Paper Info
Title
Establishing a balanced neighborhood of discrete points for local quadric surface fitting.
Abstract
This paper presents a novel algorithm to establish a balanced neighborhood of points for reliable local quadric surface fitting, a common task in point cloud data processing. The underlying smooth surface geometry of a point cloud in the vicinity of a point can be locally approximated by the best fitted quadric surface at the point. The quality of the fitted surface considerably depends on what neighboring points are selected for the fitting. Specifically, if the selected neighboring points carry a biased distribution, the fitted geometry becomes biased, resulting in loss of accuracy in the fitting. The presented algorithm in this paper is able to reliably select neighboring points considering measures of both distance and direction. The main feature is the development of a geometric relationship, named as Territory Claiming, between the selected and the candidate neighboring points. The fundamental principle is for the selected point set to cover the whole neighborhood domain without redundancy. The selection procedure starts with a distance-based sequence of neighboring points with the territory claiming relationship functioning as a filter to establish a well-balanced neighborhood. The neighborhood can be expanded to incorporate sufficient number of points for the quadric surface fitting while maintaining the balance of the overall neighborhood. The implementation results have demonstrated that the presented method is robust and selects local neighboring points with superior fitting performance in comparison with the distance-based neighbors, mesh neighbors, and elliptic Gabriel graph neighbors.
Year
DOI
Venue
2017
10.1016/j.cad.2016.12.001
Computer-Aided Design
Keywords
Field
DocType
Point cloud,Local geometry,Quadric surface fitting,Fitting bias,Balanced point neighborhood
Topology,Discrete points,Mathematical optimization,Surface geometry,Gabriel graph,Redundancy (engineering),Point set,Point cloud,Quadric,Mathematics
Journal
Volume
ISSN
Citations 
84
0010-4485
0
PageRank 
References 
Authors
0.34
16
2
Name
Order
Citations
PageRank
Farbod Khameneifar100.68
Hsi-yung Feng215215.49