3 Graph Analysis 6 3.1 Analysis Based on Spectral Graph Theory . . . . . . . . . . . . . 7 3.2 Analysis Based on Random Field Theory . . . . . . . . . . . . . . 9 3.2.1 Markov Random Fields . . . . . . . . . . . . . . . . . . . . 9 3.2.2 Conditional Random Fields . . . . . . . . . . . . . . . . . 10 3.2.3 Gaussian Random Fields . . . . . . . . . . . . . . . . . . . 11 3.3 Analysis Based onMatri...

in this paper, an unsupervised classification method using spatial contextual information for polarimetric sar (polsar) image classification is proposed. first, an unsupervised classification based on 2d h/▁α plane was performed, using cloude/pottier target decomposition algorithm. in order to compute the initial values of the cluster centers and hence a rapid convergence of the algorithm, the ...

The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations (parametric identification problems, filtering problems, interpolation problems and others). Therefore, approximation of arbitrary random fields by Markov fields...

Gaussian Markov random fields (GMRFs) are specified conditionally by its precision matrix meaning that its inverse, the covariance matrix, is not explicitly known. Computing the often dense covariance matrix directly using matrix inversion is often unfeasible due to time and memory requirement. In this note, we discuss a simple and fast algorithm to compute the marginal variances for a GMRF. We...

A combinatorial random variable is a discrete random variable defined over a combinatorial set (e.g., a power set of a given set). In this paper we introduce combinatorial Markov random fields (Comrafs), which are Markov random fields where some of the nodes are combinatorial random variables. We argue that Comrafs are powerful models for unsupervised learning by showing their relationship with...

We present a PTAS for computing the maximum a posteriori assignment on Pairwise Markov Random Fields with non-negative weights in planar graphs. This algorithm is practical and not far behind state-of-the-art techniques in image processing. MAP on Pairwise Markov Random Fields with (possibly) negative weights cannot be approximated unless P = NP, even on planar graphs. We also show via reductio...