Pattern Theory: From representation to inference

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Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website.
The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

Pattern Theory: From representation to inference Review

Professor Grenander has developed his beautiful, but ofen difficult to understand in mathematical terms, a grand theory for representing various patterns (everthing?) in the real-world for the last 40 years. Now we finally have a book that ordinary folks may hope to understand and appreciate this important, and potentially very useful work, thanks to his productive collaborator, Michael Miller, an EE-turned statistician and biomedical researcher. What is nice about the book is the fact that there are much more background materials which nearly cover everything you need to know to fill in the gaps, and much recent developments since Grenander's 1993 tombstone: General Pattern Theory are covered here. The number of figures in the book illustrate that this is a very APPLIED book, though certainly not the usual standard of applied statistics. For the initiated researchers working on related problems, this is a much awaited text which should allow users to apply the theory to potentially many other applications and subject-specific developments. The only complain I have, if any, will be the lack of motivations in the uses of sometimes very diffuclt and very deep theory such as transformation theory. I think the authors could have given more account of the biological origins of these ideas in Darcy Thompson On Growth and Form, and some background in the "easier" theory of statistical shape theory. However I do like their overviews at the beginnings of each chapter and longer review in the first chapter. I also like to see more pointers in the computational details or software implementation. I assume these are also active research areas. Although a grand achivement, I don't think that there exists a theory that can "solve" everything. I think the book focuses mainly on statistical techniques for analyzing shapes and image registration, but it does not address more complicated spatial-temporal processes such as biological pattern formation or emergence in complex dynamical systems. Nevertheless, I think this is really a book which is worthy reading over and over, and which will make a difference in your research. Enjoy reading, grab a copy while you can, or better, try out the theory yourself.

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