Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables systematic development of optimal vision algorithms when used with optimization principles. This detailed and thoroughly enhanced third edition presents a comprehensive study / reference to theories, methodologies and recent developments in solving computer vision problems based on MRFs, statistics and optimisation. It treats various problems in low- and high-level computational vision in a systematic and unified way within the MAP-MRF framework. Among the main issues covered are: how to use MRFs to encode contextual constraints that are indispensable to image understanding; how to derive the objective function for the optimal solution to a problem; and how to design computational algorithms for finding an optimal solution. Easy-to-follow and coherent, the revised edition is accessible, includes the most recent advances, and has new and expanded sections on such topics as: Discriminative Random Fields (DRF) Strong Random Fields (SRF) Spatial-Temporal Models Total Variation Models Learning MRF for Classification (motivation + DRF) Relation to Graphic Models Graph Cuts Belief Propagation Features: Focuses on the application of Markov random fields to computer vision problems, such as image restoration and edge detection in the low-level domain, and object matching and recognition in the high-level domain Presents various vision models in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation Uses a variety of examples to illustrate how to convert a specific vision problem involving uncertainties and constraints into essentially an optimization problem under the MRF setting Introduces readers to the basic concepts, important models and various special classes of MRFs on the regular image lattice and MRFs on relational graphs derived from images Examines the problems of parameter estimation and function optimization Includes an extensive list of references This broad-ranging and comprehensive volume is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It has been class-tested and is suitable as a textbook for advanced courses relating to these areas.

Markov Random Field Modeling in Image Analysis

A multiresolution approach based on a modified wavelet transform called the tree-structured wavelet transform or wavelet packets is proposed. The development of this transform is motivated by the observation that a large class of natural textures can be modeled as quasi-periodic signals whose dominant frequencies are located in the middle frequency channels. With the transform, it is possible to zoom into any desired frequency channels for further decomposition. In contrast, the conventional pyramid-structured wavelet transform performs further decomposition in low-frequency channels. A progressive texture classification algorithm which is not only computationally attractive but also has excellent performance is developed. The performance of the present method is compared with that of several other methods. >

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Texture analysis and classification with tree-structured wavelet transform

Texture classification and segmentation using multiresolution simultaneous autoregressive models

The authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be assumed to be degraded by pointwise nonlinearities such as film saturation and additive noise. Iterative algorithms allow for the incorporation of various types of prior knowledge about the class of feasible solutions, can be used to remove nonstationary blurs, and are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms after a finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed. >

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Iterative methods for image deblurring

Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but...

Random field models in image analysis

This paper is concerned with a systematic exposition of the usefulness of two-dimensional (2-D) discrete Gaussian Markov random field (GMRF) models for image processing applications. Specifically, we discuss the following topics; notion of Markovianity on a plane, statistical inference in GMRF models, and their applications in several image related problems such as, image synthesis, texture classification, segmentation and image restoration.

R Chellappa

Papers

Two-Dimensional Discrete Gaussian Markov Random Field Models for Image Processing