COMBINATORIAL MARKOV RANDOM FIELDS AND THEIR APPLICATIONS TO INFORMATION ORGANIZATION

Hidden Markov random fields appear naturally in problems such as image segmentation, where an unknown class assignment has to be estimated from the observations at each pixel. Choosing the probabilistic model that best accounts for the observations is an important first step for the quality of the subsequent estimation and analysis. A commonly used selection criterion is the Bayesian Informatio...

A natural definition of the Markov property for multi-parameter random processes (random fields) is the following. Let {Xt, tEIR N} be a multiparameter process. For any set D in N. N, let a D denote the a-field generated by {Xt, tED}. The field {Xt, tEN. u} is said to be Markov (or Markov of degree 1 [6], or sharp Markov) if, for any bounded open set D with smooth boundary, oD and ape are condi...

A reversible, ergodic, Markov process taking values in the space of polygonally segmented images is constructed. The stationary distribution of this process can be made to correspond to a Gibbs-type distribution for polygonal random fields introduced by Arak and Surgailis and a few variants thereof, such as those arising in Bayesian analysis of such random fields. Extensions to generalized poly...

Removing noise from original image is still a challenging problem for researchers. There have been several published algorithm and each approach has its assumptions, advantages and disadvantages. Markov Random Field is ndimensional random process defined on a on a discrete lattice. Markov Random Field is a new branch of probability theory that promises to be important both in theory and applica...

Removing noise from original image is still a challenging problem for researchers. There have been several published algorithm and each approach has its assumptions, advantages and disadvantages. Markov Random Field is n-dimensional random process defined on a on a discrete lattice. Markov Random Field is a new branch of probability theory that promises to be important both in theory and applic...

Piecewise smooth models. Markov Random Fields. EM. Mean Field Theory. NOTE: NOT FOR DISTRIBUTION!!

5 Domains of research 10 5.1 Mixture models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.1.1 Learning and classification techniques . . . . . . . . . . . . . . . . . . 11 5.1.2 Taking into account the curse of dimensionality. . . . . . . . . . . . 12 5.2 Markov models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.2.1 Triplet Markov Fields f...

  Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we have learned Gaussian mixture model to the pixels of an image. The parameters of the model have estimated by EM-algorithm.   In addition pixel labeling corresponded to each pixel of true image is made by Bayes rule. In fact, ...

The correspondence addresses the intriguing question of which random models are equivalent to the discrete cosine transform (DCT) and discrete sine transform (DST). Common knowledge states that these transforms are asymptotically equivalent to first-order Gauss causal Markov random processes. We establish that the DCT and the DST are exactly equivalent to homogeneous one-dimensional (1-D) and t...