A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance

A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance

In this paper, we propose an algorithm that, from a maximum error and a digital curve (4- or 8-connected), computes a simplification of the curve (a polygonal curve) such that the Fréchet distance between the original and the simplified curve is less than the error. The Fréchet distance is known to...

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Main Author: Isabelle Sivignon
Format: Article
Language:English
Published: Image Processing On Line 2014-05-01
Series:Image Processing On Line
Online Access:http://www.ipol.im/pub/art/2014/70/
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spelling doaj-a242a8646f8e4609b5a4c3ceedaf6bb52020-11-24T21:02:18ZengImage Processing On LineImage Processing On Line2105-12322014-05-01411612710.5201/ipol.2014.70A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet DistanceIsabelle SivignonIn this paper, we propose an algorithm that, from a maximum error and a digital curve (4- or 8-connected), computes a simplification of the curve (a polygonal curve) such that the Fréchet distance between the original and the simplified curve is less than the error. The Fréchet distance is known to nicely measure the similarity between two curves. The algorithm we propose uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in O(n log(n)), experiments show a linear behaviour in practice.http://www.ipol.im/pub/art/2014/70/
collection DOAJ
language English
format Article
sources DOAJ
author Isabelle Sivignon
spellingShingle Isabelle Sivignon
A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
Image Processing On Line
author_facet Isabelle Sivignon
author_sort Isabelle Sivignon
title A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
title_short A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
title_full A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
title_fullStr A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
title_full_unstemmed A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
title_sort near-linear time guaranteed algorithm for digital curve simplification under the fréchet distance
publisher Image Processing On Line
series Image Processing On Line
issn 2105-1232
publishDate 2014-05-01
description In this paper, we propose an algorithm that, from a maximum error and a digital curve (4- or 8-connected), computes a simplification of the curve (a polygonal curve) such that the Fréchet distance between the original and the simplified curve is less than the error. The Fréchet distance is known to nicely measure the similarity between two curves. The algorithm we propose uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in O(n log(n)), experiments show a linear behaviour in practice.
url http://www.ipol.im/pub/art/2014/70/
work_keys_str_mv AT isabellesivignon anearlineartimeguaranteedalgorithmfordigitalcurvesimplificationunderthefrechetdistance
AT isabellesivignon nearlineartimeguaranteedalgorithmfordigitalcurvesimplificationunderthefrechetdistance
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