Analyzing and Extending the Distance-to-Measure Gradient Flow Using Higher Order Voronoi Diagrams
Date
2017
Authors
O'Neil, Patrick
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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.
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Keywords
Mathematics, Computational Geometry, Computational Topology, Piecewise-Smooth Dynamical Systems, Point Clouds, Voronoi Diagrams