Random Neural Network Filter for Land Mine Detection - UCF CS

Random Neural Network Filter for Land Mine Detection Hossam Abdelbaki, Student Member IEEE , Erol Gelenbe, Fellow IEEE School of Computer Science University of Central Florida Orlando, FL 32789 fahossam,[email protected] Taskn Kocak, Student Member IEEE Said E. El-Khamy, Fellow IEEE Mitsubishi Semiconductor America Department of Electrical Engineering Three Diamond Lane Alexandria University Durham, NC 27704 Alexandria, Egypt, 21544 [email protected] [email protected]

Abstract

The two primary measures of land mine detection performance are the probability of detection Pd and the probability of false alarm Pfa .These two measures are highly interdependent and must be evaluated together. The relationship between the two probabilities directly aects the overall performance of the sensor in the eld. In this paper we introduce a novel false alarm non-parametric lter based on the Random Neural Network (RNN) model [2, 3, 4] and the -Technique [1], the study is based on mine detection using Electromagnetic Induction (EMI) sensors. The mine eld data are pre-processed via the -Technique before applying it to the RNN. The RNN has a prede ned structure that tries to implement a mapping close enough in some precise sense to the discrimination function between non-mine and mine patterns [8]. Limited number of non-mine and mine patterns, extracted from a small calibration area for a certain mine eld provided by DARPA [5], are used for training the RNN. We show that the RNN gives eective decisions on patterns measured on other locations using dierent EMI sensor. The results show that the RNN produces probability of detection up to 100 percent with a substantial reduction of false alarms over the -Technique (up to 40 percent false alarm ltering).

Key-words: Mine Detection, Binary Random Neural Network, -Technique, False Alram Filtering, Anthropic Clutter, Decision Boundary Function Approximation, EMI sensor.

1 Introduction A land mine is easy to build, and some go for $1 a piece in quantity. In some ways, land mines are ideal weapons, designed to kill enemy forces or restrict their movements. After the war ends, armies leave the battle eld leaving behind land mines which can lie hidden in the ground for more than 30 years. It is estimate that there may be some 100 million land mines worldwide, maiming or killing about 26000 people a year, according to the international committee of the Red Cross. More than 60 countries, most of them in the third world, are rife with land mines. Kuwait recently spent $1 billion to remove 7 million mines scattered across the desert during the 1

Gulf War. In Egypt, there are about 23 million mines and in Bosnia, about 1.7 million buried land mines are faced. Therefore there is a crying need for technologies which can detect land mines eectively. Unexploded ordnance (UXO) creates very similar problems, both in areas where armed con icts have taken place, and in military bases and training areas which need to be decommissioned and returned to civilian usage. Detection of buried mines and unexploded ordnance (UXO) has proven to be a very dicult problem. The Electromagnetic Induction eld sensors (EMI), which are essentially metal detectors, are eective pieces of equipment for mine detection [6]. In an EMI system, the transmitter coil creates a magnetic eld which can penetrate the ground to reach a buried object, and the response of the object to the magnetic eld, which varies according to the nature of the object, is sensed by the receiver coil. The main drawback of the EMI sensors is the high false alarm rates (detection of metallic clutter) which are caused by a variety of sources. Some of them due to geological features such as soil conductivity and magnetic rocks and the other due to man made clutter (anthropic clutter). These detectors can provide a 100 percent detection rate, but they can also produce a high false alarm rate in many environments. The high false alarm rate reduces the usefulness of the detectors in the eld. Thus since thousands of false alarms can occur during sweeping of a relatively small mine eld, it is important to nd signal processing techniques which can produce a high probability of mine detection with false alarm rates which are much lower than those resulting from the conventional detectors. The mine eld data used in this study uses the data provided by DARPA [5], at four sites across two U.S. locations: Fort Carson, Colorado and Fort A.P. Hill, Virginia. The sites have dierent soil types and dierent anthropic clutter. The four sites are referred to as Firing Point (FP 20), Firing Point (FP 22), Seabee and Turkey Creek. Three of the four sites have a small amount of clutter, while at one of the sites (FP 20) the amount of such clutter was substantial. In this paper, the performance is explored using data from two types of handheld EMI sensors, which were collected during the DARPA Background Clutter Data Collection Experiment [5]. The rst sensing system considered is a Geonics EM61 - 3D which is a three component time-domain pulsed EMI system. It consists of a multichannel pulsed induction system having a 1 m square transmitter coil and three orthogonal 0.5m receiver coils which are positioned approximately 0.3m above the ground. The second system, the Geonics EM61 sensor, is a single channel time-domain EMI sensor, consists of a two 0.5m square coils. One coil (Z1) is placed approximately 0.4m above the other coil (Z2), which is 0.3m above the ground. The lower coil, Z2, is used for both transmitting and receiving the electromagnetic eld. The upper coil, Z1, is used to receive the induction eld only. In both sensors the magnetic eld transmitted from the coils is pulsed into a de ned area of terrain (typically measuring one square meter or less). We will propose a novel model for improving the mine detection based on the function approximation capability of the Random Neural Network [7, 8]. The validation is conducted on calibrated mine eld data provided by DARPA.

