provided that the (configuration) integral over the cross-section of the confining potential is equal to the width of the solid channel. We then calculate the Probability Distribution and average velocity in the case of a sinusoidal variation in the width of the channels. The reduction on the average velocity is larger in the case of soft channels at small P\'eclet numbers and for relatively narrow channels and the opposite is true at large P\'eclet numbers and for wide channels. In the limit of large P\'eclet numbers the convergence to bulk velocity is faster in the case of soft channels. The leading order correction to the average velocity and Marginal Probability Distribution agree well with Brownian Dynamics simulations for the two types of confinement and over a wide range of P\'eclet numbers.

  • transport properties of brownian particles confined to a narrow channel by a periodic potential
    Physics of Fluids, 2009
    Co-Authors: Xinli Wang, German Drazer
    Abstract:

    We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick–Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the Marginal Probability Distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Peclet numbers.

  • transport properties of brownian particles confined to a narrow channel by a periodic potential
    arXiv: Statistical Mechanics, 2009
    Co-Authors: Xinli Wang, German Drazer
    Abstract:

    We investigate the transport of Brownian particles in a two-dimensional potential under the action of a uniform external force. The potential is periodic in one direction and confines the particle to a narrow channel of varying cross-section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of the parabolic potential in the cross-section. We obtain excellent agreement for the Marginal Probability Distribution, the average velocity of the Brownian particles and the asymptotic dispersion coefficient, over a wide range of Peclet numbers.

George Stefanou - One of the best experts on this subject based on the ideXlab platform.

  • Response variability of cylindrical shells with stochastic non-Gaussian material and geometric properties
    Engineering Structures, 2011
    Co-Authors: George Stefanou
    Abstract:

    Abstract In this paper, the effect of combined uncertain material (Young’s modulus, Poisson’s ratio) and geometric (thickness) properties on the response variability of cylindrical shells is investigated taking into account various non-Gaussian assumptions for the uncertain parameters. These parameters are described by two-dimensional univariate homogeneous non-Gaussian stochastic fields using the spectral representation method in conjunction with translation field theory. The response variability is computed by means of direct Monte Carlo simulation (MCS). It is shown that the Marginal Probability Distribution and the correlation scale of the stochastic fields used for the description of the material and thickness variability affect significantly the shell response statistics.

  • Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties
    International Journal of Solids and Structures, 2009
    Co-Authors: Vissarion Papadopoulos, George Stefanou, Manolis Papadrakakis
    Abstract:

    AbstractIn this paper, the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections is investigated. To this purpose, a random spatial variability of the elastic modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric deviations of the shell structure from its perfect geometry. The main novelty of this paper compared to previous works is that a non-Gaussian assumption is made for the Distribution of the two aforementioned uncertain parameters i.e. the modulus of elasticity and the shell thickness which are described by two-dimensional uni-variate (2D-1V) homogeneous non-Gaussian stochastic fields. The initial geometric imperfections are described as a 2D-1V Gaussian non-homogeneous stochastic field with properties derived from corresponding experimental measurements. Numerical examples are presented focusing on the influence of the non-Gaussian assumption on the variability of the buckling load, which is calculated by means of the Monte Carlo Simulation method. It is shown that the choice of the Marginal Probability Distribution for the description of the material and thickness variability is crucial since it affects significantly the statistics of the buckling load of imperfection sensitive shell-type structures

Fahmi Khalifa - One of the best experts on this subject based on the ideXlab platform.

  • accurate modeling of tagged cmr 3d image appearance characteristics to improve cardiac cycle strain estimation
    International Conference on Image Processing, 2012
    Co-Authors: Matthew Nitzken, Georgy Gimelfarb, Ahmed Elnakib, Fahmi Khalifa, Garth M Beache, Ayman Elbaz
    Abstract:

    To reduce noise within a tag line, unsharpen the tag edges in spatial domain, and amplify the tag-to-background contrast, a 3D energy minimization framework for the enhancement of tagged Cardiac Magnetic Resonance (CMR) image sequences, based on learning first- and second-order visual appearance models, is proposed. The first-order appearance modeling uses adaptive Linear Combinations of Discrete Gaussians (LCDG) to accurately approximate the empirical Marginal Probability Distribution of CMR signals for a given sequence, and separates tag and background submodels. It is also used to classify the tag lines and the background. The second-order model considers image sequences as samples of a translation- and rotation-invariant 3D Markov-Gibbs Random Field (MGRF) with multiple pairwise voxel interactions. A 3D energy function for this model is built by using the analytical estimation of the spatio-temporal geometry and Gibbs potentials of interaction. To improve the strain estimation, by enhancing the tag and background homogeneity and contrast, the given sequence is adjusted using comparisons to the energy minimizer. Special 3D geometric phantoms, motivated by statistical analysis of the tagged CMR data, have been designed to validate the accuracy of our approach. Experiments with the phantoms and eight real data sets have confirmed the high accuracy of the functional parameters that are estimated for the enhanced tagged sequences when using popular spectral techniques, such as spectral Harmonic Phase (HARP).

