Riemannian geometric statistics in medical image analysis

Riemannian geometric statistics in medical image analysis – Ebook Instant Download/Delivery ISBN(s): 9780128147252,0128147253,9780128147269, 0128147261

Product detail:

• ISBN 10:  0128147261
• ISBN 13: 9780128147269
• Author:  Xavier Pennec, Hamdan Alghamd

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.

Table of contents:

1. 1: Introduction to differential and Riemannian geometry
2. 2: Statistics on manifolds
3. 3: Manifold-valued image processing with SPD matrices
4. 4: Riemannian geometry on shapes and diffeomorphisms
5. 5: Beyond Riemannian geometry
6. 6: Object shape representation via skeletal models (s-reps) and statistica
7. 7: Efficient recursive estimation of the Riemannian barycenter on the hypersphere and the special orthogonal group with applications
8. 8: Statistics on stratified spaces
9. 9: Bias on estimation in quotient space and correction methods
10. 10: Probabilistic approaches to geometric statistics

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