1
An abrupt change detection algorithm for buried landmines localization Delphine Potin, Philippe Vanheeghe, Senior Member IEEE, Emmanuel Duflos, Member IEEE , and Manuel Davy
Abstract Ground Penetrating Radars (GPRs) are very promising sensors for landmines detection as they are capable of detecting landmines with low metal contents. GPRs deliver so-called Bscan data which are, roughly, vertical slice images of the ground. However, due to the high dielectric permittivity contrast at the air-ground interface, a strong response is recorded at early time by GPRs. This response is the main component of the so-called clutter noise and it blurs the responses of landmines buried at shallow depths. The landmine detection task is therefore quite difficult. This paper proposes a new method for automated detection and localization of buried objects from Bscan records. A Support Vector Machine (SVM) algorithm for online abrupt change detection is implemented and proves to be efficient in detecting buried landmines from Bscan data. The proposed procedure performance is evaluated using simulated and real data.
Index Terms Ground Penetrating Radar, clutter reduction, landmines detection , novelty detection
I. I NTRODUCTION The global landmine crisis is one of the most pervasive problems facing today’s world. It is estimated that 45 to 50 million landmines are buried in the ground of at least 70 countries. Landmines reportedly maim or kill 20,000 civilians every year. Beyond the immediate dangers to life and limb, landmines impose a heavy economic burden on the mine-affected communities [1]. Eliminating landmines is thus a major issue, and it entirely depends on the ability of systems to detect buried landmines. The detection problem is made complicated by many landmines types and burying areas: roads, fields, buildings, forests and deserts. State-of-the-art systems include various sensors such as Ground Penetrating Radars (GPRs), infrared cameras, metal detectors, etc. In this paper, we focus on GPRs: they are very promising as they can detect plastic as well as very low metal contents landmines. There are two kinds of GPRs used in landmines detection D. Potin, ISEN - ERASM, 41 boulevard Vauban, 59046 Lille Cedex, (e-mail:
[email protected]) P. Vanheeghe, E.Duflos and M. Davy, LAGIS CNRS UMR 8146, Ecole Centrale de Lille, Cité scientifique BP48, 59651 Villeneuve d’Ascq Cedex (e-mail:
[email protected],
[email protected])
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applications : frequency stepped continuous wave (FSCW) radars and pulse radars [2]. FSCW radars emit stepped ratio frequency signals towards the ground and records the response. Pulse radars emit short duration electromagnetic pulses which propagate into the soil and reflect on the dielectric permittivity discontinuities. When recorded at a given location the recorded pulse radar response is an Ascan, which actually is the magnitude of the reflected wave with respect to time. Due to propagation time, waves reflected on an object arrive to the GPR with a time lag which is related1 to the distance between the object and the GPR. The image obtained by concatenating Ascans recorded along a survey line is called a Bscan. The horizontal axis of a Bscan corresponds to the GPR spatial location2 whereas the vertical axis corresponds to time (i.e., depth). A Bscan can be seen as an image of a vertical slice of the ground. Typical Ascan and Bscan recorded in the context of landmines detection are plotted in Fig. 1 and Fig. 2. This paper investigates landmines detection from pulse radar Bscans, as a step towards a multisensors detection system. Pulse radars, for humanitarian demining, have the ability to scan the ground from the surface to one meter depth, which is the required depth range. However, the emitted electromagnetic pulse strongly reflects at the airground interface. This results in a hindering high amplitude response which appears at the early time of the Ascan. This phenomenon is known as clutter, and makes difficult the detection of landmines from Ascans/Bscans. More specifically, many landmines are laid flush with the ground or buried at shallow depths (1-5 cm): their responses to the GPR emitted pulse overlap with clutter. Moreover their metallic contents can be very low, their responses are therefore much weaker than those coming from the air-ground interface resulting in a poor signal-to-noise ratio. As stated above, clutter is mainly caused by the air-ground interface response. To a lower extent, it is also created by antenna coupling problems and multiple reflections on the air-ground interface. 4
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Fig. 1.
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A typical Ascan record obtained by a GPR pulse radar.
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Fig. 2.
A Bscan image obtained by concatenating consecutive
Clutter is characterized by large amplitude oscillations at early
Ascans recorded along a survey line. Two typical landmine signa-
times. This Ascan is represented by a vertical dash line on the
tures (hyperbola) can be seen below the horizontal clutter stripes
Bscan of Fig. 2.
(see arrows).
