# Medial/skeletal linking structures for multi-region configurations

@article{Damon2014MedialskeletalLS,
title={Medial/skeletal linking structures for multi-region configurations},
author={James N. Damon and Ellen Gasparovic},
journal={arXiv: Differential Geometry},
year={2014}
}
• Published 22 February 2014
• Mathematics
• arXiv: Differential Geometry
We 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 smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way. We 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…
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A skeletal structure (M, U) in ${\mathbb R}^{n+1}$ is a special type of n-dimensional Whitney stratified set M on which is defined a multivalued ‘radial vector field’ U. This is an extension of the
For a compact region Ω in Rn+1 with smooth generic boundary B, the Blum medial axis M is the locus of centers of spheres in Ω which are tangent to B at two or more points. The geometry of Ω is
ELLEN GASPAROVIC: The Blum Medial Linking Structure for Multi–Region Analysis (Under the direction of James Damon) The Blum medial axis of a region with smooth boundary in R is a skeleton-like
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This work considers a region Ω in R2 or R3 with generic smooth boundary B and Blum medial axis M, on which is defined a multivalued “radial vector field” U from points x on M to the points of tangency of the sphere at x with B, and defines a “geometric medial map” on M which corresponds to the differential geometric properties of B.
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