Riemannian Geometric Statistics in Medical Image Analysis

Xavier Pennec’s research interest is at the intersection of statistics, differential geometry, computer science and medicine. He is particularly interested in the mathematics involved in computational anatomy: geometric statistics involving statistical computing on Riemannian manifolds and other geometric structures . He has contributed mathematically grounded methods and algorithms for medical image registration, statistics on shapes, and their translation to clinical research applications. Stefan Sommer’s research focus is on modeling and statistics of non-linear data with application to shape spaces, functional data analysis, and image registration. This includes foundational and algorithmic aspects of statistics on manifold valued data, and computational modeling and statistical analysis of deformations occurring in computational anatomy. Tom Fletcher’s research focus is on solving problems in medical image analysis and computer vision through the combination of statistics and differential geometry

• Part 1 Foundations of geometric statistics1. Introduction to differential and Riemannian geometry2. Statistics on manifolds3. Manifold-valued image processing with SPD matrices4. Riemannian geometry on shapes and diffeomorphisms5. Beyond Riemannian geometryPart 2 Statistics on manifolds and shape spaces6. Object shape representation via skeletal models (s-reps) and statistical analysis7. Efficient recursive estimation of the Riemannian barycenter on the hypersphere and the special orthogonal group with applications8. Statistics on stratified spaces9. Bias on estimation in quotient space and correction methods10. Probabilistic approaches to geometric statistics11. On shape analysis of functional dataPart 3 Deformations, diffeomorphisms and their applications12. Fidelity metrics between curves and surfaces: currents, varifolds, and normal cycles13. A discretize–optimize approach for LDDMM registration14. Spatially adaptive metrics for diffeomorphic image matching in LDDMM15. Low-dimensional shape analysis in the space of diffeomorphisms16. Diffeomorphic density registration