I will post some reviews of books that I find useful in the course of my study. I am not sure how technical I want my reviews to be or how general and vague.
For the time being I’ll try to do both 🙂

The first book I would like to review is the book “Shapes and Diffeomorphisms” by Laurent Younes, Johns Hopkins University.
This book summarizes a lot of work done by the author at the Center for Imaging Science, where Michael Miller’s group does a lot of interesting and exciting work on medical images.

This is a wonderful book for anyone who would want to learn about shape representation and matching. Very thoroughly written. It starts with curves, how they could be represented, then moves onto surfaces. Talks about Euler-Lagrange (Euler-Arnold) equations on the groups of diffeomorphisms which is a fundamental equation for all the Computational Anatomy, or pattern matching in general. A wonderful overview of methods and techniques that are in use today. Author also discusses numerical implementation and issues that arise in the field.

Sometimes I find notation a bit too heavy, with many sub- and super-scripts and names for variables that are not intuitive (to me, at least). In particular in the Diffeomorphic Matching chapter (Chapter 11) first a general construction is presented and then it is demonstrated on several examples. The general notation is reused in the examples which I find a bit cumbersome. One can be better off rewriting a specific construction in the landmarks case introducing his own notation. After moving on to the general case it seems to make more sense. At least that’s how it worked for me.

Later I am going to post a computation, which is just an expanded proof of a theorem from the book.

I recommend this book to anyone trying to learn about Pattern Theory, and in particular the emerging applied discipline, Computational Anatomy.

P.S. If your institution is subscribed to Springer publishing house, then you can view this book for free online.

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