Medial/Skeletal Linking Structures for Multi-Region Configurations

The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{ \Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way.