Markov random field

About: Markov random field is a research topic. Over the lifetime, 5669 publications have been published within this topic receiving 179568 citations. The topic is also known as: MRF.

Efficient recursions for general factorisable models

Abstract: Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.

Application of the EM algorithm for the multitarget/multisensor tracking problem

Abstract: An important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies. A number of approaches have been proposed for this multitarget/multisensor tracking problem ranging from reasonably simple, though ad hoc, schemes to fairly complex, but theoretically optimum, approaches. In this paper, we describe an iterative procedure for time-recursive multitarget/multisensor tracking based on use of the expectation-maximization (EM) algorithm. More specifically, we pose the multitarget/multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data, whereas the target-associated sensor outputs constitute the complete data. Target updates at each time use an EM-based approach that calculates the maximum a posteriori (MAP) estimate of the target states, under the assumption of appropriate motion models, based on the outputs of disparate sensors. The approach uses a Markov random field (MRF) model of the associations between observations and targets and allows for estimation of joint association probabilities without explicit enumeration. The advantage of this EM-based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities. We provide selected results illustrating the performance/complexity characteristics of this EM-based approach compared with competing schemes.

Modeling spatial-temporal binary data using Markov random fields

Abstract: An autologistic regression model consists of a logistic regression of a response variable on explanatory variables and an autoregression on responses at neighboring locations on a lattice. It is a Markov random field with pairwise spatial dependence and is a popular tool for modeling spatial binary responses. In this article, we add a temporal component to the autologistic regression model for spatial-temporal binary data. The spatial-temporal autologistic regression model captures the relationship between a binary response and potential explanatory variables, and adjusts for both spatial dependence and temporal dependence simultaneously by a space-time Markov random field. We estimate the model parameters by maximum pseudo-likelihood and obtain optimal prediction of future responses on the lattice by a Gibbs sampler. For illustration, the method is applied to study the outbreaks of southern pine bettle in North Carolina. We also discuss the generality of our approach for modeling other types of spatial-temporal lattice data.