Tom-Fletcher

Riemannian Geometry, Manifold Statistics and Diffeomorphisms and Image Registration

part 1 Riemannian Geometry Basics

• Motivation; introduction to manifold statistics
• Metrics, geodesics
• Covariant derivative, parallel translation
• Lie groups, homogeneous spaces

part 2 Manifold Statistics

• Frechet mean
• Geometric median
• Principal geodesic analysis(PGA)
• Regression models

part 3 Diffeomorphisms and Image Registration

• Diffeomorphisms metrics and geodesic equations
• Image registration
• Atlas building
• PGA and regression models for diffeomorphisms