Determination of the magnetic polarizability tensor and three dimensional object location for...

Publication Title

Determination of the magnetic polarisability tensorand three dimensional object location for multiple

objects using a walk-through metal detector

Authors

Liam A Marsh, Christos Ktistis, Ari Jarvi, David W Armitage and Anthony J Peyton

NOTICE: this is the authors version of a work that was accepted for publication in

Measurement Science and Technology. Changes resulting from the publishing process,

such as peer review, editing, corrections, structural formatting, and other quality control

mechanisms may not be reflected in this document. Changes may have been made to

this work since it was submitted for publication. A definitive version was subsequently

published in Meas. Sci. Technol. Vol. 25 (2014), 055107 (12pp).

DOI link: doi:10.1088/0957-0233/25/5/055107

Determination of the magnetic polarisability tensor

and three dimensional object location for multiple

objects using a walk-through metal detector

Liam A Marsh1, Christos Ktistis1, Ari Jarvi2,

David W Armitage1 and Anthony J Peyton1

1School of Electrical and Electronic Engineering, The University of Manchester,

Manchester, M13 9PL, UK2Rapiscan Systems Oy, Klovinpellontie 3, Torni 2, FIN-02180 Espoo, Finland

E-mail: [email protected]

Abstract. A previously reported tomographic metal detector which is capable of

inverting the location and magnetic polarisability tensor for a single object has been

modified such that it is capable of inverting the location and magnetic polarisability

tensor for multiple objects. In this paper, the term ‘multiple objects’ refers to up to

three indepdent metallic objects. The results from this paper show that the algorithm

works well for objects vertically separated by greater than 40 cm, however the reliability

varies as objects are brought closer together, or are at the same vertical height;

the estimation of position for multiple objects tends to perform well, however the

estimation of the magnetic polarisability tensor becomes poorer. Interactions taking

place between objects is presented as one possible explanation for this.

Keywords: walk-through metal detector, security, tensor

1. Introduction

Walk-through metal detectors (WTMDs) play a key role in screening of large volumes

of people for a variety of purposes including security and loss prevention. Advances in

analogue electronics have allowed manufacturers to detect ever smaller objects, and the

technology has reached the point where commercial products are capable of detecting

objects as small as razorblades and detonator caps concealed on a person [1]. However,

despite these advances and the widespread deployment of the technology, there has been

little development in the use of algorithms to process data acquired from WTMDs in

order to gain information about metallic targets.

In a real-world scenario, for example at an airport, it is common for people to

be in posession of several legitimate metallic items. Examples of such include mobile

phones, belt buckles, keys, watches and other jewellery. Using the current generation of

detectors it is not possible to discriminate between all items which are innocuous and

those which are threatening. As a consequence of this, manual inspection of all positive

detections is required in order to determine whether an object presents a threat. In the

Multiple object inversion using a walk-through metal detector 2

United Kingdom, current regulation dictates that travellers must remove any metallic

objects prior to screening [2] to ensure that the only positive detections are as a result of

restricted items. The removal of items is widely considered to be time-consuming and

highly disruptive to passengers, and is considered by some to be disproportionate to

the perceived threats [3]; however until such time that walk-through metal detectors

are capable of discriminating between threatening and non-threatening objects this

procedure is unlikely to change.

Previous work on the calculation of object parameters and characterisation using

walk-through metal detectors has considered single-object cases only, as is discussed in

the following section. Such applications are not suitable for security screening purposes

and consequently the research outcomes have little or no commercial value. However,

the multiple-object approach described in this paper demonstrates the potential for

practical systems capable of determining object characteristics and locating multple

targets on candidates.

2. Background

One method of characterising the perceived threat from metallic items is to examine the

properties of the magnetic polarisability tensor,↔M [4]. This is a complex, symmetric

and frequency-dependent quantity which is commonly expressed as a 3×3 matrix of the

following format:

↔M (f) =

M11 + jN11 M12 + jN12 M13 + jN13

M12 + jN12 M22 + jN22 M23 + jN23

M13 + jN13 M23 + jN23 M33 + jN33

A tomographic system has been previously been described [5] which is capable of

locating a single metallic object and describing it by means of inverting↔M. This system

consists of 16 coils – eight transmit and eight receive. Each transmit coil operates

at a separate frequency at approximately 10 kHz. Measurements are taken for each

receive coil coupled to each of the transmit coils – i.e. 64 complex measurements,

however due to poor SNR measurements for pairs separated by large distances only 32

complex measurements are recorded. The system has been shown in [5] to be capable

of determining the object position to within ± 3 cm, and with a parameter variation of

<20% for the object tensor. However, the system is significantly limited because it can

only deal with a single object at one time. In order for the system to be suitable for use

as a security system it must be capable of responding to multiple targets.

