Point ordering with natural distance based on Brownian motion
type: Item
instance of: scholarly article
title: Point ordering with natural distance based on Brownian motion
zbMATH Open document ID: 1198.65041
DOI: 10.1155/2010/450460
published in: Mathematical Problems in Engineering
publication date: 2010-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/225266
review text: Summary: We consider a curve reconstruction problem from unorganized point clouds with noise. In general, the result of curve reconstruction depends on how to select and order the representative points to resemble the shape of the clouds. We exploit a natural distance based on a property of one-dimensional Brownian motion to order sample points, which simultaneously reflect smoothness and nearness of points, so that our algorithm is able to reconstruct not only simple curves but also nonsimple curves. Numerous examples show that this algorithm is effective. The natural distance proposed in this paper is able to play an important role in a variety of fields of measuring the distance of points with considering direction.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 5728489
zbMATH Keywords: numerical examples
zbMATH Keywords: curve reconstruction
zbMATH Keywords: Brownian motion
zbMATH Keywords: algorithm
Wikidata QID: Q58653088
author: Philsu Kim
author: Hyoung Seok Kim
MaRDI profile type: Publication
OpenAlex ID: W2072185104
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description: scientific article; zbMATH DE number 5728489