CONICET | Buscador de Institutos y Recursos Humanos

The medial axis and the inner parallel body of a set $C$ are different formal translations for the notions of the ``central core´´ and the ``bulk´´, respectively, of $C$. On the basis of their applications in image analysis, both notions (and especially the first one) have been extensively studied in the literature, from different points of view. A modified version of the medial axis, called $lambda$-medial axis, has been recently proposed in order to get better stability properties. The estimation of these relevant subsets from a random sample of points is a partially open problem which has been considered only very recently. Our aim is to show that standard, relatively simple, techniques of set estimation can provide natural, consistent, easy-to-implement estimators for both the $lambda$-medial axis ${mathcal M}_lambda(C)$ and the inner parallel body $I_lambda(C)$ of $C$. extcolor{blue}{The consistency of these estimators follows from two results of stability (i.e. continuity in the Hausdorff metric) of ${mathcal M}_lambda(C)$ and $I_lambda(C)$ obtained under some, not too restrictive, regularity assumptions on $C$}. As a consequence, natural algorithms for the approximation of the $lambda$-medial axis and the inner parallel body can be derived. The whole approach could be useful for some practical problems in image analysis where estimation techniques are needed.