Curve reconstruction from noisy samples

Siu Wing Cheng; Stefan Funke; Mordecai Golin; Piyush Kumar; Sheung Hung Poon; Edgar Ramos

doi:10.1016/j.comgeo.2004.07.004

Curve reconstruction from noisy samples

Siu Wing Cheng, Stefan Funke, Mordecai Golin, Piyush Kumar, Sheung Hung Poon, Edgar Ramos

Research output: Journal Publication › Article › peer-review

39 Citations (Scopus)

Abstract

We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases.

Original language	English
Pages (from-to)	63-100
Number of pages	38
Journal	Computational Geometry: Theory and Applications
Volume	31
Issue number	1-2
DOIs	https://doi.org/10.1016/j.comgeo.2004.07.004
Publication status	Published - May 2005
Externally published	Yes

Keywords

Computational geometry
Curve reconstruction
Homeomorphism
Probabilistic analysis

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2004.07.004

Cite this

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title = "Curve reconstruction from noisy samples",

abstract = "We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases.",

keywords = "Computational geometry, Curve reconstruction, Homeomorphism, Probabilistic analysis",

author = "Cheng, {Siu Wing} and Stefan Funke and Mordecai Golin and Piyush Kumar and Poon, {Sheung Hung} and Edgar Ramos",

note = "Funding Information: * Corresponding author. E-mail addresses: scheng@cs.ust.hk (S.-W. Cheng), funke@mpi-sb.mpg.de (S. Funke), golin@cs.ust.hk (M. Golin), piyush@ams.sunysb.edu (P. Kumar), hung@cs.ust.hk (S.-H. Poon), eramosn@cs.uiuc.edu (E. Ramos). 1 Research of S.-W. Cheng and S.-H. Poon are partly supported by Research Grant Council, Hong Kong, China (project no. HKUST 6190/02E and HKUST 6169/03E). Research of M. Golin is partly supported by Research Grant Council, Hong Kong, China (project no. HKUST 6082/01E and HKUST 6206/02E). 2 Partly supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG—Effective Computational Geometry for Curves and Surfaces).",

year = "2005",

month = may,

doi = "10.1016/j.comgeo.2004.07.004",

language = "English",

volume = "31",

pages = "63--100",

journal = "Computational Geometry: Theory and Applications",

issn = "0925-7721",

publisher = "Elsevier",

number = "1-2",

}

TY - JOUR

T1 - Curve reconstruction from noisy samples

AU - Cheng, Siu Wing

AU - Funke, Stefan

AU - Golin, Mordecai

AU - Kumar, Piyush

AU - Poon, Sheung Hung

AU - Ramos, Edgar

N1 - Funding Information: * Corresponding author. E-mail addresses: scheng@cs.ust.hk (S.-W. Cheng), funke@mpi-sb.mpg.de (S. Funke), golin@cs.ust.hk (M. Golin), piyush@ams.sunysb.edu (P. Kumar), hung@cs.ust.hk (S.-H. Poon), eramosn@cs.uiuc.edu (E. Ramos). 1 Research of S.-W. Cheng and S.-H. Poon are partly supported by Research Grant Council, Hong Kong, China (project no. HKUST 6190/02E and HKUST 6169/03E). Research of M. Golin is partly supported by Research Grant Council, Hong Kong, China (project no. HKUST 6082/01E and HKUST 6206/02E). 2 Partly supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG—Effective Computational Geometry for Curves and Surfaces).

PY - 2005/5

Y1 - 2005/5

N2 - We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases.

AB - We present an algorithm to reconstruct a collection of disjoint smooth closed curves from noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation in the normal directions. Our reconstruction is faithful with probability approaching 1 as the sampling density increases.

KW - Computational geometry

KW - Curve reconstruction

KW - Homeomorphism

KW - Probabilistic analysis

UR - http://www.scopus.com/inward/record.url?scp=84867932970&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2004.07.004

DO - 10.1016/j.comgeo.2004.07.004

M3 - Article

AN - SCOPUS:84867932970

SN - 0925-7721

VL - 31

SP - 63

EP - 100

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 1-2

ER -

Curve reconstruction from noisy samples

Abstract

Keywords

ASJC Scopus subject areas

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