Riemannian Geometric Statistics in Medical Image Analysis

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Statistics on stratified spaces

Aasa Feragen^a; Tom Nye^b    aUniversity of Copenhagen, Department of Computer Science, Copenhagen, Denmark^bNewcastle University, School of Mathematics, Statistics and Physics, Newcastle upon Tyne, United Kingdom

Abstract

Although manifold statistics is an established tool for computational anatomy, a number of structures are not well modeled on manifolds. Examples include data with variable topological structure, such as trees and graphs, as well as objects invariant with respect to groups that do not act freely on the space of measurements. Such data can often be represented more faithfully as residing on a stratified space, which consists of multiple manifold components, potentially with different dimensions, joined ...