The Experts below are selected from a list of 60111 Experts worldwide ranked by ideXlab platform
Dietrich Harder - One of the best experts on this subject based on the ideXlab platform.
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Spatial resolution of 2D ionization chamber arrays for IMRT dose verification: single-detector size and Sampling Step width.
Physics in medicine and biology, 2007Co-Authors: Björn Poppe, Armand Djouguela, Arne Blechschmidt, Kay Willborn, A. Rühmann, Dietrich HarderAbstract:The spatial resolution of 2D detector arrays equipped with ionization chambers or diodes, used for the dose verification of IMRT treatment plans, is limited by the size of the single detector and the centre-to-centre distance between the detectors. Optimization criteria with regard to these parameters have been developed by combining concepts of dosimetry and pattern analysis. The 2D-ARRAY Type 10024 (PTW-Freiburg, Germany), single-chamber cross section 5 × 5 mm2, centre-to-centre distance between chambers in each row and column 10 mm, served as an example. Additional frames of given dose distributions can be taken by shifting the whole array parallel or perpendicular to the MLC leaves by, e.g., 5 mm. The size of the single detector is characterized by its lateral response function, a trapezoid with 5 mm top width and 9 mm base width. Therefore, values measured with the 2D array are regarded as sample values from the convolution product of the accelerator generated dose distribution and this lateral response function. Consequently, the dose verification, e.g., by means of the gamma index, is performed by comparing the measured values of the 2D array with the values of the convolution product of the treatment planning system (TPS) calculated dose distribution and the single-detector lateral response function. Sufficiently small misalignments of the measured dose distributions in comparison with the calculated ones can be detected since the lateral response function is symmetric with respect to the centre of the chamber, and the change of dose gradients due to the convolution is sufficiently small. The Sampling Step width of the 2D array should provide a set of sample values representative of the sampled distribution, which is achieved if the highest spatial frequency contained in this function does not exceed the 'Nyquist frequency', one half of the Sampling frequency. Since the convolution products of IMRT-typical dose distributions and the single-detector lateral response function have no or very small frequency contributions beyond 0.1 mm−1, the mathematical approach introduced by Nyquist and Shannon shows that the Sampling frequency of 0.2 mm−1 is appropriate. Overall it is shown that the spatial resolution of the 2D-ARRAY Type 10024 is appropriate for the dose verification of IMRT plans. The insights obtained are also applied in the discussion of other available two-dimensional detector arrays.
Frank Dellaert - One of the best experts on this subject based on the ideXlab platform.
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MCMC-based particle filtering for tracking a variable number of interacting targets
IEEE transactions on pattern analysis and machine intelligence, 2005Co-Authors: Zia Khan, Tucker Balch, Frank DellaertAbstract:We describe a particle filter that effectively deals with interacting targets, targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multitarget filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance Sampling Step in the particle filter with a novel Markov chain Monte Carlo (MCMC) Sampling Step to obtain a more efficient MCMC-based multitarget filter. We also show how to extend this MCMC-based filter to address a variable number of interacting targets. Finally, we present both qualitative and quantitative experimental results, demonstrating that the resulting particle filters deal efficiently and effectively with complicated target interactions.
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ECCV (4) - An MCMC-Based Particle Filter for Tracking Multiple Interacting Targets
Lecture Notes in Computer Science, 2004Co-Authors: Zia Khan, Tucker Balch, Frank DellaertAbstract:We describe a Markov chain Monte Carlo based particle filter that effectively deals with interacting targets, i.e., targets that are influenced by the proximity and/or behavior of other targets. Such interactions cause problems for traditional approaches to the data association problem. In response, we developed a joint tracker that includes a more sophisticated motion model to maintain the identity of targets throughout an interaction, drastically reducing tracker failures. The paper presents two main contributions: (1) we show how a Markov random field (MRF) motion prior, built on the fly at each time Step, can substantially improve tracking when targets interact, and (2) we show how this can be done efficiently using Markov chain Monte Carlo (MCMC) Sampling. We prove that incorporating an MRF to model interactions is equivalent to adding an additional interaction factor to the importance weights in a joint particle filter. Since a joint particle filter suffers from exponential complexity in the number of tracked targets, we replace the traditional importance Sampling Step in the particle filter with an MCMC Sampling Step. The resulting filter deals efficiently and effectively with complicated interactions when targets approach each other. We present both qualitative and quantitative results to substantiate the claims made in the paper, including a large scale experiment on a video-sequence of over 10,000 frames in length.
