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.

State-of-the-art research on MRFs, successful MRF applications, and advanced topics for future study. This volume demonstrates the power of the Markov random field (MRF) in vision, treating the MRF both as a tool for modeling image data and, utilizing recently developed algorithms, as a means of making inferences about images. These inferences concern underlying image and scene structure as well as solutions to such problems as image reconstruction, image segmentation, 3D vision, and object labeling. It offers key findings and state-of-the-art research on both algorithms and applications. After an introduction to the fundamental concepts used in MRFs, the book reviews some of the main algorithms for performing inference with MRFs; presents successful applications of MRFs, including segmentation, super-resolution, and image restoration, along with a comparison of various optimization methods; discusses advanced algorithmic topics; addresses limitations of the strong locality assumptions in the MRFs discussed in earlier chapters; and showcases applications that use MRFs in more complex ways, as components in bigger systems or with multiterm energy functions. The book will be an essential guide to current research on these powerful mathematical tools.

Markov random field (MRF) modeling provides a basis for the characterization of contextual constraints on visual interpretation and enables us to develop optimal vision algorithms systematically based on sound principles. This book presents a comprehensive study on using MRFs to solve computer vision problems, covering the following parts essential to the subject: introduction to fundamental theories, formulations of various vision models in the MRF framework, MRF parameter estimation, and optimization algorithms. Various MRF vision models are presented in a unified form, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This book is an excellent reference for researchers working in computer vision, image processing, pattern recognition and applications of MRFs. It is also suitable as a text for advanced courses in the subject.

Markov Random Fields in Image Segmentation provides an introduction to the fundamentals of Markovian modeling in image segmentation as well as a brief overview of recent advances in the field. Segmentation is formulated within an image labeling framework, where the problem is reduced to assigning labels to pixels. In a probabilistic approach, label dependencies are modeled by Markov random fields (MRF) and an optimal labeling is determined by Bayesian estimation, in particular maximum a posteriori (MAP) estimation. The main advantage of MRF models is that prior information can be imposed locally through clique potentials. MRF models usually yield a non-convex energy function. The minimization of this function is crucial in order to find the most likely segmentation according to the MRF model. Classical optimization algorithms including simulated annealing and deterministic relaxation are treated along with more recent graph cut-based algorithms. The primary goal of this monograph is to demonstrate the basic steps to construct an easily applicable MRF segmentation model and further develop its multi-scale and hierarchical implementations as well as their combination in a multilayer model. Representative examples from remote sensing and biological imaging are analyzed in full detail to illustrate the applicability of these MRF models. Furthermore, a sample implementation of the most important segmentation algorithms is available as supplementary software. Markov Random Fields in Image Segmentation is an invaluable resource for every student, engineer, or researcher dealing with Markovian modeling for image segmentation.

This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.

Stochastic Image Processing provides the first thorough treatment of Markov and hidden Markov random fields and their application to image processing. Although promoted as a promising approach for over thirty years, it has only been in the past few years that the theory and algorithms have developed to the point of providing useful solutions to old and new problems in image processing. Markov random fields are a multidimensional extension of Markov chains, but the generalization is complicated by the lack of a natural ordering of pixels in multidimensional spaces. Hidden Markov fields are a natural generalization of the hidden Markov models that have proved essential to the development of modern speech recognition, but again the multidimensional nature of the signals makes them inherently more complicated to handle. This added complexity contributed to the long time required for the development of successful methods and applications. This book collects together a variety of successful approaches to a complete and useful characterization of multidimensional Markov and hidden Markov models along with applications to image analysis. The book provides a survey and comparative development of an exciting and rapidly evolving field of multidimensional Markov and hidden Markov random fields with extensive references to the literature.

Image Modeling compiles papers presented at a workshop on image modeling in Rosemont, Illinois on August 6-7, 1979. This book discusses the mosaic models for textures, image segmentation as an estimation problem, and comparative analysis of line-drawing modeling schemes. The statistical models for the image restoration problem, use of Markov random fields as models of texture, and mathematical models of graphics are also elaborated. This text likewise covers the univariate and multivariate random field models for images, stochastic image models generated by random tessellations of the plane, and long crested wave models. Other topics include the Boolean model and random sets, structural basis for image description, and structure in co-occurrence matrices for texture analysis. This publication is useful to specialists and professionals working in the field of image processing.