Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups

摘要

7.1 Introduction Over the last 30 years, there was an explosion of imaging modalities which allows observing both the anatomy in vivo and in situ at multiple spatial scales (from cells to the whole body), multiple time scales (beating heart, growth, aging, evolution of species), and on multiple subjects. The combination of these new observation means with the computerized methods is at the heart of computational anatomy, an emerging discipline at the interface of geometry, statistics and image analysis which aims at developing algorithms to model and analyze the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information.