Pattern Theory: From Representation to Inference [Englisch] [Gebundene Ausgabe]

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.

I bought this book because it covers a wide range of topics. This aspect of the book is very impressive.

However, after attempting to delve into this material, I have discovered that the writing is sub-par. The author depends on the reader's understanding of an obscure algebra that isn't self-evident.

If the book were two or three times longer, with more words to explain the equations, then I think this would be a good book; but in it's present form, I cannot recommend it.