Digital Steiner sets and Matheron semi-groups

Jean Serra
2010 Image and Vision Computing  
The Euclidean hirerachies of openings satisfy Matheron semi-groups law γ λ γµ = γ max(λ,µ) , where λ is a size factor. One finds this law when the γ λ are adjunction openings by Steiner convex sets, i.e. by Minkowski sums of segments. The conditions under which, in Z n , the law remains valid, and the Steiner sets are convex, and connected, are established.
doi:10.1016/j.imavis.2009.06.016 fatcat:6yhgr4obu5apdjmjpdpgiq5v4y