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Fieguth P. Statistical Image Processing and Multidimensional Modeling

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Fieguth P. Statistical Image Processing and Multidimensional Modeling
Издательство Springer, 2011, -478 pp.
As a young professor in 1997 I taught my graduate course in Stochastic Image Processing for the first time. Looking back on my rough notes from that time, the course must have been a near impenetrable disaster for the graduate students enrolled, with a long list of errors, confusions, and bad notation.
With every repetition the course improved, with significant changes to notation, content, and flow. However, at the same time that a cohesive, large-scale form of the course took shape, the absence of any textbook covering this material became increasingly apparent. There are countless texts on the subjects of image processing, Kalman filtering, and signal processing, however precious little for random fields or spatial statistics. The few texts that do cover Gibbs models or Markov random fields tend to be highly mathematical research monographs, not well suited as a textbook for a graduate course.
More than just a graduate course textbook, this text was developed with the goal of being a useful reference for graduate students working in the areas of image processing, spatial statistics, and random fields. In particular, there are many concepts which are known and documented in the research literature, which are useful for students to understand, but which do not appear in many textbooks. This perception is driven by my own experience as a PhD student, which would have been considerably simplified if I had had a text accessible to me addressing some of the following gaps:
- FFT-based estimation
- A nice, simple, clear description of multigrid,
- The inference of dynamic models from cross-statistics,
- A clear distinction and relationship between squared and unsquared kernels,
- A graphical summary relating Gibbs and Markov models.
To facilitate the use of this textbook and the methods described within it, I am making available online much of the code which I developed for this text. This code, some colour figures, and (hopefully few) errata can be found from this book’s home page: http://ocho.uwaterloo.ca/book
Introduction
Part I Inverse Problems and Estimation
Inverse Problems
Static Estimation and Sampling
Dynamic Estimation and Sampling
Part II Modelling of Random Fields
Multidimensional Modelling
Markov Random Fields
Hidden Markov Models
Changes of Basis
Part III Methods and Algorithms
Linear Systems Estimation
Kalman Filtering and Domain Decomposition
Sampling and Monte Carlo Methods
Part IV Appendices
A Algebra
B Statistics
C Image Processing
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