In this paper the same walk-through metal detection system presented in [5] is used

as a data acquisition system, however a modified ‘multi-object’ algorithm is presented.

A summary of the key underlying theory from [5] is provided below as an introduction

to the main theory presented later in this paper.

The object reponse,V, is modelled by taking the product of the magnetic

polarisability tensor with that of the two H-fields produced by the transmit and receive


coils [10] as shown in equation 1. Multiplication by jωµ0 allows for expression of the

response as a voltage.

V = jωµ0

⇀

Htx ·↔M ·

⇀

Hrx (1)

For convenience of notation it is possible to express equation 1 as a function of two

variables; the first of these variables is magnetic polarisability tensor↔M and the second

is the object location within the detector volume⇀

P. This second variable relates to the

fact that the magnetic field data varies as a function of object position. This function

is represented in subsequent equations as f(⇀

P,↔M)

.

The inversion algorithm then attempts to minimise the error between the measured

values,⇀

V, and the simulated values by fitting a tensor and location,↔M and

⇀

P

respectively, as shown in equation 2. A modified Levenberg-Marquardt algorithm is

used for the inversion as shown in equation 3. The algorithm uses the matrix containing

the iterative solution for the unknown values, L, and varies a regularisation parameter,

λ, updating the jacobean, J, so as to minimse the residual function⇀

R as shown in

equation 4. Under normal operation the regularisatiion parameter λ reduces with each

iteration, however the parameter can increase if the condition of the matrix JTJ+λLTL

as in equation 3. The algorithm is fully described in [5].

arg min

(∥∥∥∥⇀V −f (⇀

P,↔M)∥∥∥∥2

)(2)

[↔M

⇀

P]

=(JTJ + λLTL

)−1JT

⇀

R (3)

⇀

R =⇀

V −f(⇀

P,↔M)

(4)

Multi-object inversion presents some practical challenges that the single object case

does not. Firstly, in the single object case, the algorithm can be optimised to invert

a single object given certain trigger conditions – e.g. measurements exceed a certain

pre-defined threshold. However, when dealing with more than one object, the algorithm

must be capable of determining how many objects to invert for, and also be able to

determine which ‘objects’ are real, and which may be an over-fitting of the data set

to noise. As security officers do not have any a priori knowledge about the number of

objects that candidates may be concealing the ideal system should be able to detect

and invert for an unknown number of objects without any knowledge on the number of

objects, or their location. In this paper, between one and three objects will be used per

scan.

There have been several previous publications in the field of multiple object

inversion and multiple object detection using electromagnetic induction; some examples


are provided in [6, 7, 8]. One such study in the field of unexploded ordnance (UXO)

detection [6] describes the implementation of a multiple-object inversion algorithm

similar to that described in this paper. It identifies some problems which are also

applicable in this application area; these include reconstruction of multiple objects which

are located near to one another, dealing with estimating the number of objects present,

and error increases non-linearly with respect to the number of objects the algorithm is

solving for.

The effect of multiple objects on the single object algorithm described in [5] is

shown in figure 1. In the case of figure 2(a) two NIJ [11] handgun phantoms were

carried through the detector, one in the candidate’s left pocket and the other in the

right pocket. The response shows a smooth trajectory in the direction of travel, however

it is possible to see that the inverted trajectory is in the centre of the detector. The

object is consequently assumed to be positioned in between the candidate’s pockets,

an approximate average of the two positions. This is often seen in cases where one

object has signals with a significantly larger SNR, which in this case the aluminium

gun does, in comparison with the steel gun. In figure 2(b) two similarly-sized pocket

mirrors were carried through the detector in the same way as the guns. The calculated

object trajectory appears to drift between the two correct locations as the candidate

passes through the detector, resulting in a curved trajectory. This response is typical

for multi-object scans where the objects offer signals of similar SNR values.

