The course will last 5 days and will be a mixture of lectures and practicals. In order to get the 2.5 ECTS, the students will have to submit a report, consisting of one of the following:
- A poster on their own research (to be presented during the Monday poster session), OR
- A selection of exercises made during the practical sessions (details will be given during the course).
Details on social programme
- On Thursday, directly after the lectures (1615), we will be picked up by a bus that takes us to the center, where we will go on a canal tour of Copenhagen. Please bring an umbrella in case of rain :-)
- After the canal tour, we will walk to Kulturhuset Islands Brygge, where we will have a conference dinner from 18:30. This culture house is beautifully situated near the water.
Please see syllabus and suggested reading for more information.
Tom Fletcher (TF)
Riemannian geometry basics
- Motivation: intro to manifold statistics
- Metrics, geodesics
- Covariant derivative, parallel translation
- Lie groups, homogeneous spaces
- Frechet mean
- Geometric median
- Principal geodesic analysis (PGA)
- Regression models
Diffeomorphisms and Image Registration
- Diffeomorphism metrics and geodesic equations
- Image registration
- Atlas building
- PGA and regression models for diffeomorphisms
Anuj Srivastava (AS)
Part 1: Functional Data Analysis
Estimating functions from data; function registration problem; use of L2
norms and its limitations; square-root slope function; elastic metric and
Fisher-Rao metric; functional alignment under Fisher-Rao metric.
Part 2: Shape Analysis of Euclidean Curves
Past techniques in shape analysis; registration problem; elastic Riemannian metric;
Square-root velocity function; shape metric; mean and covariances; simple shape models.
Part 3: Additional Topics:
Shapes of trajectories on manifolds; TSRVF representations; shape analysis of
surfaces; square-root normal fields representations.
Tom Nye (TN)
Introduction to non-smooth examples and to phylogenetics
BHV tree-space and geodesics
More general CAT(0) geometry and orthant spaces
The Fréchet mean: algorithms; stickiness; central limit theorems
Correlations and the shape of distributions: use of the log map; principal geodesics; principal surfaces
Stochastic processes in non-smooth spaces
Stefan Sommer (SS)
Differential geometry computations using the Theano framework