A Bayesian approach to joint tracking and identification of geometric shapes in video sequences

Minvielle, Pierre; Doucet, Arnaud; Marrs, A.; Maskell, Simon

doi:10.1016/j.imavis.2009.05.002

Cited by 15 publications

(10 citation statements)

References 24 publications

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“…where (β k ) 0≤k≤n is a sequence of number increasing from 0 to 1, so that η 0 is the prior distribution of density p(x), easy to sample, and the terminal measure η n is the target distribution η (see, for instance, [4,30,37,38]). If we take V := x → − log(p(y|x)) and m(dx) := p(x) dx, then the η k coincide with the Boltzmann-Gibbs measures µ β k defined in (3.1).…”

Section: 1 Some Motivationsmentioning

confidence: 99%

“…Some nonasymptotic theorems have been recently developed [10,18], but unfortunately none of them apply to analyze annealed and adaptive FK particle models. On the other hand, these type of nonhomogeneous IPS algorithms are of current use for solving concrete problems arising in numerical physics and engineering sciences (see, e.g., [4,13,27,30,34,[37][38][39]). By the lack of nonasymptotic estimates, these particle algorithms are used as natural heuristics.Nonasymptotic analysis of adaptive and annealed Feynman-Kac particle models…”

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confidence: 99%

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Nonasymptotic analysis of adaptive and annealed Feynman–Kac particle models

Giraud¹,

Moral²

2017

Bernoulli

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Sequential and quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution spaces. The performance of these population Monte Carlo algorithms is strongly related to the stability properties of nonlinear Feynman-Kac semigroups. In this paper, we analyze these models in terms of Dobrushin ergodic coefficients of the reference Markov transitions and the oscillations of the potential functions. Sufficient conditions for uniform concentration inequalities w.r.t. time are expressed explicitly in terms of these two quantities. We provide an original perturbation analysis that applies to annealed and adaptive Feynman-Kac models, yielding what seems to be the first results of this kind for these types of models. Special attention is devoted to the particular case of Boltzmann-Gibbs measures' sampling. In this context, we design an explicit way of tuning the number of Markov chain Monte Carlo iterations with temperature schedule. We also design an alternative interacting particle method based on an adaptive strategy to define the temperature increments. The theoretical analysis of the performance of this adaptive model is much more involved as both the potential functions and the reference Markov transitions now depend on the random evolution on the particle model. The nonasymptotic analysis of these complex adaptive models is an open research problem. We initiate this study with the concentration analysis of a simplified adaptive models based on reference Markov transitions that coincide with the limiting quantities, as the number of particles tends to infinity.

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Section: 1 Some Motivationsmentioning

confidence: 99%

mentioning

confidence: 99%

Nonasymptotic analysis of adaptive and annealed Feynman–Kac particle models

Giraud¹,

Moral²

2017

Bernoulli

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“…. 10 6 900.0km 2 3.8 0.5 15 6 10251.6km 2 43.5 5.5 Simoncelli [1999], Minvielle et al [2010], and the references therein. The remainder of the discussion will focus on static 2D images.…”

Section: Introductionmentioning

confidence: 99%

Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model

Moores¹,

Nicholls²,

Pettitt³

et al. 2020

Bayesian Anal.

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The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There are a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open source implementation of our algorithm is available in the R package bayesImageS.

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“…By now, many JTC methods have been proposed [1][2][3][4][5][6][7][8][9][10], and these methods can roughly be divided into three categories. The first category is the most popular one and is dedicated to point targets.…”

Section: Introductionmentioning

confidence: 99%

Joint Tracking and Classification of Multiple Targets with Scattering Center Model and CBMeMBer Filter

Zhan

Wang

Zhang

2020

Sensors

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This paper deals with joint tracking and classification (JTC) of multiple targets based on scattering center model (SCM) and wideband radar observations. We first introduce an SCM-based JTC method, where the SCM is used to generate the predicted high range resolution profile (HRRP) with the information of the target aspect angle, and target classification is implemented through the data correlation of observed HRRP with predicted HRRPs. To solve the problem of multi-target JTC in the presence of clutter and detection uncertainty, we then integrate the SCM-based JTC method into the CBMeMBer filter framework, and derive a novel SCM-JTC-CBMeMBer filter with Bayesian theory. To further tackle the complex integrals’ calculation involved in targets state and class estimation, we finally provide the sequential Monte Carlo (SMC) implementation of the proposed SCM-JTC-CBMeMBer filter. The effectiveness of the presented multi-target JTC method is validated by simulation results under the application scenario of maritime ship surveillance.

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A Bayesian approach to joint tracking and identification of geometric shapes in video sequences

Cited by 15 publications

References 24 publications

Nonasymptotic analysis of adaptive and annealed Feynman–Kac particle models

Nonasymptotic analysis of adaptive and annealed Feynman–Kac particle models

Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model

Joint Tracking and Classification of Multiple Targets with Scattering Center Model and CBMeMBer Filter

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