Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants

Abstract

The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects that can be computed for different threat and non-threat objects and has an established theoretical background, which shows that the induced voltage is a function of the hidden object's MPT coefficients. In this article, we describe the additional characterisation information that measurements of the induced voltage over a range of frequencies offer compared with measurements at a single frequency. We call such object characterisations its MPT spectral signature. Then, we present a series of alternative rotational invariants for the purpose of classifying hidden objects using MPT spectral signatures. Finally, we include examples of computed MPT spectral signature characterisations of realistic threat and non-threat objects that can be used to train machine learning algorithms for classification purposes.

Measurement of GMPT Coefficients for Improved Object Characterisation in Metal Detection

“…and use a fast Fourier transform to determine the amplitudes |c n |. Considering the products of rotation matrices in (17) that describe how the coefficients of M and D transform under object rotation and writing powers of cosine and sine functions in terms of multiple angles, e.g. cos 2 θ " p1 `cosp2θqq{2, cos 3 θ " p3 cos θ `cosp3θq{4 and cos 4 θ " p3 `4 cosp2θq cosp4θqq{8, we conclude that, if V ind,meas pθq can be described by a rank 2 tensor description, it will have c n being nonzero for n " 0, ˘2 while, if it additionally contains terms associated with a rank 3 description, then, c n for n " ˘1, ˘3 will also be non-zero.…”

“…Considerable benefits have been seen to be offered by exploiting the spectral behaviour of the MPT coefficients, known as its spectral signature, which provides much richer information than the MPT at a single frequency. This has been understood theoretically [15], efficient algorithms have been developed to compute the MPT spectral signature [33] and these have been applied to compute libraries of MPT spectral signature object characterisations [17]. Machine learning approaches for object classification based on measured and simulated libraries of MPT spectral signatures have also been developed in [19], [20] and [34], respectively.…”

Identification of Metallic Objects using Spectral Magnetic Polarizability Tensor Signatures: Object Classification

“…In [20] we have considered different choices for the F features in the input vector x P R F , which are associated with either the eigenvalues, principal invariants or deviatoric invariants of RrαB, ω, σ ˚, µ r s and IrαB, ω, σ ˚, µ r s, respectively, evaluated at different frequencies ω " ω m , m " 1, . .…”

“…As an example, Figure 1 shows a comparison of the principal tensor invariants for a selection of 4 different metallic watch styles computed by the MPT-Calculator software. These calculations were performed in a similar manner to those for other geometries in [20]. The object dimensions are in mm so α " 0.001m and the results shown are for where the material is gold, so that σ ˚" 4.25 ˆ10 7 S/m and µ r " 1 (MPT-Library also includes MPT spectral signatures for watches made of platinum and silver).…”

“…This paper builds on our earlier work [20] and our recent MPT-Library open data set [41], where we have established an extensive suite of simulated threat and non-threat object characterisations using their magnetic polarizability tensor (MPT) spectral signatures. The complex symmetric MPT MrαB, ω, σ ˚, µ r s " pMrαB, ω, σ ˚, µ r sq ij e i b e j " p RrαB, ω, σ ˚, µ r s `iIrαB, ω, σ ˚, µ r sq ij e i b e j ,…”