École Nationale Supérieure de
Techniques Avancées

Abstract

Set estimation deals with the problem of estimating or approximating an unknow compact set and some of its properties by statistical approaches. Generally, the set is a support of a probability density, it lives in an Euclidian space and is estimated from a random sample of points drawn into this set. A good enough estimation of the set allows also to estimate its dimension and its medial axis for example. This topic is a bridge between geometry and statistics and has a lot of applications.