Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object classification

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 characterization information. The magnetic polarizability tensor (MPT) offers an economical characterization of metallic objects and its spectral signature provides additional object characterization information. The MPT spectral signature can be determined from measurements of the induced voltage over a range of frequencies in a metal signature for a hidden object. With classification in mind, it can also be computed in advance for different threat and non-threat objects. In this article, we evaluate the performance of probabilistic and non-probabilistic machine learning algorithms, trained using a dictionary of computed MPT spectral signatures, to classify objects for metal detection. We discuss the importance of using appropriate features and selecting an appropriate algorithm depending on the classification problem being solved, and we present numerical results for a range of practically motivated metal detection classification problems.

Properties of Generalised Magnetic Polarizability Tensors

“…Next, by applying integration by parts ż `ξδ e j ˆξq ¯dξ, (15) and following analogous steps to the proof of Lemma 5.1 obtain…”

“…In a series of works, we have explored the properties of MPTs including providing several different splittings and formulations for obtained MPT coefficients [7,9] and also investigated the spectral properties of their coefficients [9]. Together with Wilson, we have also developed efficient computational algorithms for the computation of the MPT coefficients and their spectral signature [14] that have allowed us to generate a large dictionary of object characterisations [12] and apply machine learning algorithms to identify hidden objects using classification [15], which exploit the MPT's spectral signature.…”

Benchmark computations for the polarization tensor characterization of small conducting objects

“…However, an alternative approach is offered by combining dictionaries of object characterisations using PSTs with classification techniques, such as those in ML algorithms (see [12] for a discussion of different approaches), due to the separation of object characterisation and in position in (1). A ML approach to object classification using polarizability tensors has already been shown to be effective for metal detection [13], but for such an approach to be effective for EIT problems, a description of accurate PST coefficients is required.…”

“…This approximate tensor T h is shown in(12) For the key the best approximation is obtained by choosing β " 0.3, θ " 0.6 and η " max η i on a mesh with 34 354 surface triangles. This approximate tensor T h is shown in(13).…”

Properties of generalized magnetic polarizability tensors

“…In a series of works, we have explored the properties of MPTs including providing several different splittings and formulations for obtained MPT coefficients 4,5 and also investigated the spectral properties of their coefficients. 5 Together with Wilson, we have also developed efficient computational algorithms for the computation of the MPT coefficients and their spectral signature 6 that have allowed us to generate a large dictionary of object characterizations 7 and apply machine learning algorithms to identify hidden objects using classification, 8 which exploit the MPT's spectral signature.…”