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

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dc.contributor.advisor Wanner, Thomas
dc.contributor.author O'Neil, Patrick
dc.creator O'Neil, Patrick
dc.date.accessioned 2018-10-22T01:19:47Z
dc.date.available 2018-10-22T01:19:47Z
dc.date.issued 2017
dc.identifier.uri https://hdl.handle.net/1920/11241
dc.description.abstract Point 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.extent 191 pages
dc.language.iso en
dc.rights Copyright 2017 Patrick O'Neil
dc.subject Mathematics en_US
dc.subject Computational Geometry en_US
dc.subject Computational Topology en_US
dc.subject Piecewise-Smooth Dynamical Systems en_US
dc.subject Point Clouds en_US
dc.subject Voronoi Diagrams en_US
dc.title Analyzing and Extending the Distance-to-Measure Gradient Flow Using Higher Order Voronoi Diagrams
dc.type Dissertation
thesis.degree.level Ph.D.
thesis.degree.discipline Mathematics
thesis.degree.grantor George Mason University


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