Gabriel Stoltz - One of the best experts on this subject based on the ideXlab platform.
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Free energy methods for Bayesian inference: efficient exploration of univariate Gaussian mixture posteriors
Statistics and Computing, 2011Co-Authors: Nicolas Chopin, Tony Lelièvre, Gabriel StoltzAbstract:Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the Sampling of MCMC in this context, using a biasing procedure which originates from computational Statistical Physics. The principle is first to choose a "reaction coordinate", that is, a "direction" in which the target distribution is multimodal. In a second Step, the marginal log-density of the reaction coordinate with respect to the posterior distribution is estimated; minus this quantity is called "free energy" in the computational Statistical Physics literature. To this end, we use adaptive biasing Markov chain algorithms which adapt their targeted invariant distribution on the fly, in order to overcome Sampling barriers along the chosen reaction coordinate. Finally, we perform an importance Sampling Step in order to remove the bias and recover the true posterior. The efficiency factor of the importance Sampling Step can easily be estimated a priori once the bias is known, and appears to be rather large for the test cases we considered. A crucial point is the choice of the reaction coordinate. One standard choice (used for example in the classical Wang-Landau algorithm) is minus the log-posterior density. We discuss other choices. We show in particular that the hyper-parameter that determines the order of magnitude of the variance of each component is both a convenient and an efficient reaction coordinate. We also show how to adapt the method to compute the evidence (marginal likelihood) of a mixture model. We illustrate our approach by analyzing two real data sets.
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Free Energy Methods for Bayesian Inference: Efficient Exploration of Univariate Gaussian Mixture Posteriors
arXiv: Computation, 2010Co-Authors: Nicolas Chopin, Tony Lelièvre, Gabriel StoltzAbstract:Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the Sampling of MCMC in this context, using a biasing procedure which originates from computational Statistical Physics. The principle is first to choose a "reaction coordinate", that is, a "direction" in which the target distribution is multimodal. In a second Step, the marginal log-density of the reaction coordinate with respect to the posterior distribution is estimated; minus this quantity is called "free energy" in the computational Statistical Physics literature. To this end, we use adaptive biasing Markov chain algorithms which adapt their targeted invariant distribution on the fly, in order to overcome Sampling barriers along the chosen reaction coordinate. Finally, we perform an importance Sampling Step in order to remove the bias and recover the true posterior. The efficiency factor of the importance Sampling Step can easily be estimated \emph{a priori} once the bias is known, and appears to be rather large for the test cases we considered. A crucial point is the choice of the reaction coordinate. One standard choice (used for example in the classical Wang-Landau algorithm) is minus the log-posterior density. We discuss other choices. We show in particular that the hyper-parameter that determines the order of magnitude of the variance of each component is both a convenient and an efficient reaction coordinate. We also show how to adapt the method to compute the evidence (marginal likelihood) of a mixture model. We illustrate our approach by analyzing two real data sets.
Björn Poppe - One of the best experts on this subject based on the ideXlab platform.
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Spatial resolution of 2D ionization chamber arrays for IMRT dose verification: single-detector size and Sampling Step width.
