How to define a locally adaptive sampling criterion for topologically correct reconstruction of multiple regions

► We show that previous sampling conditions of the refinement reduction algorithm are insufficient. ► We define new locally adaptive sampling conditions based on a new pruned medial axis. ► The new sampling conditions guaranty the pruned medial axis components to be correctly separated. ► Based on our results we propose a new criterion for locally adaptive point set decimation. ► We discuss why our sampling conditions lead to a refinement instead of a correct reconstruction itself.