Riemannian Geometric Statistics in Medical Image Analysis

ISBN-13: 9780128147252 / Angielski / Miękka / 2019 / 636 str.

Xavier Pennec; Stefan Sommer; Tom Fletcher

Spis treści

Part 1 Foundations of geometric statistics 1. Introduction to differential and Riemannian geometry 2. Statistics on manifolds 3. Manifold-valued image processing with SPD matrices 4. Riemannian geometry on shapes and diffeomorphisms 5. Beyond Riemannian geometry

Part 2 Statistics on manifolds and shape spaces 6. Object shape representation via skeletal models (s-reps) and statistical analysis 7. Efficient recursive estimation of the Riemannian barycenter on the hypersphere and the special orthogonal group with applications 8. Statistics on stratified spaces 9. Bias on estimation in quotient space and correction methods 10. Probabilistic approaches to geometric statistics 11. On shape analysis of functional data

Part 3 Deformations, diffeomorphisms and their applications 12. Fidelity metrics between curves and surfaces: currents, varifolds, and normal cycles 13. A discretize-optimize approach for LDDMM registration 14. Spatially adaptive metrics for diffeomorphic image matching in LDDMM 15. Low-dimensional shape analysis in the space of diffeomorphisms 16. Diffeomorphic density registration