Hyperelastic

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Non-Linear Field Theories of Mechanics has become a classic treatise in the field of continuum mechanics. Originally published nearly forty years ago, it probably has influenced practically all subsequent monographs on the subject. Its main parts are:

Our goal is to develop automated methods for the segmentation of thr- dimensional biomedical images. Here, we describe the segmentation of c- focal microscopy images of bee brains (20 individuals) by registration to one or several atlas images. Registration is performed by a highly parallel imp- mentation of an entropy-based nonrigid registration algorithm using B-spline transformations. We present and evaluate different methods to solve the cor- spondence problem in atlas based registration. An image can be segmented by registering it to an individual atlas, an average atlas, or multiple atlases. When registering to multiple atlases, combining the individual segmentations into a ?nalsegmentationcanbeachievedbyatlasselection,ormulticlassi?erdecision fusion. Wedescribeallthesemethodsandevaluatethesegmentationaccuracies that they achieve by performing experiments with electronic phantoms as well as by comparing their outputs to a manual gold standard. The present work is focused on the mathematical and computational t- ory behind a technique for deformable image registration termed Hyperelastic Warping, and demonstration of the technique via applications in image regist- tion and strain measurement. The approach combines well-established prin- ples of nonlinear continuum mechanics with forces derived directly from thr- dimensional image data to achieve registration. The general approach does not require the de?nition of landmarks, ?ducials, or surfaces, although it can - commodate these if available. Representative problems demonstrate the robust and ?exible nature of the approach. Three-dimensional registration methods are introduced for registering MRI volumes of the pelvis and prostate. The chapter ?rst reviews the applications, xi xii Preface challenges,and previous methods of image registration in the prostate.

Nonlinear Continuum Mechanics is a rapidly growing field of research. Since the last edition of this book, many important results in this field have been published. This new edition refers to the most important results.

Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering.