The Blum medial linking structure for multi-region analysis Public Deposited

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Last Modified
  • March 21, 2019
Creator
  • Gasparovic, Ellen
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • 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.
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  • In Copyright
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  • ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics.
Advisor
  • Damon, James
Degree granting institution
  • University of North Carolina at Chapel Hill
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