Many detection algorithms based on different signal processing approaches have been developed to localize 1 The
wave arrival time lag is almost proportional to the buried object distance. The proportionality coefficient depends on the physical
parameters of the soil. 2 It
is assumed here that the GPR is moved along a straight line. The horizontal axis actually gives the distance covered by the GPR from its
initial position.
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landmines on Bscan data. Some approaches ([3],[4]) search for hyperbolas, which characterize the landmines responses on Bscans, so as to determine the presence of a landmine. In [3], the approach is based on fuzzy logic and neural networks whereas in [4], it is based on an adaptive approach using a least mean square algorithm for anomaly detection and polynomial fitting. Other detection algorithms require a GPR signals modeling. In [5], hidden Markov models are used to model the signal returns from landmines and backgrounds and estimate the likelihood that signal returns are due to landmines. A Support Vector Machine based on an inverse scattering procedure is used in [6] to estimate the position of a buried object. This approach requires a mathematical model of the electric field scattered by buried targets. Statistical signal processing techniques have also been used to localize buried landmines. In [7], the approach is based on the use of linear prediction in the frequency domain: GPR vector samples are modeled by a linear prediction model. Then, a constant false alarm rate technique together with the likelihood function of clutter samples are used to detect landmines. In [8], a landmine detection algorithm based on the principal components analysis is used. The method consists in distinguishing Bscans that contain objects from Bscans that do not, based on their maximum likelihood distances calculated in the subspace spanned by the principal components. In [9], a change detection method based on energy detection is used to localize buried landmines on Bscan data. After clutter reduction, changes are detected in the spatial and time direction in order to find the landmines horizontal positions and their response times. Changes in both directions are detected thanks to a sequential probability ratio test. In this paper, a new method based on abrupt changes detection is proposed in order to detect and localize landmines in Bscans. Abrupt changes detection is a difficult signal processing task. Strong theoretical results hold in the case of known statistical models of the data [10]. However, GPR data are difficult to model accurately since it consists in modeling the propagation of electromagnetic waves into an heterogenous soil. Model-based statistical techniques are therefore difficult to use in such a case. The core idea of our approach is to apply a nonparametric abrupt changes detection technique to Bscans, as follows: •
Step 1: abrupt changes are sought along the spatial (horizontal) Bscan axis.
•
Step 2: abrupt changes are sought along the time (vertical) axis. Of course, step 2 is only implemented in areas where horizontal abrupt changes have been detected. An important difficulty in step 2 is that clutter might cause abrupt changes, it has thus to be removed.
This paper is organized as follows. Section II presents the clutter reduction technique to be used in step 2. It consists of applying a digital high pass filter to GPR data. This filter is designed from a geometrical model of both clutter and landmine signatures in a Bscan. The online abrupt change detection algorithm is detailed in Section III. It is based on data comparison using a Support Vector Machine. Section IV describes the full landmines detection procedure. Simulations results on simulated and real data are finally given in Section V. II. C LUTTER REMOVAL METHOD The chosen clutter reduction method is based on the use of a two dimensional digital filter which is adapted to GPR data. This method is fully described in [11] and can be summarized as follows. (In this paragraph, clutter is 29th August 2005
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also referred to as noise and the buried object response is referred to as signal.) A. Clutter characterization in the frequency domain In a typical Bscan (see Fig. 3), the clutter appears as three horizontal bands. These bands have a very high contrast, i.e. they can be accurately modeled as a rectangle function. Let Bscans be defined as functions I(x, t) where x represents the spatial coordinate ranging from 0 to x1 and t the time coordinate ranging from 0 to T . Each clutter band on a Bscan can be modeled by a function Π(x, t) defined as follows: Π(x, t) = Π1 (x)Π2 (t) x ∈ [0, x1 ] Π2 (t) = 1 t ∈ [t1 , t2 ] where t1 and t2 are the time instants that delimit a x∈ / [0, x1 ] Π2 (t) = 0 t ∈ / [t1 , t2 ] 1 clutter band, see Fig. 4. In order to design a clutter removal filter, we map the data into the frequency domain.
Π (x) = 1 1 with Π (x) = 0
Each clutter band has the following 2D magnitude spectrum: |Π(νx , ν)| = x1 T sinc(πx1 νx ) sinc(πT ν)
(1)
where νx is the spatial frequency parameter, ν is the frequency and T is the width of a clutter band (T = t2 − t1 ). By considering that the main energy of such a function is located inside the two first lobes of the sinc functions, the clutter energy is located inside the subspace Sc (x1 , νmax ) defined by: ½ ¾ 2 Sc (x1 , νmax ) = (νx , ν) such that |νx | ∈ [0, ], |ν| < νmax x1 2 T
where νmax =
.
