Analyzing and Extending the Distance-to-Measure Gradient Flow Using Higher Order Voronoi Diagrams

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dc.contributor.advisorWanner, Thomas
dc.contributor.authorO'Neil, Patrick
dc.creatorO'Neil, Patrick
dc.date.accessioned2018-10-22T01:19:47Z
dc.date.available2018-10-22T01:19:47Z
dc.date.issued2017
dc.description.abstractPoint cloud data arises naturally from 3D scanners, LiDAR sensors, and industrial computed tomography among other sources. Most point clouds obtained through experimental means exhibit some level of noise, inhibiting mesh reconstruction algorithms and topological data analysis techniques. To alleviate the problems caused by noise, smoothing algorithms are often employed as a preprocessing step before attempting to reconstruct the sampled measure. Moving least squares is one such technique, however it is designed to work on surfaces in R^3 . As many interesting point clouds naturally live in higher dimensions, we seek a method for smoothing higher dimensional point clouds. To this end, we turn to the distance-to-measure function.
dc.format.extent191 pages
dc.identifier.urihttps://hdl.handle.net/1920/11241
dc.language.isoen
dc.rightsCopyright 2017 Patrick O'Neil
dc.subjectMathematics
dc.subjectComputational Geometry
dc.subjectComputational Topology
dc.subjectPiecewise-Smooth Dynamical Systems
dc.subjectPoint Clouds
dc.subjectVoronoi Diagrams
dc.titleAnalyzing and Extending the Distance-to-Measure Gradient Flow Using Higher Order Voronoi Diagrams
dc.typeDissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorGeorge Mason University
thesis.degree.levelPh.D.

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