The objective of mathematical modeling in image processing and computer vision is to capture the intrinsic character of the image in a few parameters so as to understand the nature of the phenomena generating the image. Models are also useful to specify natural constraints and general assumptions about the physical world; such constraints and assumptions are necessary to solve the ``inverse'' problem of three-dimensional scene interpretation, given two-dimensional image(s) of the scene. The introduction of stochastic or random field models has led to the development of algorithms for image restoration, segmentation, texture modeling, classification, and sensor fusion. In particular, Gibbs and Markov random fields for modeling spatial context and stochastic interaction among observable quantities have been quite useful in many practical problems, including medical image analysis and interpretation of remotely sensed images. As a result, Markov random field models have generated a substantial amount of excitement in image processing, computer vision, applied statistics, and neural network research communities.

This monograph presents an exposition of Markov random fields (MRFS) that is likely to be extensively used by researchers in many scientific disciplines. In particular, those investigating the applicability of MRFs to process their data or images are bound to find its contents very useful. The main focus of the monograph, however, is 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. Using a variety of examples, the author illustrates how to convert a specific vision problem involving uncertainties and constraints into essentially an optimization problem under the MRF setting. In doing so, the author introduces the reader to the various special classes of MRFs, including MRFs on the regular lattice (e.g., auto models and multi-level logistic models) that are used for low-level modeling, and MRFs on relational graphs that are used for high-level modeling.

The author devotes considerable attention to the problems of parameter estimation and function optimization, both of which are crucial in the MRF paradigm. Specific attention is given to the estimation of MRF parameters in the context of object recognition, and to the issue of algorithm selection for MRF-based function optimization. Another contribution of the book is a study on discontinuities, an important issue in the application of MRFs to image analysis. The extensive list of references, high-level descriptions of algorithms and computational issues associated with various optimization algorithms are some of the nice features of this book.

On the whole, the contents of this monograph nicely complement the material in Kindermann and Snell's book ``Markov Random Fields and Their Applications,'' and Chellappa and Jain's edited volume entitled ``Markov Random Fields: Theory and Applications.'' In my opinion, the main contribution of this book is the manner in which significant MRF-related concepts are lucidly illustrated via examples from computer vision.

Anil K. Jain East Lansing, Michigan