The Blum medial linking structure for multi-region analysis
Ellen Gasparovic · Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2019
The Blum medial axis of a region with smooth boundary in Rsuperscript{n+1} is a skeleton-like topological structure that captures shape and geometric properties of the region and its boundary. We introduce a structure, called the Blum medial linking structure, which extends the advantages of the medial axis to configurations of multiple disjoint regions in order to capture both their individual and positional or relative geometry. We use singularity theory to classify the generic local normal forms of the medial linking structure for generic configurations of regions in dimensions n is less than or equal to 6, which requires proving a transversality theorem for families of multi--distance functions. We show how invariants of the geometry of the regions and their complement may be computed directly from the linking structure. We conclude with applications of the linking structure to the analysis of multiple objects in medical images.