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Markov chains provided us with a way to model 1D objects such as contours probabilistically, in a way that led to nice, tractable computations. We now consider 2D Markov models. These are more powerful, but not as easy to compute with. In addition we will consider two additional issues. First, we will consider adding observations to our models. These observations are conditioned on the value of...

We take the point of view that a Markov random field is a collection of so-called full conditional mutual independencies. Using the theory of -Measure, we have obtained a number of fundamental characterizations related to conditional mutual independence and Markov random fields. We show that many aspects of conditional mutual independence and Markov random fields have very simple set-theoretic ...

Magnetic resonance (MR) medical image segmentation plays an increasingly important role in computer-aided detection and diagnosis (CAD) of abnormalities. MRI segmentation manually is time consuming and consumes valuable human resources. Hence a great deal of efforts has been made to automate this process. Markov Random Field (MRF) has been one of the most active research areas of MRI brain segm...

Statistical models based on Markov random fields present a flexible means for modeling statistical dependencies in a variety of situations including, but not limited to, spatial problems with observations on a lattice. The simplest of such models, sometimes called “auto-models” are formulated from sets of conditional one-parameter exponential family densities or mass functions. Despite the attr...

In this paper, we present a new technique for statistical modeling of speech segments based on Markov random fields. Classical and multi-stream HMMs are particular cases of this more general family of models. However, the Random Field Model (RFM) proposed here can be seen as an extension of the multiband HMM in which interactions between the frequency bands have been added. In a first experimen...