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Identification of an algebraic domain in two dimensions from a finite number of its generalized polarization tensors

Lookup NU author(s): Professor Mihai Putinar

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by Springer, 2019.

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Abstract

This paper aims at studying how finitely many generalized polarization tensors of an algebraic domain can be used to determine its shape. Precisely, given a planar set with real algebraic boundary, it is shown that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The size of the matrix depends polynomially on the degree of the boundary of the algebraic domain. The density with respect to Hausdorff distance of algebraic domains among all bounded domains invites to extend via approximation our reconstruction procedure beyond its natural context. Based on this, a new algorithm for shape recognition/classification is proposed with some strong hints about its efficiency.

Publication metadata

Author(s): Ammari H, Putinar M, Steenkamp A, Triki F

Publication type: Article

Publication status: Published

Journal: Mathematische Annalen

Year: 2019

Volume: 375

Issue: 3-4

Pages: 1337-1354

Print publication date: 01/12/2019

Online publication date: 16/11/2018

Acceptance date: 08/11/2018

Date deposited: 09/11/2018

ISSN (print): 0025-5831

ISSN (electronic): 1432-1807

Publisher: Springer

URL: https://doi.org/10.1007/s00208-018-1780-y

DOI: 10.1007/s00208-018-1780-y

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