In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear Feynman-Kac ow in distribution space. One interpretation of the Feynman-Kac ow corresponds to a nonlinear Markov kernel admitting a speci ed invariant distribution and is a natural nonlinear extension of the standard Metropolis-Hastings algorithm. Many theoretical results have already been established for such ows and their particle approximations. We demonstrate the use of these algorithms through simulation.

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 multi-target filter render it unusable for large numbers of targets. Conse-quently, 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 multi-target 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.

In this paper, we present a Bayesian framework for the fully automatic tracking of a variable number of interacting targets using a fixed camera. This framework uses a joint multi-object state-space formulation and a transdimensional Markov Chain Monte Carlo (MCMC) particle filter to recursively estimate the multi-object configuration and efficiently search the state-space. We also define a global observation model comprised of color and binary measurements capable of discriminating between different numbers of objects in the scene. We present results which show that our method is capable of tracking varying numbers of people through several challenging real-world tracking situations such as full/partial occlusion and entering/leaving the scene. 1.

Semantically-enhanced 3D model reconstruction in urban environments is useful in a variety of applications, such as extracting metric and semantic information about buildings, visualizing the data in a way that outlines important aspects, or urban planning. We present a probabilistic image-based approach to the semantic interpretation of building facades. We are motivated by the 4D Atlanta project at Georgia Tech, which aims to create a system that takes a collection of historical imagery of a city and infers a 3D model parameterized by time. Here it is necessary to recover, from historical imagery, metric and semantic information about buildings that might no longer exist or have undergone extensive change. Current approaches to automated 3D model reconstruction typically recover only geometry, and a systematic approach that allows hierarchical classification of structural elements is still largely missing. We extract metric and semantic information from images of facades, allowing us to decode the structural elements in them and their inter-relationships, thus providing access to highly structured descriptions of buildings. Our method is based on constructing a Bayesian generative model from stochastic context-free grammars that encode knowledge about facades. This model combines low-level segmentation and high-level hierarchical labelling so that the levels reinforce each other and produce a detailed hierarchical partition of the depicted facade into structural blocks. Markov chain Monte Carlo sampling is used to approximate the posterior over partitions given an image. We show results on a variety of real images of building facades. While we have currently tested only limited models of facades, we believe that our framework can be applied to much more general models, and are currently working towards that goal. 1

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Sequential Monte Carlo (SMC) methods are a class of importance sampling and resampling techniques designed to simulate from a sequence of probability distributions. These approaches have become very popular over the last few years to solve sequential Bayesian inference problems (e.g. Doucet et al. 2001). However, in comparison to Markov chain Monte Carlo (MCMC), the application of SMC remains limited when, in fact, such methods are also appropriate in such contexts (e.g. Chopin (2002); Del Moral et al. (2006)). In this paper, we present a simple unifying framework which allows us to extend both the SMC methodology and its range of applications. Additionally, reinterpreting SMC algorithms as an approximation of nonlinear MCMC kernels, we present alternative SMC and iterative self-interacting approximation (Del Moral & Miclo 2004; 2006) schemes. We demonstrate the performance of the SMC methodology on static and sequential Bayesian inference problems.

We introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. These problems are usually addressed using Sequential Monte Carlo (SMC) methods. The alternative Sequentially Interacting Markov Chain Monte Carlo (SIMCMC) scheme proposed here works by generating interacting non-Markovian sequences which behave asymptotically like independent Metropolis-Hastings (MH) Markov chains with the desired limiting distributions. Contrary to SMC methods, this scheme allows us to iteratively improve our estimates in an MCMC-like fashion. We establish convergence of the algorithm under realistic verifiable assumptions and demonstrate its performance on several examples arising in Bayesian time series analysis.

Abstract. We present novel sequential Monte Carlo (SMC) algorithms for the simulation of two broad classes of rare events which are suitable for the estimation of tail probabilities and probability density functions in the regions of rare events, as well as the simulation of rare system trajectories. These methods have some connection with previously proposed importance sampling (IS) and interacting particle system (IPS) methodologies, particularly those of [8, 4], but differ significantly from previous approaches in a number of respects: especially in that they operate directly on the path space of the Markov process of interest. 1.

We investigate the automated reconstruction of piecewise smooth 3D curves, using subdivision curves as a simple but flexible curve representation. This representation allows tagging corners to model nonsmooth features along otherwise smooth curves. We present a reversible jump Markov chain Monte Carlo approach which obtains an approximate posterior distribution over the number of control points and tags.

Images are the source of information in many areas of scientific enquiry. A common objective in these applications is reconstruction of the true scene from a degraded image. When objects in the image can be described parametrically, reconstruction can proceed by fitting a high level image model. In this article we consider the analysis of confocal fluorescence microscope images of cells in an area of cartilage growth. Biological questions posed by the experimenters concern the nature of the cells in the image and changes in their properties with time. Our model of the imaging process is based on a detailed analysis of the data. We treat the true scene as a realisation of a marked point process, incorporating this as the high-level prior model in a Bayesian analysis. Inference is by simulation using reversible jump versions of Markov chain Monte Carlo (MCMC) algorithms which can handle the varying dimension of the image description arising from an unknown number of cells, each with its own parameters.