Benchmark computations for the polarization tensor of small conducting objects

TL;DR

This paper provides benchmark computations for the polarization tensor of small conducting objects using an adaptive boundary element method, aiding in accurate characterisation for imaging applications and supporting machine learning classification.

Contribution

It introduces a set of benchmark numerical computations for the polarization tensor, enabling validation of software accuracy in characterising small conducting objects.

Findings

Accurate numerical approximations of tensor coefficients achieved.

Benchmark computations facilitate software validation.

Supports improved object classification in imaging applications.

Abstract

The characterisation of small low conducting inclusions in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in geological imaging using electrical resistivity tomography. It is known that such objects can be characterised by a P\'oyla-Szeg\"o (polarizability) tensor. Such characterisations have attracted interest as they can provide object features in a machine learning classification algorithm and provide an alternative imaging solution. However, to be able train machine learning algorithms, large dictionaries are required and it is essential that the characterisations are accurate. In this work, we obtain accurate numerical approximations to the tensor coefficients, by applying an adaptive boundary element method. The goal being to provide a sequence of benchmark {computations} for the tensor coefficients to allow other software developers check the accuracy of their codes.