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Set reconstruction by voronoi cells. / Reitzner, M.; Spodarev, E.; Zaporozhets, D.

In: Advances in Applied Probability, Vol. 44, No. 4, 01.12.2012, p. 938-953.

Research output: Contribution to journal › Article › peer-review

Harvard

Reitzner, M, Spodarev, E & Zaporozhets, D 2012, 'Set reconstruction by voronoi cells', Advances in Applied Probability, vol. 44, no. 4, pp. 938-953. https://doi.org/10.1239/aap/1354716584

APA

Reitzner, M., Spodarev, E., & Zaporozhets, D. (2012). Set reconstruction by voronoi cells. Advances in Applied Probability, 44(4), 938-953. https://doi.org/10.1239/aap/1354716584

Vancouver

Reitzner M, Spodarev E, Zaporozhets D. Set reconstruction by voronoi cells. Advances in Applied Probability. 2012 Dec 1;44(4):938-953. https://doi.org/10.1239/aap/1354716584

Author

Reitzner, M. ; Spodarev, E. ; Zaporozhets, D. / Set reconstruction by voronoi cells. In: Advances in Applied Probability. 2012 ; Vol. 44, No. 4. pp. 938-953.

BibTeX

@article{9f167ddf1d5e44cf868ad4af4d1b7974,
title = "Set reconstruction by voronoi cells",
abstract = "For a Borel set A and a homogeneous Poisson point process λ in Rd of intensity λ > 0, define the Poisson-Voronoi approximation Aλ of A as a union of all Voronoi cells with nuclei from λ lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AδAη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AδAη) together with their asymptotics for large λ are obtained as well. {\textcopyright} Applied Probability Trust 2012.",
keywords = "Perimeter, Poisson point process, Poisson-Voronoi cell, Poisson-Voronoi tessellation",
author = "M. Reitzner and E. Spodarev and D. Zaporozhets",
year = "2012",
month = dec,
day = "1",
doi = "10.1239/aap/1354716584",
language = "English",
volume = "44",
pages = "938--953",
journal = "Advances in Applied Probability",
issn = "0001-8678",
publisher = "Cambridge University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Set reconstruction by voronoi cells

AU - Reitzner, M.

AU - Spodarev, E.

AU - Zaporozhets, D.

PY - 2012/12/1

Y1 - 2012/12/1

N2 - For a Borel set A and a homogeneous Poisson point process λ in Rd of intensity λ > 0, define the Poisson-Voronoi approximation Aλ of A as a union of all Voronoi cells with nuclei from λ lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AδAη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AδAη) together with their asymptotics for large λ are obtained as well. © Applied Probability Trust 2012.

AB - For a Borel set A and a homogeneous Poisson point process λ in Rd of intensity λ > 0, define the Poisson-Voronoi approximation Aλ of A as a union of all Voronoi cells with nuclei from λ lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AδAη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AδAη) together with their asymptotics for large λ are obtained as well. © Applied Probability Trust 2012.

KW - Perimeter

KW - Poisson point process

KW - Poisson-Voronoi cell

KW - Poisson-Voronoi tessellation

UR - http://www.scopus.com/inward/record.url?scp=84872326972&partnerID=8YFLogxK

U2 - 10.1239/aap/1354716584

DO - 10.1239/aap/1354716584

M3 - Article

AN - SCOPUS:84872326972

VL - 44

SP - 938

EP - 953

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 4

ER -

ID: 126290227