1.1 The -Technique

The EMI sensor energy at a mine location will in general have a larger value than at the neighbouring locations, which are assumed to be clutter. Since the size of the mine is small, it will aect the response of the nearby neighbours only. However, at non-mine locations, the distribution of energies has no certain pattern. With a low enough threshold energy value, high mine detection rates can be obtained but also unacceptable high false alarm rates will be produced. One such improved detection technique is the -Technique [1]. It is a method that reduces false alarm rates by making use of the area information around each point visited during 2

the search. The -Technique can be summarized as follows: 1. For any selected threshold energy level select all data points p where the EMI sensor energy E (p) ; call this set H (). 2. Select some number m among the value 1; ; 8. For each p in H () count the number of intermediate neighbours Pn whose energy values are strictly less than E (p) and call it M (p). Obviously M (p) 8. If M (p) m classify p as a mine (or false alarm), otherwise treat it as a non-mine. In practice = m=8, and m = 7 or m = 8, so that ( = 7=8, or 8/8). The -Technique signi cantly in uences the Receiver Operation Curves (Probability of Correct Detection in the y-axis, versus the probability of False Alarms in the x-axis) by reducing the false alarm rates.

2 Random Neural Network False Alarm Filter The basic Random Neural Network (RNN) [2, 3, 4] allows arbitrary interconnections between neurons. It has a mathematical proof that it has a unique solution if the stability conditions are met. By appropriately mapping external signals and neuron states into certain physical quantities, it has been successfully applied to several engineering problems including solving NP-complete optimization problems [10, 11], texture image generation [12, 13] and image and video compression [14, 15, 16]. The empirically observed success of the network can be justi ed using the theoretical results reported in [8], where the authors showed that for any continuous multivariate function f on a compact set, it is possible to construct a RNN model with a prede ned structure that can implement a mapping close enough to f in some precise sense to to a given degree of accuracy.

2.1 BGNN for decision boundary function approximation

In this paper we try to apply the concept of function approximation using RNN to the problem of mine detection. First, we will state a theorem that illustrates the function approximation capability of RNN.

Theorem: [8] For any continuous function f : [0; 1]N ! R and any > 0, there exists a

BGNN (Binary Gelenbe Random Neural Network) with one positive output neuron (O; +), one negative output neuron (O; ;), s input variables X = (x1 ; x2 ; ; xN ), and the output variable y(X ) such that:

y(X ) = AO;+ + AO;;;

(1)

AO;+ = 1 ;qO;q+ ;

(2)

AO;; =

(3)

O;+ ;qO;; 1 ; qO;; ;

supx[0;1] jf (X ) ; y(X )j <

(4)

and q is the neuron's output . We will say that the BGNN's output uniformly approximates f (X ). 3

To make use of this theorem in mine detection, we can consider the neural network as a pattern classi er that maps feature space to decision space. The features we use here are the relative energy readings of h h declaration windows at whose central points we want to decide as mines or non-mines. Thus for each point in the mine eld, we have N = h h features, each set of the N features can be considered as an N -dimensional vector X = [x1 ; x2 ; ; xN ]0 or as a point in the N -dimensional space N . The classi cation problem is then interpreted as partitioning the feature space into two mutually exclusive regions [17], each region corresponds to a particular pattern class, such partitioning is achieved by using a discriminant function. Let us denote the two possible pattern classes to be recognized by A for mines and B for non-mines then the discriminant functions D1 (X ) associated with pattern class A and D2 (X ) associated with pattern class B are such that for all X belonging to A or B the following equation will apply:

D1 (X ) > D2 (X )

(5) Thus in the feature space x the boundary of partition, called the decision boundary, between regions corresponding to class A or B respectively is expressed as the following equation:

