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Reviewer: Fatih Kurugollu

The well-established theory of Markov random fields (MRFs) is successfully employed in a broad range of image analysis applications-from restoration, segmentation, and motion detection, to object matching, object recognition, and pose estimation. In order to solve the problem at hand, the theory incorporates different aspects, including modeling the context according to pixel or feature interaction, parameter estimation of the underlying distribution, and energy minimization according to the model. Although there are many research papers based on MRFs, and even some image analysis books include the topic in a general way, there has been a need for a comprehensive presentation of MRF theory from an image analysis point of view for researchers and graduate students in the field. Meeting this need, this book elegantly and effectively elaborates on MRF theory and related topics. Each chapter includes the problem definition, related mathematical formulation and method explanations, and very useful examples. Li presents the topic in a systematic way. First, he presents the mathematical background and the essential MRF model. Then, he considers low- and high-level vision problems, in terms of different MRF models. Finally, he addresses parameter estimation and energy minimization problems. Chapter 1 introduces the relationship between image analysis and MRF theory, emphasizing the labeling problems in image analysis. The second chapter provides the required mathematical background of MRF theory. First, it establishes the equivalence of MRFs and Gibbs distribution, which allows for a practical and simple way to specify the joint probabilities used in the MRF context. Then, it introduces different models used in MRFs, including the multi-level logistic model, the hierarchical Gibbs random field (GRF) model, the FRAME model, multiresolution modeling, conditional random fields, discriminative random fields, the strong MRF model, and ?-MRF and Nakagami-MRF models. The chapter culminates with a comparison between MRFs and Bayesian networks. MRF theory is used in both low-level image analysis problems and high-level ones that include object matching and recognition, pose estimation, and grouping. The former applications are introduced in chapter 3, while the latter are investigated in chapter 4. Both chapters are problem oriented. Chapter 3 explains observation models and examines different low-level image applications, including image restoration and reconstruction, edge detection, texture analysis, optical flow, stereo vision, spatio-temporal models for video processing, and deformable models. For each application, the problem is introduced and the related MRF modeling is provided. Chapter 4 deals with two high-level vision problems: object matching and pose computation. For the object-matching problem, relational constraints are introduced and feature-based matching is considered; the overlapping objects problem is also studied. For pose estimation, problem clustering and simultaneous matching-based estimation methods are introduced. The chapter ends with a brief discussion of face detection and recognition. One of the main assumptions in image analysis is the smoothness of the surface: the surface of an object is smooth locally, and this smoothness is everywhere. While this assumption is widely used in MRFs and regularization-based image analysis, discontinuities in the surface due to abrupt changes that occur because of step edge, occlusion, and shadowing are very common in many applications. Therefore, the smoothness assumption is easily violated in real applications. In this case, discontinuity should be incorporated in the smoothness assumption in the MRF framework. Chapter 5 addresses this problem by introducing the discontinuity adaptive (DA) MRF model and the total variation model. MRFs model the vision problem with an appropriate probability distribution that is mostly Gaussian, which requires estimating the distribution parameters. In early MRF-based methods, least squares-based estimators were used for this purpose. However, this introduces another problem in the MRF framework: outliers that violate a distributional assumption-the same way the discontinuity problem does in the smoothness assumption. Therefore, one needs robust statistical methods. Chapter 6 outlines this problem by introducing M-estimators and annealing M-estimators (AM-estimators), along with half-quadratic (HQ) and annealing HQ minimization, in the DA MRF context. After chapters 1 to 5 establish MRF theory, chapters 6 and 7 address the parameter estimation problem. Chapter 6 presents both supervised and unsupervised estimation methods in low-level vision problems. Chapter 7 is devoted to the same problem, in optimal object recognition. Once the MRF model and the related parameter estimation method are established, the next step is to determine an appropriate energy minimization method. Chapter 8 considers local energy minimization, including continuous and discrete label cases. For discrete labeling, it presents iterated conditional modes, relaxation, belief propagation, convex relaxation, highest confidence first, and dynamic programming methods; constrained minimization is also discussed. The last chapter deals with global minimization methods. It takes into account, in this context, simulated annealing, mean field annealing, graduated nonconvexity, graph cuts, and genetic algorithms. This is an excellent book on MRF theory for image analysis. Researchers and graduate students will find this book very useful for understanding the theory clearly. Online Computing Reviews Service