Unexpected spatial patterns in exponential family auto models
Graphical Models and Image Processing
Markov random field models in image processing
The handbook of brain theory and neural networks
Bayesian models for medical image biology using monte carlo markov chains techniques
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.00 |
Markov random fields (M.R.F.) on a lattice system and Gibbs distribution provide a wide area of models for interacting particle systems in image analysis, mechanical physics and statistical mechanics. Physical properties of the neighbors could be explained by partial differential equation (PDE) inside the potential function introducing PDE-MRF models. In image analysis, they have been used to describe the local characteristics of the spatial interaction between pixels. Although, in model image reconstruction, a number of fundamental issues remain unexplored, such as the specification of M.R.F. models, performance evaluation of the neighborhood structure of these models, and the phase transition phenomenon. In this work, spatial behavior of the auto-exponential model in a rectangular lattice would be investigated, concentrating on the first-order neighborhood structures. A simple deterministic model based on a univariate iterative scheme is studied which predicts the properties of these models and realizations have been generating using the Gibbs sampler to illustrate the properties. For well defined regions in the parameter space this iterative scheme is unstable leading to catastrophic and 2-cycle behavior.