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. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the "positional geometry" of the collection. The linking structure extends in a minimal way the individual "skeletal.