Advances in Pattern Recognition
For other titles published in this series, go to
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Stan Z. Li
Markov Random Field
Modeling in Image Analysis
Third Edition
1 3
Stan Z. Li
Center for Biometrics and Security Research &
National Laboratory of Pattern Recognition
Institute of Automation
Chinese Academy of Science
Beijing 100190, China
Stan.ZQ.Li@gmail.com
Series editor
Professor Sameer Singh, PhD
Research School of Informatics, Loughborough University, Loughborough, UK
ISBN: 978-1-84800-278-4
DOI: 10.1007/978-1-84800-279-1
e-ISBN: 978-1-84800-279-1
Advances in Pattern Recognition Series ISSN 1617-7916
British Library Cataloguing in Publication Data
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Library of Congress Control Number: 2008943235
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In Memory of My Mother
v
“An excellent book — very thorough and very clearly written.”
— Stuart Geman
“I have found the book to be a very valuable reference. I am very
impressed by both the breadth and depth of the coverage. This
must have been a truly monumental undertaking.”
— Charles A. Bouman
vii
Foreword by Anil K. Jain
The objective of mathematical modeling in image processing and computer
vision is to capture the intrinsic character of the image in a few parame-
ters so as to understand the nature of the phenomena generating the image.
Models are also useful to specify natural constraints and general assump-
tions about the physical world; such constraints and assumptions are neces-
sary 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 interpreta-
tion 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 (MRF’s)
that is likely to be extensively used by researchers in many scientific disci-
plines. In particular, those investigating the applicability of MRF’s to process
their data or images are bound to find its contents very useful. The main fo-
cus 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 in-
troduces the reader to the various special classes of MRF’s, including MRF’s
on the regular lattice (e.g., auto-models and multilevel logistic models) that
are used for low-level modeling and MRF’s 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
ix
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Foreword by Anil K. Jain
for MRF-based function optimization. Another contribution of the book is
a study on discontinuities, an important issue in the application of MRF’s
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 attractive 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 Ran-
dom 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
June 8, 1995