Invariance properties of generalized polarization tensors and design of shape descriptors in three dimensions
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.''
scientific article; zbMATH DE number 6363255