Date of Completion
12-8-2016
Embargo Period
12-8-2016
Advisors
Horea T.Ilies, Jiong Tang, Xu Chen
Field of Study
Mechanical Engineering
Degree
Master of Science
Open Access
Open Access
Abstract
The medial zone of a 3-dimensional semi-analytic domain Ω, denoted as MZ(Ω), can be thought of as a ``thick'' version of the shape's skeleton with important applications in design, motion planning and geometric reasoning. The utility of the medial zones stems from the fact that they theoretically are homeomorphic to and have the same dimension as the original domain, so in this sense they capture the topology of the domain. However, the original approach to compute them involved a discrete Laplace estimation commonly used in edge detection algorithms, which was used to extract the points belonging to the medial zones. Despite being fast, this computational approach produced unwanted topological artifacts and did not satisfy the convergence properties of the medial zones as formulated, which limited their effectiveness.
In this work a new approach was proposed to compute points of the medial zones based on Gaussian Kernels located on the medial axis(MA) points whose widths are mapped to an approximate but differentiable function constructed over the domain. This computing paradigm produced a family of homeomorphic medial zones that have the same topology as the domain and converge to either the MA of the domain or to the domain itself. The resulting method was general in that it can be applied to domains of arbitrary complexity. The effectiveness of this approach was demonstrated by practical examples.
Recommended Citation
Li, Weiling, "Gaussian Kernel Based Medial Zone Computation" (2016). Master's Theses. 1023.
https://digitalcommons.lib.uconn.edu/gs_theses/1023
Major Advisor
Horea T.Ilies