P (X ) = D1(X ) ; D2 (X ) = 0 (6) Thus X 2 A if P (X ) > 0 (mines) and X 2 B if P (X ) < 0 (non-mine). The mine detection

using RNN is a non-parametric method since we have no a priori knowledge of the probability density functions of the mine and non-mines patterns. To approximate the function of the decision boundary using BGNN, we should have from (1) and (5) :

y(X ) ' P (X )

(7)

and without loss of generality we can write :

D1(X ) ' +AO;+ and D2(X ) ' ;AO;;: Because of the high degree of clutter in the mine eld, the mine and non-mine patterns are not linearly separable and many non-mine patterns will be classi ed as mines (false alarms). Since we are concerned with supervised classi cation and we have no a priori knowledge of the decision boundary function P (X ) (except that P (X ) > 0 for mines and P (X ) < 0 for non mines), we can start with a certain values for the output function of the BGNN as follows:

y(XA ) = +2 and y(XB ) = ;2

(8)

Equivalently we can begin with the desired average potentials of the BGNN as follows:

AO;+ = 4 and AO;; = 2 for X 2 A mines 0

0

AO;+ = 2 and AO;; = 4 for X 2 B non mines 0

0

2.2 The RNN structure

(9) (10)

The RNN we use consists of 9 neurons (N = 9 and h = 3) in the input layer, 9 neurons in the second layer and 2 neurons in the output layer as shown in Figure 1. Each neuron in the input layer represents a cell of the 3 3declaration window taken for each visited point in the mine eld. All the input neurons are fully connected to the neurons in the second layer. The central 4

neuron in the second layer is connected to all the surrounding neurons in the same layer to encode the relationship between the central point in the declaration window and its neighbours. Finally, all the neurons in the second layer are fully connected to the output layer. q(o,-)

q(o,+)

Figure 1: Structure of the proposed RNN false alarm lter

2.3 Training the RNN

Each training and test pattern applied to the neural network was obtained by using a square spatial window of data of size 3 3 points (declaration window). The decision as to whether or not a mine was present at the center of the window based on data collected over the entire window area. Since the input domain is continuous, we suggest it to be normalized to the range from 0 to 1 by using: E = EE ;;Emin (11) E 0

max

min

where E and E are the original and the normalized values of the sensor energy measurement at any point and Emin and Emax are the minimum and the maximum values observed. The network is trained according to the algorithm in [4] with the desired output as discussed in section 2.1 Equations 8, 9 and 10. The training procedure follows the general principles in [8], which make the network try to map the functional relationship between the training patterns instead of memorizing them. 0

2.3.1 Training set Training patterns (for mines and non-mines) were chosen from the calibration area of the FP 20 (EMI 1m Z-coil measurements). This calibration area is a 30m 15m area within the much larger FP 20 area. Clearly, in this area there are around 450 measurement points (13 of them correspond to registered mines and the rest correspond to non-mines). All the 13 mine patterns were considered and for each pattern, all the corresponding eight isometric transformations were generated as shown in Figure 2. From this set (13 8 = 104 patterns), the similar and redundant patterns were excluded, the resulted set consists of 28 patterns that were applied as mine training patterns for the RNN shown in Figure 1. On the other hand, another 28 appropriate training patterns for non-mines were selected so that the training set consists of 56 patterns for mines and non-mines.

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0 deg.

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Flip & 90 deg.

Flip & 180 deg.

Flip & 270 deg.

Figure 2: Eight isometries for a declaration window

3 Experimental Results This section summarizes the performance achieved using the Random Neural Network for landmine detection

3.1 Testing set

First, the -Technique ( = 7/8) is applied to all the available data for the four sites provided by DARPA which include measurements from both 1m and 0.5m EMI sensor systems (8 separate sets). During preparing the test patterns, no certain threshold energy level is taken into consideration (since the energy measurements vary from one site to another and also for different sensory systems). The resulted patterns from the -Technique (false alarm patterns and detected mine patterns) are then applied to the trained RNN as a second stage lter for false alarms with high mine detection capability. Theoretically the RNN lter may not nd as many actual mines as the -Technique since the test patterns applied to the RNN are produced from the -Technique. Test results for the four mine eld sites based on all the available data from the EMI sensors provided in [5], with 0.5m sensors, are given in Tables 1 Site name Points searched Number of mines False alarms detected: -Technique Mines detected : -Technique False alarms detected: RNN Filter Mines detected : RNN Filter False alarms rejectted: RNN Filter