(a) (b)

Figure 1. Double object response (a) two NIJ guns, (b) two pocket mirrors

3. Theory

3.1. The Algorithm

Previous testing with the single object algorithm has shown that the quality of the

inversion results are strongly correlated with having a good initial estimate for the

position of the object. In order to achieve this, a heuristic algorithm is implemented


which uses the relative magnitudes of raw electromagnetic measurements to identify

the estimated location of the object. This is fully described in [5]. For the multi-

object inversion algorithm a further heuristic algorithm has been devised to estimate

the number of objects based on the electromagnetic data. Testing has shown that

executing the heuristic algorithm and passing the estimated object count to the inversion

algorithm is quicker and provides better results than expecting the inversion algorithm

to determine the number of objects automatically.

Once the candidate has triggered the detector, the object count estimation

algorithm described above is executed. This algorithm performs a heuristic analysis

of the peak magnitude of the parallel channels, columnated to form a vector⇀

VP . This

vector contains eight values representing values from the top to the bottom of the

detector – one for each parallel channel. A linear interpolation is applied to⇀

VP , which

provides a series of points connecting each value, producing⇀v as shown in equation

5. This is necessary as the subsequent stages containing differential operators perform

best with an increased number of points. A threshold value which has been selected

empirically, T, is then calculated as 80% of the mean value of⇀v as shown in equation 6.

⇀v = interp

(⇀

VP

)(5)

T = 0.8× v (6)

The first and second derivatives,⇀

S, of the function⇀v are then calculated to identify

local maxima. These are defined as f ′(⇀v)

and f ′′(⇀v)

respectively. Each value is

checked to ensure that it exceeds the defined trigger threshold and in any cases where

the first derivative is equal to zero and the second derivative is negative a local maxima

is identified. In cases where both the first and second derivative are both zero a second

function G(⇀v)

is executed to invesitage the first derivative of⇀v either side of the

stationary point to ensure that the point is not a minima or point of inflexion. This is

shown in equation 7.

⇀

S =

1 for

⇀v ≥ T ∧ f ′

(⇀v)

= 0 ∧ f ′′(⇀v)< 0

G(⇀v)

for⇀v ≥ T ∧ f ′

(⇀v)

= 0 ∧ f ′′(⇀v)

= 0

0 otherwise

(7)

where G(⇀v)

is a function which examines surrounding points

to confirm the presence of a local maximum point.

The total number of objects is assumed to be the number of elements in⇀

S equal

to 1. This value is then passed to the inversion algorithm as the initial guess for the

number of objects to solve for.


A modified Levenberg-Marquardt algorithm based on the single object algorithm

described in [5] is then executed as in equation 8. This adapted version of the code solves

for up to four objects by attempting to minimise the error between the measured values

and simulated measurements using the forward model from equation 1. This calculation

is expanded from the single object case (shown in equation 4) as it simulates a variable

number of tensors and locations according to the inverted solution. Previous experience

with the system has shown that successful inversions tend to yield residual values of

30% or below, while incorrect solutions can be anywhere above 40%; any exceptions to

this are rare. As a consequence of this a threshold is set at 35%. In the event that the

residual exceeds this value, the algorithm attempts to solve for an extra object. Should

the residual increase then the previous number of objects is assumed to be correct,

otherwise the algorithm keeps going until the residual is below the defined threshold.

To prevent over-fitting to noise, the algorithm rejects any inverted tensors which fall

below a certain magnitude when the absolute value of each element is summed together.

[↔M[1]

⇀

P[1] ...↔M[n]

⇀

P[n]

]=(JTJ + λLTL

)−1JT

⇀

R (8)

The inversion executes by initially running the forward model for a default tensor

at the estimated locations and calculating the error between the simulated and actual

measurements. Simulated measurements are generated for each object and are summed

together. The jacobean, J, is formed by extracting the sensitivity values corresponding

to the locations⇀

P[1] ...⇀

P[n]. The regularisation parameter , L, is set to be a

square matrix containing the product of the matrix containing the unknown values

and its transpose. The algorithm then iterates, updating the regularisation parameter

λ according to whether the locations are within the detector space. The algorithm

terminates when the residual function⇀

R (as defined in equation 9) either ceases to

improve, or begins to worsen.

⇀

R =⇀

V −f(⇀

P[1],↔M[1] ...

⇀

P[n],↔M[n]

)(9)

3.2. Limitations of the Algorithm

The initial object count is subject to the limitation that it is unable to detect multiple

objects at the same height, because it compares the relative magnitudes of parallel

channels, therefore providing only vertical spatial bins. The current generation of

WTMD portals are limited in this way, as they apply a similar algorithm to provide an

approximate location estimate. Any objects at the same height effectively eclipse one

another, and their effects must be calculated later by the inversion algorithm, not the

heuristic estimation.

The algorithm makes several assumptions regarding the problem, which are fully

explained in [5]. As a summary these are that the coils exist in free-space –i.e. the


environment is free from external metalwork; the incident field⇀

Htx is parallel across the

object(s) to be detected; and that the secondary field experienced by the receive coil can

be accurately approximated by the field of a magnetic dipole [12]. For the prototype

system, this means in practice that objects should be approximately no larger than 8

cm in any direction at the centre of the portal.

4. Experimental Procedure

The experiments presented in this paper have been planned to illustrate the effectiveness

of the object estimation algorithm and also the success of the inversion algorithm. Figure

2 shows the measured positions for any locations described in this paper. The size of each

box is indicative of the expected variation in the position as a result of the walk-through

scan.

Figure 2. Positions used for multi-object testing

In this paper three different objects will be used – two Steel NIJ guns made from

different steels, and an Aluminium NIJ gun [11]. For each object fifteen walk-through

scans have been conducted using the single object algorithm. The results of these scans

are shown in figure 3. The xx, yy and zz components are shown as circles, crosses

and plus signs respectively; off-diagonal terms are shown as dots. Each item is colour

coded such that Steel Gun 1 is blue, Steel Gun 2 is red and Aluminium Gun is black.

It is possible to see that the eigenvalues of each object produce clear clusters. This

demonstrates the consistency with which the algorithm is capable of inverting for a

single item.


Figure 3. Inverted tensors for the test objects

For each object an average tensor was computed. The eigenvalues of this tensor

were then calculated to provide an orientation-invariant representation of each object

[9]. These eigenvalues are shown below.

λStGun1 =

−0.8992 + 1.6861j

−0.8600 + 1.2009j

−0.4610 + 0.8770j

λAluGun =

2.3169 + 0.1353j

1.1157 + 0.1224j

0.7257 + 0.3204j

λStGun2 =

−0.6406 + 1.0780j

−0.5812 + 0.7960j

−0.2496 + 0.6717j

These eigenvalues will be taken as the references for each object. The eigenvalues

of all tensors inverted using the multi-object algorithm will be compared with these

values to identify the success of the algorithm. The eigenvalues are scaled against a

reference object, which is used to calibrate the system. The reference is a spherical ball,

37 mm diameter, filled with NiMn ferrite powder. The reference object produced unity

eigenvalues after the system was calibrated.

In the first experiment between one and three objects were carried through the

detector in various locations. The aim was to observe how well the object count

estimation algorithm was able to determine the actual number of objects. NIJ handguns

were placed in various combinations of locations including the left pocket, the chest, the

left sock and the right pocket. The desired outcome is that the algorithm should be able

to identify the number of items providing that they are located at different horizontal

bands; it is not expected that the algorithm will be able to count multiple objects


at similar vertical locations e.g. the left and right pockets. This is as a result of the

horizontal banding of the coil pairs as described in the previous section. The test objects

are shown in figure 4(a), and the object dimensions shown in figure 4(b) and table 1.

(a) (b)

Figure 4. (a) Test objects used in this experiment, (b) Dimension key for test objects

Table 1. Dimensions of test objects (mm)

Dimension Object 1 Object 2 Object 3

Steel Gun 1 Aluminium Gun Steel Gun 2

A 76.65 75.85 75.82

B 57.42 57.25 57.31

C 56.18 47.85 56.16

D 37.01 29.09 37.13

E 20.47 27.66 19.58

F 20.33 28.10 19.73

G 18.98 14.33 14.47

In the second experiment multiple objects will be carried through the detector in the

locations shown in table 2. The experiment is split such that two objects will be used for

the first five tests and three objects will be used for the last five. The measurements from

each scan will be processed by the object count estimation algorithm and then by the

multiple object inversion. For each test a total of five scans will be conducted; in cases

where the residual from the inversion is greater than 0.35 the scan will be considered as

failed inversion results. The resulting locations and object eigenvalues will be displayed

to allow for comparison against the reference eigenvalues shown previously.


Table 2. Object locations for testing with multiple objects

Test Number Object 1 Location Object 2 Location Object 3 Location

1 Chest R. Pocket n/a

2 Chest L. Pocket n/a

3 R.Pocket L. Pocket n/a

4 L. Wrist R. Knee n/a

5 Waist R. Pocket n/a

6 Chest R. Pocket L. Knee

7 R. Pocket L. Pocket L. Knee

8 Chest Waist R. Sock

9 Waist R. Pocket L. Pocket

10 R. Wrist L. Knee L. Pocket

5. Results and Discussion

5.1. Object Count Identification

The results of the object count testing are shown in figures 5 to 8. Each figure shows

the output from the object count estimation algorithm as described previously. In each

case the peak object response is plotted on the x-axis and the rounded y-locations are

shown on the y-axis. A blue line shows the signal magnitude profile for parallel channels

from the ground to the top of the detector. The dashed red line indicates the trigger

threshold and the magenta circles indicate estimated object locations.

In the first scan, shown in figure 5 it is possible to see that a single object has been

correctly identified. The estimated height of approximately 0.9 m is sufficiently close to

the actual location for ’Left Pocket’ (as indicated on figure 2) to demonstrate that the

system is responding to the object in question.

Figure 6 clearly shows two identified objects, one at 0.9 m and another at 1.4 m.

These locations agree with the previous result, and with the chest location shown in

figure 2.

For the three object cases in figures 7 and 8 two different results have been observed.

In the case of the objects being located at different heights on the body the algorithm

has successfully located three separate objects at 1.4 m, 0.9 m and 0.15 m. However, for

the case shown in figure 8 two of the objects were located in the locations ’L. Pocket’

and ’R. Pocket’ and hence were at the same height. As a result of this the algorithm

has only identified two objects as expected.


Figure 5. Single object in

left pocket

Figure 6. Object in left

pocket and in front of chest

Figure 7. Objects in left

pocket, in front of chest and

in left sock

Figure 8. Objects in left

pocket, right pocket and in

front of chest

The results from this testing are encouraging as they demonstrate the ability of the

algorithm to identify multiple objects. Although the correct number of objects has not

been shown in all cases, it is expected that the information should be useful in aiding

the inversion algorithm find a solution.

5.2. Multi-object Inversion

The results from the inversion for the multi-object tests defined in table 2 are shown in

figures 9 to 18.

For the two object cases in tests 1, 2, 4 and 5, the inverted locations correspond

with the object locations shown in figure 2. In test 5 the results are most encouraging as


it demonstrates the system’s ability to locate two objects which are close to one another.

In test 3, however, the algorithm has ignored the steel gun and has placed a single object

in the position of where the aluminium gun was. The eigenvalues of the inverted tensors

in tests 1, 2 and 4 are clustered around clearly defined values, however in each case it

is interesting to note that the central values of each cluster do not correspond with the

reference values. It is thought that this is due to the effect of the two objects interacting,

and therefore slightly changing the object tensors. In each of these three tests it is clear

which object is which, and the parameter variation is within the 20% experienced for

the single object algorithm in [5]. In test 5 the results are slightly worse, in that there

is some deviation from the clustering. However, it is still possible to determine the

different objects, and the algorithm has correctly assigned negative real components to

the steel gun and positive real components to the aluminium gun. In test 3 the inverted

results are labelled as ‘Inverted Object’ rather than the object name as for the other

objects. This reflects the fact that the algorithm only inverted a single object for each

scan. The eigenvalues imply that the identified object is the aluminium gun by virtue

of the positive real component and the point-clustering in the vicinity of the aluminium

gun reference values. This also agrees with the inverted location which is placed in the

position of the aluminium gun. In this test each of the the residual values were slightly

below the threshold of 0.35 implying an acceptable fit by the algorithm, however also

implying that there was room for improvement.

Figure 9. Results - Test 1



In the three object cases in tests 6 to 10 the results are generally more scattered,

both for location and for inverted tensor eigenvalues. In each figure, the blue, red and

black points correspond to the first steel gun, the aluminium gun and the second steel

gun respectively.

In test 6 the objects have been located at the correct height and at the correct

z-location for the first steel gun and the aluminium gun, however for the second steel

gun the object has been located to the right hand side of the candidate when it was on

the left knee. These errors are reflected for the inverted tensors where the eigenvalues

are scattered around the reference values for the first steel gun and the aluminium gun,

however the points for the second steel gun are scattered significantly beyond the range

occupied by the reference values to the point where it is not identifiable as the object

in question.


Test 7 shows a similar result as test 3 in that the algorithm has ignored the first steel

gun and has favoured the aluminium gun. The inverted locations for the aluminium gun


and second steel gun are noisier than for the previous test, however are broadly correct.

For the single instance where the first steel gun was identified it has been positioned

in the same place as the aluminium gun, thereby throwing doubt on the validity of the

inverted tensor. The eigenvalues of the second steel gun show some agreement with the

reference values, however there is still a large spread in some values, as is the case for

the aluminium gun. For both objects the eigenvalues have mostly the correct sign for

the real components. In all scans the residual value was in excess of the threshold of

0.35, this gives a strong indication that the result is a poor data fit.

The results for test 8 are similar to those for test 6, however in this instance the

accuracy of the inverted eigenvalues is greater for the second steel gun than for the first

steel gun. The location of the first steel gun and the aluminium guns are both correct,

however there is a considerable amount of noise on the second steel gun despite the good

tensor fit. It is thought that this is due to the fact that there are fewer coils concentrated

at floor level, and consequently the positioning of objects is more challenging.




In test 9 the second steel gun was not identified on any of the five scans. As

has previously been the case for tests with guns in opposite pockets, the steel gun has

been ignored by the inversion and the response of the aluminium gun has dominated.

The object location is very similar to that in test 4, however, in this test the objects

are swapped round. The quality of the inverted tensors is poor, and shows almost no

correlation with the reference values beyond identifying the correct sign for the real part.

In each case the residual values were in excess of the threshold value of 0.35 thereby

indicating a poor data fit.


In test 10 the object location is quite poor for all objects with respect to the z-

location as all objects are shown closer to the centre of the candidate than they should be.

The y-location is approximately correct for the first steel gun and the aluminium gun,

however for the second steel gun the only inverted location has been merged with that of

the aluminium gun when according to figure 2 it should be approximately 35 cm away.

The inverted tensors for both steel guns are also poor when compared with the reference

values. In the case of the aluminium gun the eigenvalues are more concentrated; this

is possibly due to the considerably larger SNR that the item has compared to the steel

guns.



6. Conclusions and Future Work

The results presented in this paper have demonstrated the possibility of inverting the

location and magnetic polarisability tensor for multiple objects. The results for two

objects are generally comparable with the single object results presented in [5], however

the results for three-object cases, or multiple objects clustered at the same height have

been seen to be noticeably worse. It should be noted however that all cases with poor

results were automatically flagged by the algorithm as being invalid due to the large

residual values. In such instances a manual inspection could be carried out to screen

the candidate.

It is expected that the ability to detect and identify multiple-objects should improve

with increased spatial resolution within the detector’s sensitivity map. The simplest

method of achieving this is to increase the number of coils used by the system; this

should improve both the heuristic algorithm and the inversion algorithm. A further

enhancement could be made to the system be operating all coils at multiple-frequencies

simultaneously, thereby allowing for the inversion of the broadband tensor response for

each object. This extra data would be useful if coupled with classification algorithms

as in [13] to allow for reliable automatic threat detection.

Acknowledgements

The authors would like to thank the UK Engineering and Physical Sciences Research

Council (EPSRC) and the Technology Strategy Board (TSB) for financial support of

this research under programmes DT/F002467 and TP M1649F, respectively. They are

also very grateful to Ari Visa and Juho Vihonen at Tampere University of Technology

and Bill Lionheart at the University of Manchester for their encouragement and very

useful suggestions during this research.


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Determination of the magnetic polarizability tensor and three dimensional object location for...

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Transcript of Determination of the magnetic polarizability tensor and three dimensional object location for...