Digital Steiner sets and Matheron semi-groups
Résumé
The Euclidean hierarchies of openings satisfy Matheron semi-groups law $ gamma _{lambda }gamma _{mu }=gamma _{max (lambda ,mu )}$ , where $ lambda$ is a size factor. One finds this law when the $ gamma_{lambda }$ are adjunction openings by Steiner convex sets, i.e. by Minkowki sums of segments. The conditions under which, in $ Z^{n}$ , the law remains valid, and the Steiner sets are convex, and connected, are established.