We present a recursive algorithm to compute a collection of normalising constants which can be used in a straightforward manner to sample a realisation from a Markov random field. Further we present important consequences of this result which renders possible tasks such as maximising Markov random fields, computing marginal distributions, exact inference for certain loss functions and computing...

Markov Random Fields (MRFs) are used in a large array of computer vision applications. Finding the Maximum Aposteriori (MAP) solution of an MRF is in general intractable, and one has to resort to approximate solutions, such as Belief Propagation, Graph Cuts, or more recently, approaches based on quadratic programming. We propose a novel type of approximation, Spectral relaxation to Quadratic Pr...

We present a fully automated framework for identifying multiple sclerosis (MS) lesions from multispectral human brain magnetic resonance images (MRIs). The brain tissue intensities and lesions are both modeled using Markov Random Fields (MRFs) to incorporate local spatial variations and neighborhood information. In this work, we model all brain tissues, including lesions, as separate classes as...

One important and natural application of discrete Markov Random Fields [4] in Image analysis is for texture modelling and segmenation [5]. In this report we describe texture segmentation algorithms which have been performed on two mosaics (See Figure 1). Markov Random Fields were used to model the textures and the textures were distinguished by their parameters, θ, μ, and σ. The Minimum Varianc...

We derive an approximate maximum a posteriori (MAP) method for detecting NDE defect signals using hidden Markov random fields (HMRFs). In the proposed HMRF framework, a set of spatially distributed NDE measurements is assumed to form a noisy realization of an underlying random field that has a simple structure with Markovian dependence. Here, the random field describes the defect signals to be ...

Here we describe the stereo matching problem from computer vision, and some techniques for solving it as an optimization problem, including loopy belief propagation over Markov random fields. We also discuss some possible applications of these techniques to problems in natural language processing.

This note introduces an interesting class of Gauss-Markov Random Fields designated as walk-summable. Several equivalent characterizations of this class of GMRFs are established. Also, several important subclasses of GMRFs are identified as being walk-summable. These include (i) diagonally dominant, (ii) pairwise normalizable, (iii) regular singly-connected, and (iv) regular bipartite with only ...

A Markov random field is a name given to a natural generalization of the well known concept of a Markov chain. It arrises by looking at the chain itself as a very simple graph, and ignoring the directionality implied by “time”. A Markov chain can then be seen as a chain graph of stochastic variables, where each variable has the property that it is independent of all the others (the future and p...

Recommender systems play a central role in providing individualized access to information and services. This paper focuses on collaborative filtering, an approach that exploits the shared structure among mind-liked users and similar items. In particular, we focus on a formal probabilistic framework known as Markov random fields (MRF). We address the open problem of structure learning and introd...