Results 1  10
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102
CONDENSATION  conditional density propagation for visual tracking
 International Journal of Computer Vision
, 1998
"... The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimodal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses "factored sampling", previously appli ..."
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Cited by 1159 (12 self)
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The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimodal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses "factored sampling", previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set. Condensation uses learned dynamical models, together with visual observations, to propagate the random set over time. The result is highly robust tracking of agile motion. Notwithstanding the use of stochastic methods, the algorithm runs in near realtime. Contents 1 Tracking curves in clutter 2 2 Discretetime propagation of state density 3 3 Factored sampling 6 4 The Condensation algorithm 8 5 Stochastic dynamical models for curve motion 10 6 Observation model 13 7 Applying the Condensation algorithm to videostreams 17 8 Conclusions 26 A Nonline...
Waveletbased statistical signal processing using hidden Markov models
 IEEE Transactions on Signal Processing
, 1998
"... Abstract — Waveletbased statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many realworld signals. In this paper, we develop a new framework for statistical signal pr ..."
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Cited by 331 (52 self)
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Abstract — Waveletbased statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many realworld signals. In this paper, we develop a new framework for statistical signal processing based on waveletdomain hidden Markov models (HMM’s) that concisely models the statistical dependencies and nonGaussian statistics encountered in realworld signals. Waveletdomain HMM’s are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMM’s to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of waveletdomain HMM’s, we develop novel algorithms for signal denoising, classification, and detection. Index Terms — Hidden Markov model, probabilistic graph, wavelets.
The Gaussian mixture probability hypothesis density filter
 IEEE Trans. SP
, 2006
"... Abstract — A new recursive algorithm is proposed for jointly estimating the timevarying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty, detection uncertainty, noise and false alarms. The approach involves modelling the respecti ..."
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Cited by 64 (9 self)
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Abstract — A new recursive algorithm is proposed for jointly estimating the timevarying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty, detection uncertainty, noise and false alarms. The approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density (PHD) recursion to propagate the posterior intensity, which is a first order statistic of the random finite set of targets, in time. At present, there is no closed form solution to the PHD recursion. This work shows that under linear, Gaussian assumptions on the target dynamics and birth process, the posterior intensity at any time step is a Gaussian mixture. More importantly, closed form recursions for propagating the means, covariances and weights of the constituent Gaussian components of the posterior intensity are derived. The proposed algorithm combines these recursions with a strategy for managing the number of Gaussian components to increase efficiency. This algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented Kalman filters. Index Terms — Multitarget tracking, optimal filtering, point
Bayesian Forecasting
, 1996
"... rapolation techniques, especially exponential smoothing and exponentially weighted moving average methods ([20, 71]). Developments of smoothing and discounting techniques in stock control and production planning areas led to formalisms in terms of linear, statespace models for time series with time ..."
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Cited by 59 (2 self)
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rapolation techniques, especially exponential smoothing and exponentially weighted moving average methods ([20, 71]). Developments of smoothing and discounting techniques in stock control and production planning areas led to formalisms in terms of linear, statespace models for time series with timevarying trends and seasonal patterns, and eventually to the associated Bayesian formalism of methods of inference and prediction. From the early 1960s, practical Bayesian forecasting systems in this context involved the combination of formal time series models and historical data analysis together with methods for subjective intervention and forecast monitoring, so that complete forecasting systems, rather than just routine and automatic data analysis and extrapolation, were in use at that time ([19, 22]). Methods developed in those early days are still in use now in some companies in sales forecasting and stock control areas. There have been major developments in models and methods since t
Bayesian Compressed Sensing via Belief Propagation
, 2010
"... Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, subNyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can comple ..."
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Cited by 57 (13 self)
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Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, subNyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length signal containing large coefficients, our CSBP decoding algorithm uses ( log ()) measurements and ( log 2 ()) computation. Finally, although we focus on a twostate mixture Gaussian model, CSBP is easily adapted to other signal models.
Compressed Sensing Reconstruction via Belief Propagation
, 2006
"... Compressed sensing is an emerging field that enables to reconstruct sparse or compressible signals from a small number of linear projections. We describe a specific measurement scheme using an LDPClike measurement matrix, which is a realvalued analogue to LDPC techniques over a finite alphabet. We ..."
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Cited by 42 (8 self)
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Compressed sensing is an emerging field that enables to reconstruct sparse or compressible signals from a small number of linear projections. We describe a specific measurement scheme using an LDPClike measurement matrix, which is a realvalued analogue to LDPC techniques over a finite alphabet. We then describe the reconstruction details for mixture Gaussian signals. The technique can be extended to additional compressible signal models. 1
Gaussian sum particle filtering
 Signal Processing 51
, 2003
"... Abstract—In this paper, we use the Gaussian particle filter introduced in a companion paper to build several types of Gaussian sum particle filters. These filters approximate the filtering and predictive distributions by weighted Gaussian mixtures and are basically banks of Gaussian particle filters ..."
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Cited by 42 (2 self)
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Abstract—In this paper, we use the Gaussian particle filter introduced in a companion paper to build several types of Gaussian sum particle filters. These filters approximate the filtering and predictive distributions by weighted Gaussian mixtures and are basically banks of Gaussian particle filters. Then, we extend the use of Gaussian particle filters and Gaussian sum particle filters to dynamic state space (DSS) models with nonGaussian noise. With nonGaussian noise approximated by Gaussian mixtures, the nonGaussian noise models are approximated by banks of Gaussian noise models, and Gaussian mixture filters are developed using algorithms developed for Gaussian noise DSS models. 1 As a result, problems involving heavytailed densities can be conveniently addressed. Simulations are presented to exhibit the application of the framework developed herein, and the performance of the algorithms is examined. Index Terms—Dynamic statespace models, extended Kalman
A hybrid bootstrap filter for target tracking in clutter
 IEEE Trans on Aerospace and Electronic Systems
, 1997
"... ..."
Sequential Monte Carlo Methods to Train Neural Network Models
, 2000
"... We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/ sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequentia ..."
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Cited by 34 (8 self)
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We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/ sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving online, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the onestepahead probability density functions of the options prices.
Visual Motion Analysis by Probabilistic Propagation of Conditional Density
, 1998
"... This thesis establishes a stochastic framework for tracking curves in visual clutter, using a Bayesian randomsampling algorithm. The approach is rooted in ideas from statistics, control theory and computer vision. The problem is to track outlines and features of foreground objects, modelled as curv ..."
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Cited by 30 (0 self)
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This thesis establishes a stochastic framework for tracking curves in visual clutter, using a Bayesian randomsampling algorithm. The approach is rooted in ideas from statistics, control theory and computer vision. The problem is to track outlines and features of foreground objects, modelled as curves, as they move in substantial clutter, and to do it at, or close to, video framerate. The algorithm, named Condensation, for Conditional density propagation, has recently been derived independently by several researchers, and is generating signi cant interest in the statistics and signal processing communities. This thesis contributes to the literature on Condensationlike lters by presenting some novel applications of and extensions to the basic algorithm, and contributes to the visual motion estimation literature by demonstrating high tracking performance in cluttered environments. Despite its power the Condensation algorithm has a remarkably simple form and this allows the use of nonlinear motion models which combine characteristics of discrete Hidden Markov Models with the continuous AutoRegressive Process motion models traditionally used in Kalman lters. These mixed discretecontinuous models have promising applications to the emerging eld of perception of action. This thesis also implements two algorithms to smooth the output of the Condensation lter which improves the accuracy of motion estimation in a batchmode procedure after tracking is complete.