Physics in medicine and biology, 2007Co-Authors: Björn Poppe, Armand Djouguela, Arne Blechschmidt, Kay Willborn, A. Rühmann, Dietrich HarderAbstract:The spatial resolution of 2D detector arrays equipped with ionization chambers or diodes, used for the dose verification of IMRT treatment plans, is limited by the size of the single detector and the centre-to-centre distance between the detectors. Optimization criteria with regard to these parameters have been developed by combining concepts of dosimetry and pattern analysis. The 2D-ARRAY Type 10024 (PTW-Freiburg, Germany), single-chamber cross section 5 × 5 mm2, centre-to-centre distance between chambers in each row and column 10 mm, served as an example. Additional frames of given dose distributions can be taken by shifting the whole array parallel or perpendicular to the MLC leaves by, e.g., 5 mm. The size of the single detector is characterized by its lateral response function, a trapezoid with 5 mm top width and 9 mm base width. Therefore, values measured with the 2D array are regarded as sample values from the convolution product of the accelerator generated dose distribution and this lateral response function. Consequently, the dose verification, e.g., by means of the gamma index, is performed by comparing the measured values of the 2D array with the values of the convolution product of the treatment planning system (TPS) calculated dose distribution and the single-detector lateral response function. Sufficiently small misalignments of the measured dose distributions in comparison with the calculated ones can be detected since the lateral response function is symmetric with respect to the centre of the chamber, and the change of dose gradients due to the convolution is sufficiently small. The Sampling Step width of the 2D array should provide a set of sample values representative of the sampled distribution, which is achieved if the highest spatial frequency contained in this function does not exceed the 'Nyquist frequency', one half of the Sampling frequency. Since the convolution products of IMRT-typical dose distributions and the single-detector lateral response function have no or very small frequency contributions beyond 0.1 mm−1, the mathematical approach introduced by Nyquist and Shannon shows that the Sampling frequency of 0.2 mm−1 is appropriate. Overall it is shown that the spatial resolution of the 2D-ARRAY Type 10024 is appropriate for the dose verification of IMRT plans. The insights obtained are also applied in the discussion of other available two-dimensional detector arrays.
Zia Khan - One of the best experts on this subject based on the ideXlab platform.
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MCMC-based particle filtering for tracking a variable number of interacting targets
IEEE transactions on pattern analysis and machine intelligence, 2005Co-Authors: Zia Khan, Tucker Balch, Frank DellaertAbstract:We describe a particle filter that effectively deals with interacting targets, targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multitarget filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance Sampling Step in the particle filter with a novel Markov chain Monte Carlo (MCMC) Sampling Step to obtain a more efficient MCMC-based multitarget filter. We also show how to extend this MCMC-based filter to address a variable number of interacting targets. Finally, we present both qualitative and quantitative experimental results, demonstrating that the resulting particle filters deal efficiently and effectively with complicated target interactions.
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ECCV (4) - An MCMC-Based Particle Filter for Tracking Multiple Interacting Targets
Lecture Notes in Computer Science, 2004Co-Authors: Zia Khan, Tucker Balch, Frank DellaertAbstract:We describe a Markov chain Monte Carlo based particle filter that effectively deals with interacting targets, i.e., targets that are influenced by the proximity and/or behavior of other targets. Such interactions cause problems for traditional approaches to the data association problem. In response, we developed a joint tracker that includes a more sophisticated motion model to maintain the identity of targets throughout an interaction, drastically reducing tracker failures. The paper presents two main contributions: (1) we show how a Markov random field (MRF) motion prior, built on the fly at each time Step, can substantially improve tracking when targets interact, and (2) we show how this can be done efficiently using Markov chain Monte Carlo (MCMC) Sampling. We prove that incorporating an MRF to model interactions is equivalent to adding an additional interaction factor to the importance weights in a joint particle filter. Since a joint particle filter suffers from exponential complexity in the number of tracked targets, we replace the traditional importance Sampling Step in the particle filter with an MCMC Sampling Step. The resulting filter deals efficiently and effectively with complicated interactions when targets approach each other. We present both qualitative and quantitative results to substantiate the claims made in the paper, including a large scale experiment on a video-sequence of over 10,000 frames in length.
