Invariance properties of generalized polarization tensors and design of shape descriptors in three dimensions
type: Item
instance of: scholarly article
title: Invariance properties of generalized polarization tensors and design of shape descriptors in three dimensions
zbMATH Open document ID: 1304.35759
author: Daewon Chung
author: Hyeonbae Kang
author: Han Wang
author: Habib Ammari
published in: Applied and Computational Harmonic Analysis
publication date: 2014-11-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1212.3519
review text: From the introduction: ``It is the purpose of this letter to extend results of [\textit{H. Ammari} et al., Found. of Comput. Math. 14, No. 1, 27--62 (2014; Zbl 1294.94006)] to construct invariants using GPTs (generalized polarization tensors) in three dimensions. In fact, using contracted GPTs (CGPTs), which are harmonic combinations of GPTs, we are able to construct an infinite number of shape descriptors. Using transformation formulas of spherical harmonics under rigid motions [\textit{E. O. Steinborn} and \textit{K. Ruedenberg}, ``Rotation and translation of regular and irregular solid spherical harmonics'', Adv. Quantum Chem. 7, 1--81 (1973)], we are able to derive transformation formulas obeyed by the CGPTs. We then use these formulas and the method for registration to construct invariants which can be used for target shape description.''
reviewed by: Matthias Schlottbom
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 33C55
zbMATH DE Number: 6363255
zbMATH Keywords: generalized polarization tensors
zbMATH Keywords: rigid and scaling transformations
zbMATH Keywords: invariance
zbMATH Keywords: shape descriptors
MaRDI profile type: Publication
OpenAlex ID: W2963984041
arXiv ID: 1212.3519
cites work: Target identification using dictionary matching of generalized polarization tensors
cites work: Mathematical and statistical methods for multistatic imaging
cites work: Generalized polarization tensors for shape description
cites work: Polarization and moment tensors. With applications to inverse problems and effective medium theory
DOI: 10.1016/J.ACHA.2014.05.004
description: scientific article; zbMATH DE number 6363255