FP 20 7819 24 1377 (17.61 %) 23 (95.83 %) 1047 (13.39 %) 23 (95.83 %) 23.96 %

FP 22 7819 23 1388 (17.75 %) 22 (95.65 %) 940 (12.02 %) 22 (95.65 %) 32.27 %

Seabee 10318 24 1668 (16.16 %) 24 (100 %) 1027 (9.95 %) 24 (100 %) 38.42 %

Turkey Creek 7868 24 1416 (17.99 %) 24 (100 %) 853 (10.84 %) 24 (100 %) 39.75 %

Table 1: Performance comparison between the -Technique and the proposed RNN lter for dierent sites with 0.5m Z-coil EMI Data To illustrate the performance improvement acheived by the RNN false alarms lter, the Receiver Operating Curves (ROC) for the four sites under consideration are plotted as shown in Figures 3 and 4. Each (ROC) curve represents the relation between the probability of detection 6

and the probability of false alarms for a certain mine eld and a certain detector. In each gure, 3 ROC curves are plotted namely, ROC curve for the pure energy detector, ROC curve for the -Technique and ROC curve for the peoposed RNN detector. It can be noticed that the RNN detector has better performance than the -Technique and the pure energy detector. For example, in Figure 3b to obtain 10 % probability of false alarms, the probability of detection will be around 80 %, 90 % and 95 % for the pure energy detector, the -Technique and the RNN detector respectively. Similar improvements can be noticed from the other curves. ROC Curve for FP22 0.5m Z Coil 1

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Figure 4: ROC curves for 1 m Z coil data (a) SeaBee site (b) Turkey Creek site Figures 5 and 6 show the percentage of false alarms reduction of the -Technique and RNN 7

detector w.r. to energy detector. It is obvious from the gures that for a given probability of detection, the RNN detector gives higher percentage false alarms reduction than the -Technique. Notice also that for a certain probability of detection, there may be multiple values of percentage of false alarms reduction. The reason is that for some values of energy threshold, the probability of detection may be unchanged while the probability of false alarms may vary. We observe similar improvements for all the other sites, but we do not report all the curve in this paper because of space limitations. Percentage FA Reduction versus Probability of Detection for FP20 0.5m Z Coil

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Figure 5: False alarms reduction of -Technique and RNN w.r. to energy detector for 0.5 m Z coil data (a) FP 20 site (b) FP 22 site Percentage FA Reduction versus Probability of Detection for Seabee 1m Z Coil

Percentage FA Reduction versus Probability of Detection for Seabee 1m Z Coil

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Figure 6: False alarms reduction of -Technique and RNN w.r. to energy detector for 1 m Z coil data (a) SeaBee site (b) Turkey Creek site 8

From the previous table and gures, it is obvious that the proposed RNN detector can signi cantly reduce the false alarms during search in the mine eld with detection accuracy that is better than the -Technique and the pure energy detector.

4 Conclusions and further work In this paper we have proposed a random neural network model for mine detection and false alarm ltering (RNN false alarm lter). Pre-processing of the input data, using -Technique, before using the RNN proved to be vital for better performance. It is shown through extensive simulations that the proposed model is very eective in detecting mines and rejecting false alarms. The RNN lter is a robust non-parametric technique that is based on training on a limited calibration data on a certain mine eld. The lter shows very good performance for data extracted from a variety of geographic locations and recorded with dierent sensors, i.e, the network trained with limited data extracted from one site using a certain EMI sensor, performs robustly at all other sites, with data obtained using another sensor. Although the training phase of the RNN is computationally costly, its testing phase is a real time very fast operation since the calculation of the output from the trained network depends only on the basic mathematical operations (no non-linear function calculations needed). This makes the RNN candidate for hardware implementation using microcontrollers or FPGAs. The o-line training is conducted only once with the aid of a personal computer and after the network is trained, the weights and other parameters can be coded into hardware. Thus the RNN based detector, as a battery operated decision device, can be used as a processing unit for the data obtained from the handheld EMI sensor. We can expect better performance if functional approximation of probability density functions (PDFs) [17] on non-mine and mine classes was applied. By this technique, the PDFs can be represented as polynomials and after that a suitable RNN with prede ned parameters, extracted from the coecients of the polynomials, can be constructed based on the theorems in [8]. The resulting RNN can be trained on patterns from the eld to give a more precise non parametric estimation to the PDFs of the mines and non-mines patterns.

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