Riemannian geometric statistics in medical image analysis Pennec X 1st edition – eBook PDF

Riemannian geometric statistics in medical image analysis 1st edition – Ebook PDF Instant Delivery – ISBN(s): 9780128147252,0128147253, 9780128147269, 0128147261

Product details:

• ISBN-10 ‏ : ‎ 0128147261
• ISBN-13 ‏ : ‎ 9780128147269
• Author:  Xavier Pennec, Stefan Sommer, Tom Fletcher 

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:

Part 1: Foundations of geometric statistics

1: Introduction to differential and Riemannian geometry

Abstract

1.1. Introduction

1.2. Manifolds

1.3. Riemannian manifolds

1.4. Elements of analysis in Riemannian manifolds

1.5. Lie groups and homogeneous manifolds

1.6. Elements of computing on Riemannian manifolds

1.7. Examples

1.8. Additional references

References

2: Statistics on manifolds

Abstract

2.1. Introduction

2.2. The Fréchet mean

2.3. Covariance and principal geodesic analysis

2.4. Regression models

2.5. Probabilistic models

References

3: Manifold-valued image processing with SPD matrices

People also search: