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Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data.

Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods.

Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology

Content includes:

The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications

As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science.

A complete reference covering both the foundations and state-of-the-art methods Edited and authored by leading researchers in the field Contains theory, examples, applications, and algorithms Gives an overview of current research challenges and future applications

For centuries Italy has fascinated travelers and artists. From the crumbling ruins of ancient Rome to the crystal- clear light of Venice, artists have found inspiration not only in the cities but also in the countryside and in the deep history and culture. From as early as the 1500s, artists visiting from France, England, the Netherlands, and Germany drew sketches to preserve vivid memories, often creating work of extraordinary atmosphere and beauty in the process. A growing number of tourists in the subsequent centuries fueled a further demand for souvenir views, spurring local artists to craft their own masterpieces. This little book is a narrated assemblage of some of these beautiful views, which transport the reader effortlessly to Italy, rekindling memories, setting intentions, or provoking curiosity. A central essay provides new insights into the topographical renditions of Italian scenes over the centuries, while compelling illustrations of works from the Getty collection by artists such as R. P. Bonington, J. M. W. Turner, Claude Lorrain, Giovanni Battista Lusieri, Canaletto, and many more capture the essence and spirit of Italy.