Block pickard models for two-dimensional constraints
IEEE Transactions on Information Theory
Extending models for two-dimensional constraints
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Computation of image spatial entropy using quadrilateral Markov random field
IEEE Transactions on Image Processing
Two-dimensional constrained coding based on tiling
IEEE Transactions on Information Theory
Bilateral Markov mesh random field and its application to image restoration
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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