Surface and Medial Axis Topology Through Distance Flows Induced by Discrete Samples
Sadri, Bardia
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https://hdl.handle.net/2142/81755
Description
Title
Surface and Medial Axis Topology Through Distance Flows Induced by Discrete Samples
Author(s)
Sadri, Bardia
Issue Date
2006
Doctoral Committee Chair(s)
Edgar A. Ramos
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
Specifically, we present an algorithm for homeomorphic reconstruction of surfaces in 3D. This algorithm generalizes to higher dimensions with a slight change in the type of the provided topological guarantee. We also present an algorithm for medial axis approximation that computes a piece-wise linear core for the given sample. This core is guaranteed to be homotopy equivalent to the medial axis of the shape enclosed by the original surface. We then show that the core can be enhanced by any geometric medial axis approximation scheme without compromising the topological equivalence of the output and the medial axis being approximated. Finally, we present an analysis of Herbert Edelsbrunner's well-known WRAP reconstruction algorithm and show that under relative epsilon-sampling in 3D, the output of WRAP is homotopy equivalent to the original shape.
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