Statistics on manifolds and landmarks based image analysis: A nonparametric theory with applications

This paper provides an exposition of some recent developments in nonparametric inference on manifolds, along with a brief account of an emerging theory on data analysis on stratified spaces. Much of the theory is developed around the notion of Fréceht means with applications, for the most part, to landmark based shape spaces. A number of applications are illustrated with real data in such areas as paleomagnetism, morphometrics and medical diagnostics. Connections to scene recognition and machine vision are also explored.