In an earlier report a consistent estimation scheme was given for Gaussian Markov random field models. In this report we consider some statistical properties of the resulting estimate. Specifically, we derive an expression for the symptotic mean square error of the estimate for a general model and compare the efficiency of this estimate with the popular coding estimate for a simple first order isotropic model. (Author).
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie
We are interested in fitting two-dimensional, Gaussian conditional Markov random field (CMRF) models to images. The given finite image is assumed to be represented on a finite lattice of specific structure, obeying a CMRF model driven by correlated noise. The stochastic model is characterized by a set of unknown parameters. We describe two sets of experimental results. First, by assigning values to parameters in the stationary range, two-dimensional patterns are generated. It appears that quite a variety of patterns can be generated. Next, we consider the problem of estimating the unknown parameters of a given model for an image, and suggest a consistent estimation scheme. We also implement a decision rule to choose an appropriate CMRF model from a class of such competing models. The usefulness of the estimation scheme and the decision rule to choose an appropriate model is illustrated by application to synthetic patterns. Unilateral approximations to CMRF models are also discussed. (Author).
Introduces the theory and application of Markov random fields in image processing/computer vision. Modelling images through the local interaction of Markov models produces algorithms for use in texture analysis, image synthesis, restoration, segmentation and surface reconstruction.
This work describes a Gaussian Markov random field model that includes several previously proposed models, and studies properties of their maximum likelihood (ML) and restricted maximum likelihood (REML) estimators in a special case. Specifically, for models where a particular relation holds between the regression and precision matrices of the model, we provide sufficient conditions for existence and uniqueness of ML and REML estimators of the covariance parameters, and provide a straightforward way to compute them. It is found that the ML estimator always exists while the REML estimator may not exist with positive probability. A numerical comparison suggests that for this model ML estimators of covariance parameters have, overall, better frequentist properties than REML estimators.
Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This third edition includes the most recent advances and has new and expanded sections on topics such as: Bayesian Network; Discriminative Random Fields; Strong Random Fields; Spatial-Temporal Models; Learning MRF for Classification. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in these areas.
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Abstract: "Markov random fields (MRF) have proven useful for modeling the a priori information in Bayesian tomographic reconstruction problems. However, optimal parameter estimation of the MRF model remains a difficult problem due to the intractable nature of the partition function. In this report, we propose a fast parameter estimation scheme to obtain optimal estimates of the free parameters associated with a general MRF model formulation. In particular, for the generalized Gaussian MRF (GGMRF) case, we show that the ML estimate of the temperature T has a simple closed form solution. We present an efficient scheme for the ML estimate of the shape parameter p by an off-line numerical computation of the log of the partition function. We show that this approach can be extended to compute the parameters associated with a general MRF model. In the context of tomographic reconstruction, the difficulty of the ML estimation problem is compounded by the fact that the parameters depend on the unknown image. The EM algorithm is used to solve this problem. We derive fast simulation techniques for efficient computation of the expectation step. We also propose a method to extrapolate the estimates when the simulations are terminated prematurely prior to convergence. Experimental results for the emission and transmission case show that the proposed methods result in substantial savings in computation and superior quality images."
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie
