Realistic Subsurface Anomaly Discrimination Using Electromagnetic Induction and an SVM Classifier
© 2010 Juan Pablo Fernández et al. 2010
Received: 31 July 2009
Accepted: 12 February 2010
Published: 11 May 2010
The environmental research program of the United States military has set up blind tests for detection and discrimination of unexploded ordnance. One such test consists of measurements taken with the EM-63 sensor at Camp Sibert, AL. We review the performance on the test of a procedure that combines a field-potential (HAP) method to locate targets, the normalized surface magnetic source (NSMS) model to characterize them, and a support vector machine (SVM) to classify them. The HAP method infers location from the scattered magnetic field and its associated scalar potential, the latter reconstructed using equivalent sources. NSMS replaces the target with an enclosing spheroid of equivalent radial magnetization whose integral it uses as a discriminator. SVM generalizes from empirical evidence and can be adapted for multiclass discrimination using a voting system. Our method identifies all potentially dangerous targets correctly and has a false-alarm rate of about 5%.
The millions of unexploded ordnance (UXO) strewn about in former battlefields and military practice ranges, of which a significant fraction involve marine or underwater environments, constitute a pressing humanitarian and environmental hazard worldwide . The high false-alarm rates of current sensors and the need to treat every detected anomaly as potentially dangerous result in decontamination costs running into the millions of dollars per acre and extend remediation timescales by decades if not centuries. This state of affairs can only be resolved by developing methodologies that will quickly and reliably identify hazardous items and discriminate them from the morass of innocuous clutter typically found in the field.
The discrimination process comprises three tasks: localization, characterization, and classification. The secondary field from a visually obscured object depends both on the intrinsic features of the target and on its location and orientation relative to the sensor. Attempts to invert simultaneously for positional and intrinsic parameters often result in slow, ill-posed, computationally expensive optimizations that can easily get stuck in local minima. Our method [3, 4] clears that hurdle by performing the localization step independently at the outset and then using its results to help in the characterization. This permits a fast and accurate determination of the intrinsic parameters of the model. To classify the targets we feed those parameters to an open-source implementation  of a support vector machine (SVM) , a machine-learning methodology based on statistical learning theory [7, 8] that in the past has been used to perform binary classification  and regression  and has recently been adapted for multicategory classification . The method has been employed in UXO research, either to classify or regress, in combination with the point-dipole model [1, 12, 13], the Standardized Excitation Approach [14–16], and finite elements [17, 18], and has shown to be competitive in its discrimination ability in relation to neural networks [15, 19] and other statistical methods [20, 21].
In a previous paper , we studied the Camp Sibert data using the same characterization model in combination with nonlinear least squares for the localization step and both template-matching and a Probability Neural Network for classification. We have already noted  that the localization procedure described below results in much better discrimination. The SVM-based classification showcased in this paper improves upon the template-matching used before [3, 4] in that it requires less human intervention and is thus faster to run and easier to adapt to other sets of observations. The template-matching procedure made predictions essentially identical to those we report here, perhaps even marginally better, but only after much close monitoring.
SVMs have previously been used for multicategory UXO-related classification , though in that reference the authors' choice of forward model and treatment of positional information differ from ours. While they construct parameter libraries at different locations in order to cancel out the geometric effects and enhance classification, we determine those effects separately; that way not only do we recover critically important information but also obtain parameters whose classification is perhaps easier (and thus faster) to perform and still of high quality.
In summary, our procedure aims to be a powerful and efficient discrimination method for UXO. The precise location and orientation estimates supplied by the so-called HAP technique  allow an almost instantaneous determination of an unambiguous time-dependent electromagnetic signature, the total NSMS ; this in turn can be distilled further using an empirical decay law  whose fitting parameters can be mixed into discriminating features that tend to group in well-separated tight clusters, allowing for clear-cut automated classification using the SVM algorithm.
This paper is organized as follows: in Section 2 we introduce the methods we use to locate and characterize scatterers, in Section 3 we briefly present the principles behind SVM classification, in Section 4 we discuss the results we obtain when we apply the combined procedure to the Camp Sibert data, and in Section 5 we conclude.
2. A Procedure to Locate and Characterize Obscured Targets
The eddy currents and magnetic dipoles induced or realigned by an EMI sensor on and inside a scatterer are distributed nonuniformly and tend to concentrate at some particular points. Under certain conditions, the response of the entire scatterer can be reproduced to arbitrary precision using a set of responding elementary sources—charges, dipoles, or the like—placed at those singularities [26, 27]. This consideration underlies the methods that we use to locate and characterize hidden targets.
2.1. A Dipole-Based Method to Estimate Location
The technique we use to locate an obscured target assumes that the whole scatterer responds as a point dipole. The location and orientation of that dipole are then found by exploiting analytic relations involving a dipole field and its associated scalar potential . (The method originally used the vector potential as well and has since been dubbed "HAP" .) To construct the potential from the field, one distributes elementary sources on an auxiliary planar layer located between the sensor and the object and finds the sources' amplitudes by fitting measured data.
2.2. The Normalized Surface Magnetic Source Model
To encapsulate the electromagnetic signature of a target, we use the fast and robust normalized surface magnetic source (NSMS) model . The particular version we use here associates a scatterer with a surrounding prolate spheroid on which a continuum of radially oriented dipoles are distributed. The strengths of these dipoles—normalized by the normal component of the primary field to take monostaticity into account—are determined as those that best reproduce actual measurements. The composite dipole moment, referred to as the "total NSMS" and denoted by , varies significantly for different targets but is remarkably consistent for different specimens of the same object.
where is a vector that points from the location of the -th infinitesimal patch on the spheroid to the observation point and is the unit vector normal to the patch. To factor out the particulars of location and orientation we have introduced the normalized surface polarization distribution . The integral can again be transformed to a matrix-vector product via numerical quadrature; each column of corresponds to a different source element and each row to a measurement point. The amplitude array is determined by minimizing in a least-squares sense the difference between measured data with a known object-sensor configuration (as in the case of the Camp Sibert training data) and the predictions of (8).
Our analysis of the time dependence of has been presented elsewhere [3, 4, 22] but is worth summarizing here. At early times, where higher frequencies are involved, the skin depth is small and the induced eddy currents are superficial. As time passes and lower frequencies start to dominate, the currents diffuse into the object, making the late-time response involve the whole volume of the scatterer rather than just its surface. Thus a smaller but solid body like the base plate of Figure 1(b) has a relatively weak early response that dies down slowly, while a large but essentially hollow object like the partial mortar of Figure 1(c) has a strong initial response that decays quickly. The unexploded mortar is large and compact and has a substantial early response that takes a while to die off. Our aim is to use these characteristics of to highlight quantitatively the differences between the various targets.
Various combinations of these fitting parameters can be used as inputs to classifier programs, of which the support vector machine (SVM) is an example.
3. Support Vector Machines for Subsurface Object Classification
A support vector machine learns from data: when fed a series of answered training examples, it attempts to make sense of them by weighing the available empirical evidence, with no need for an underlying model, and applies this knowledge to make predictions about unseen cases. The examples can be any combination of model parameters expected to contain evidence of the essence of an object. In the simplest instance of binary classification, each -dimensional example has an associated yes/no attribute ; the SVM performs the classification by finding a hyperplane that divides the parameter space into two distinct regions, each of which ideally contains points from only one of the categories. During the learning or training process the machine readjusts the hyperplane parameters to accommodate every training vector until it strikes an optimal balance between fitting accuracy and model simplicity. All information about the hyperplane is contained in a subset of the examples—the support vectors that give the method its name—which are then combined to specify a predicting function.
The SVM algorithm uses two different strategies to tackle the nonseparability of realistic data. On one hand, it projects the examples into a space of higher dimensionality by means of a kernel function . The separating surface thus found is flat by construction in the new space but can be curved and even multiply connected in the original. On the other hand, the technique tries to control overfitting—and thus concentrate on essentials rather than on details, resulting in better generalization—by having an adjustable penalty on misclassifications. This penalty is represented by a single scalar parameter, the capacity of the machine .
whose solution is a vector of coefficients that measure the information content of the examples and are nonzero only for the support vectors. The coefficients are prescribed not to exceed the capacity , which limits the influence of potentially problematic points on the final result.
which surrounds every example with a surface that in a sense "repels" the separating hyperplane. The Gaussian width is a second adjustable parameter and usually has a scale on the order of the average separation between points. In  it was found that polynomial kernels may outperform the RBF kernel in some electromagnetic inverse problems. We find that the linear kernel makes similar predictions and runs faster than the RBF, though the difference in run time is negligible for the number of training data and example features that we use in this study.
There are several ways to generalize the SVM procedure to perform multiclass categorization. These have been reviewed in , whose authors conclude that the methods more suitable for practical use perform several binary classifications instead of attempting to separate all classes at once. In this work we adopt a one-against-one approach  in which the system carries out optimizations and obtains the same number of decision functions of the form (14). When given an example to predict, the algorithm proceeds by ballot: it evaluates the decision functions one by one on the example and adds a vote to the one category (out of two) in which it is predicted to be. At the end, the example is assigned to the category with the most votes; should there be a tie between two classes, the program arbitrarily selects that with the smallest label.
4.1. Data Acquisition
4.2. Target Location and Characterization
For each data set we run the HAP method of Section 2.1 to locate the target and a fully three-dimensional implementation of the NSMS model of Section 2.2 to characterize it. Consider again the example cell shown on Figure 4. To find the target, we take a fictitious flat square surface concentric with the plot and located 30 cm below the sensor (i.e., at ground level) and divide it into patches, each of which is assumed to contain a magnetic-charge distribution of uniform density. We take the measured field data (as seen for example on the left column of Figure 4) and use (5) to determine , which in turn allows us to determine using (7) and construct the matrices of (4) to find the location. We do this separately for every time channel and get consistent location estimates from gate to gate, which lends credence to their precision. For the case of Cell no. 7, we obtain a target depth of 55 cm, acceptably close to the ground truth of 60 cm.
We have previously found [3, 4] that the ratio of at the 15th time channel to at the first time channel, which involves a fixed superposition of and , shows discernible clustering for this particular data set when combined with the third parameter . (The 15th time channel, centered at about 2.7 ms, was chosen because it takes place late enough to show the behavior described above but early enough that all targets still have an acceptable signal-to-noise ratio; nearby time channels produce similar results.) The values of for the mortars are particularly well grouped and for the most part noticeably distinct from those of the others, suggesting that this two-dimensional feature space may be used to perform dependable classification. This suggestion is confirmed by our SVM analysis.
4.3. SVM Classification
The false alarms, two pieces of non-UXO clutter, appear on Figures 5(b) and 5(c). They are seen to be similar to the mortars in size and metal content (cf. Figure 5(a)), which makes their and values lie closer to the tight UXO cluster than to any other anomaly in Figure 6. Here we note that, as can be seen in Figure 1(d), the training data provided by the examiners was somewhat biased toward UXO, while clutter and scrap samples were underrepresented (this was not the case with the testing data and should not be expected in future tests). If we switch training and testing data in the SVM analysis, we can achieve perfect discrimination without varying the capacity—though in this case we have more training data than tests. This highlights the importance of having a diverse collection of representative samples to use during the training stage.
In this paper, we have applied the NSMS model to EM-63 Camp Sibert discrimination data sets. First the locations of the objects were inverted for by the fast and accurate dipole-inspired HAP method. Subsequently, each anomaly was characterized at each time channel through its total NSMS strength. Discrete intrinsic features were selected and extracted for each object using the Pasion-Oldenburg decay law and then used as input for a support vector machine that classified the items.
Our study reveals that the ratio of an object's late response to its early response can be used as a robust discriminator when combined with the Pasion-Oldenburg amplitude . Other mixtures of these parameters also result in good classifiers. Moreover, we can use directly, completely obviating the need for the Pasion-Oldenburg fit. In each case, the classifier runs by itself and does not require any human intervention. The SVM can be trained very quickly, even when the feature space has more than 20 dimensions, and it is a simple matter to add more training data on-the-fly. It is also possible to use already processed data to classify examples as yet unseen.
We should stress that none of our classifications yielded false negatives: all UXO were identified correctly in every instance. (This is due in part to the clean, UXO-intensive training data provided by the examiners and may change under different conditions.) The number of false alarms (false positives) varies with the classification features, but is in general low and can be as low as 2 out of 36 reported positives. Figures 6 and 5 show, among others, how these false alarms come to be: some of the clutter items have a response that closely resembles that of UXO. While this will inevitably arise, it may still be possible to make the SVM more effective—and perhaps get close to reaching 100% accuracy—by including some of these refractory cases during the training. That said, there will certainly be cases in the field where the nonuniqueness inherent to noisy inverse scattering problems will cause the whole procedure to fail and yield dubious estimates. In those cases it will be necessary to assume the target is dangerous and dig it out.
In a completely realistic situation, where in principle no training data are given and the ground truth can be learned only as the anomalies are excavated, one can never be sure that the data already labeled constitute a representative sample containing enough of both dangerous and innocuous items. This difficulty is mitigated by two facts: ( ) usually at the outset we have some idea of the kind of UXO present in the field and ( ) the (usually great) majority of detected anomalies will not be UXO and thus random digging will produce a varied sampling of the clutter present. Methods involving semi supervised learning exploit this gradual revealing of the truth and have been found to perform better at UXO discrimination than supervised learning methods like SVM when starting from the point dipole model [35, 36]. (Active learning methods, which try to infer which anomalies would contain the most useful information and could thus serve to guide the anomaly unveiling, show further, though fairly minor, improvement.) Combining this more powerful learning procedure with the excellent performance of the HAP/NSMS method may enhance the discrimination protocol and should be the subject of further research.
In summary, the results presented here show that our search and characterization procedure, whose effectiveness is apparent from several recent studies [3, 4, 37, 38], can be combined with an SVM classifier to produce a UXO discrimination system capable of correctly singling out dangerous items from among munitions-related debris and other natural and artificial clutter. In future investigations, we will continue to hone these algorithms and use them on other blind tests, including some already carried out in saltwater instead of soil.
This work was supported by the Strategic Environmental Research and Development Program through Grants no. MM-1572 and no. MM-1573.
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