Riemannian Geometric Statistics in Medical Image Analysis

5

Beyond Riemannian geometry

The affine connection setting for transformation groups

Xavier Pennec; Marco Lorenzi    Université Côte d'Azur and Inria, Epione team, Sophia Antipolis, France

Abstract

In computational anatomy, the statistics from the object space (images, surfaces, etc.) are often lifted to the group of deformation acting on their embedding space. Statistics on transformation groups have been considered in the previous chapters by providing the Lie group with a left- or right-invariant metric, which may (or may not) be consistent with the group action on our original objects. In this chapter we take the point of view of statistics on abstract transformations, independently of their action. In this case it is reasonable to ask that our ...