Riemannian Geometric Statistics in Medical Image Analysis

Over the last 15 years there has been a growing need in the medical image computing community for principled methods to process non-linear geometric data. Riemannian geometry has established itself as one the most powerful mathematical and computational structures. Riemannian Geometric Statistics in Medical image Analysis is a complete reference on Riemannian Geometric Statistics in medical image analysis for researchers and graduate students. It provides a foundation into the core methods followed by a presentation of state-of-the-art methods. Content includes the foundations of Riemannian geometric computing methods for statistics on manifolds with an emphasis on the concepts rather than on proofs; Applications of statistics on manifolds and shape spaces in medical image computing and Dieomorphic deformations and their applications. As well as medical imaging scientists, this book is also suitable for electronic engineers and computer scientists as the methods described also apply to domains such as signal processing (radar and brain computer interaction) and computer vision (object and face recognition) and other domains where statistics of geometric features appear. A complete reference covering both the foundations and state-of-the-art methodsEdited and authored by the leading researchers Contains examples, applications, and algorithmsGives an overview of current research challenges and future applications INDICE: Part 1: Foundations of Geometric Statistics 1. Riemannian geometry 2. Statistics on manifolds 3. Manifold valued-image processing with SPD matrices 4. Riemannian Geometry on Shapes and Diffeomorphisms 5. Beyond Riemannian: the affine connection setting and SVFs Part 2: Statistics on Manifolds and Shape Spaces 6. Inductive Fréchet Mean Computation on S(n) and SO(n) with Applications 7. Statistics in stratified spaces. 8. Bias in quotient space and its correction 9. Stochastic Processes and Transition Distributions on Manifolds 10. Elastic Shape Analysis, Square-Root Representations and Their Inverses Part 3: Deformations, Diffeomorphisms and their Applications 11. Geometric RKHS models for handling curves and surfaces in Computational Anatomy: Currents, varifolds, f-shapes, normal cycles 12. A Discretize-Optimize Approach for LDDMM Registration 13. Spatially varying metrics in the LDDMM framework 14. Low-dimensional Shape Analysis In the Space of Diffeomorphisms 15. Object Shape Representation via Skeletal Models (s-reps) and Statistical Analysis' 16. Diffeomorphic density matching

• ISBN: 978-0-12-814725-2
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 550
• Fecha Publicación: 01/09/2019
• Nº Volúmenes: 1
• Idioma: Inglés