By Topic

Stationary Markov random fields on a finite rectangular lattice

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Champagnat, F. ; Lab. des Signaux et Syst. Supelec, Gif-sur-Yvette, France ; Idier, J. ; Goussard, Y.

This paper provides a complete characterization of stationary Markov random fields on a finite rectangular (non-toroidal) lattice in the basic case of a second-order neighborhood system. Equivalently, it characterizes stationary Markov fields on Z2 whose restrictions to finite rectangular subsets are still Markovian (i.e., even on the boundaries). Until now, Pickard random fields formed the only known class of such fields. First, we derive a necessary and sufficient condition for Markov random fields on a finite lattice to be stationary. It is shown that their joint distribution factors in terms of the marginal distribution on a generic (2×2) cell which must fulfil some consistency constraints. Second, we solve the consistency constraints and provide a complete characterization of such measures in three cases. Symmetric measures and Gaussian measures are shown to necessarily belong to the Pickard class, whereas binary measures belong either to the Pickard class, or to a new nontrivial class which is further studied. In particular, the corresponding fields admit a simple parameterization and may be simulated in a simple, although nonunilateral manner

Published in:

Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 7 )