Riemannian Geometric Statistics in Medical Image Analysis

Table of Contents

Cover image

Title page

Copyright

Contributors

Introduction

Introduction

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