  • improving full cardiac cycle strain estimation from tagged cmr by accurate modeling of 3d image appearance characteristics
    International Symposium on Biomedical Imaging, 2012
    Co-Authors: Matthew Nitzken, Georgy Gimelfarb, Ahmed Elnakib, Fahmi Khalifa, Garth M Beache, Ayman Elbaz
    Abstract:

    To reduce noise within a tag line, unsharpen tag edges in the spatial domain, and amplify the tag-to-background contrast, a 3D energy minimization framework for the enhancement of tagged Cardiac Magnetic Resonance (CMR) images, that is based on first- and second-order learned visual appearance models, is proposed. The first-order appearance modeling uses an adaptive Linear Combination of Discrete Gaussians (LCDG) to accurately approximate the empirical Marginal Probability Distribution of CMR signals for a given sequence, and to separate the tag and background submodels. It is also used to classify the tag lines and the background. The second-order model considers image sequences as samples of a translation- and rotation-invariant 3D Markov-Gibbs Random Field (MGRF), with multiple pairwise voxel interactions. A 3D energy function for this model is built by using the analytical estimation of the spatiotemporal geometry and the Gibbs potentials of interaction. To improve the strain estimation, through enhancement of the tag and background homogeneity and contrast, the given sequence is adjusted using comparisons to the energy minimizer. Special 3D geometric phantoms, motivated by the statistical analysis of the tagged CMR data, have been designed to validate the accuracy of our approach. Experiments with the phantoms and eight in-vivo data sets have confirmed the high accuracy of functional parameter estimation for the enhanced CMR images when using popular spectral techniques, such as spectral Harmonic Phase (HARP).

  • precise segmentation of 3 d magnetic resonance angiography
    IEEE Transactions on Biomedical Engineering, 2012
    Co-Authors: Ayman Elbaz, Ahmed Elnakib, Fahmi Khalifa, Mohamed Abou Elghar, Patrick Mcclure, Ahmed Soliman, G Gimelrfarb
    Abstract:

    Accurate automatic extraction of a 3-D cerebrovascular system from images obtained by time-of-flight (TOF) or phase contrast (PC) magnetic resonance angiography (MRA) is a challenging segmentation problem due to the small size objects of interest (blood vessels) in each 2-D MRA slice and complex surrounding anatomical structures (e.g., fat, bones, or gray and white brain matter). We show that due to the multimodal nature of MRA data, blood vessels can be accurately separated from the background in each slice using a voxel-wise classification based on precisely identified Probability models of voxel intensities. To identify the models, an empirical Marginal Probability Distribution of intensities is closely approximated with a linear combination of discrete Gaussians (LCDG) with alternate signs, using our previous EM-based techniques for precise linear combination of Gaussian-approximation adapted to deal with the LCDGs. The high accuracy of the proposed approach is experimentally validated on 85 real MRA datasets (50 TOF and 35 PC) as well as on synthetic MRA data for special 3-D geometrical phantoms of known shapes.

H J Kappen - One of the best experts on this subject based on the ideXlab platform.

  • bounds on Marginal Probability Distributions
    Neural Information Processing Systems, 2008
    Co-Authors: Joris M Mooij, H J Kappen
    Abstract:

    We propose a novel bound on single-variable Marginal Probability Distributions in factor graphs with discrete variables. The bound is obtained by propagating local bounds (convex sets of Probability Distributions) over a subtree of the factor graph, rooted in the variable of interest. By construction, the method not only bounds the exact Marginal Probability Distribution of a variable, but also its approximate Belief Propagation Marginal ("belief"). Thus, apart from providing a practical means to calculate bounds on Marginals, our contribution also lies in providing a better understanding of the error made by Belief Propagation. We show that our bound outperforms the state-of-the-art on some inference problems arising in medical diagnosis.

  • NIPS - Bounds on Marginal Probability Distributions
    2008
    Co-Authors: Joris M Mooij, H J Kappen
    Abstract:

    We propose a novel bound on single-variable Marginal Probability Distributions in factor graphs with discrete variables. The bound is obtained by propagating local bounds (convex sets of Probability Distributions) over a subtree of the factor graph, rooted in the variable of interest. By construction, the method not only bounds the exact Marginal Probability Distribution of a variable, but also its approximate Belief Propagation Marginal ("belief"). Thus, apart from providing a practical means to calculate bounds on Marginals, our contribution also lies in providing a better understanding of the error made by Belief Propagation. We show that our bound outperforms the state-of-the-art on some inference problems arising in medical diagnosis.

  • Novel Bounds on Marginal Probabilities
    arXiv: Probability, 2008
    Co-Authors: Joris M Mooij, H J Kappen
    Abstract:

    We derive two related novel bounds on single-variable Marginal Probability Distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second method propagates bounds over the self-avoiding walk tree starting at the variable. By construction, both methods not only bound the exact Marginal Probability Distribution of a variable, but also its approximate Belief Propagation Marginal (``belief''). Thus, apart from providing a practical means to calculate bounds on Marginals, our contribution also lies in an increased understanding of the error made by Belief Propagation. Empirically, we show that our bounds often outperform existing bounds in terms of accuracy and/or computation time. We also show that our bounds can yield nontrivial results for medical diagnosis inference problems.