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Fig. 3.
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The Bscan of Fig. 2 before clutter reduction.
Fig. 4. Zoom of the Bscan of Fig. 3. t1 and t2 indicate the edges of the first clutter band.
B. Signal characterization in the frequency domain As opposed to clutter, a buried object appears as a hyperbola in Bscans. A landmine signature can therefore be modeled by a hyperbola. In the frequency domain, it is shown in [11] that the approximated magnitude spectrum of such a signal for frequency less than few GHz is given by: |Is (νx , ν)| w 2∆x sinc(π∆xνx )
(2)
where ∆x is equal to half the hyperbola width recorded on the Bscan. 29th August 2005
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C. Clutter removal in the frequency domain An important remark is that the magnitude of the signal spectrum is almost independent of ν at the considered 2 2 GPR signal frequencies and its main energy is localized inside the interval νx ∈ [− ∆x ; ∆x ]. In the spectral domain,
the signal (buried object response) bandwidth is much larger than the noise (clutter) bandwidth: for example, in the Bscan in Fig. 3, x1 = 1m and ∆x = 0.05cm, and the noise main energy is within a spatial frequency band of width 2 m−1 whereas the signal is within a band of width 40 m−1 . Hence, the spread of the noise spectrum along the νx axis is very small in comparison with the spread of the signal spectrum. By using a two dimensional digital high pass filter with a very sharp transition band along the νx frequencies axis the clutter can be reduced without degrading the signal, see Fig. 5. The signal being almost independent of ν for frequencies less than few GHz, the noise can be filtered out for all ν < νmax with νmax = 5 GHz. The denoising filter gain should therefore equal 0 inside Sc (1, 5 GHz) and equal 1 outside. The practical implementation of this filter requires specific developments, such as discretization, that are not reported here for the sake of brevity, see [11] for a full description. The result of applying this filter is shown in Fig. 6. It can be seen that the three clutter bands are effectively filtered out and that the hyperbolic signatures of the landmines are not distorted. 9
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Fig. 5.
Magnitude spectrum of the Bscan plotted in Fig. 2. A
logarithmic scale is applied on the magnitude spectrum.
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Fig. 6. The Bscan of Fig. 2 after clutter reduction. The landmine signatures are still visible.
This clutter reduction method is well adapted to GPR data. It reduces significantly clutter without distorting too much the landmine signatures. Moreover, its implementation is simple and its computational cost is low. The next section presents the abrupt change detection algorithm. Results obtained by combining clutter reduction and the abrupt change detector are presented in Section IV. III. O NLINE ABRUPT CHANGE DETECTION ALGORITHM Due to the significant variability of landmine signatures, it is quite difficult to implement model-based detection. Indeed an accurate and tractable GPR signals model is very hard to define since it requires accurate modeling of electromagnetic waves propagation into an heterogeneous soil. A natural model-free approach relies on the following remark: the landmine detection problem can be cast into an abrupt change detection problem in Bscans. The following subsection presents a model-free approach to abrupt change detection, initially introduced in [12] for time series segmentation and formulated here for Bscans landmine detection. 29th August 2005
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A. Model-free abrupt change detection The on-line abrupt changes detection problem can be stated as follows [12]. Assume that data xa in a space X are extracted online from a signal. In our case the word signal refers to either the horizontal axis or the vertical axis of Bscans, see Section IV. Considering an analysis point xa where a is some index, and two data subsets: x1 = {xa−m1 , ..., xa−1 } and x2 = {xa , ..., xa+m2 −1 }. Let D(x1 , x2 ) be a dissimilarity measure between the sets x1 and x2 . The abrupt change detection problem can be cast as follows ([12], [10]): •
Hypothesis H0 : D(x1 , x2 ) ≤ η (No abrupt change occurs)
•
Hypothesis H1 : D(x1 , x2 ) > η (An abrupt change occurs)
where η is a threshold that tunes the sensibilty/robustness tradeoff, as in every detection problem. The detection performance is thus highly dependent on the dissimilarity measure D(·, ·) selected. In this section, the dissimilarity measure D(·, ·) is built from the so-called level sets of x1 and x2 . The ν-Support Vector (ν-SV) level set estimation technique can be used to estimate the density support of an unknown pdf. B. ν-SV level set estimation Support vector level set estimation, also referred to as novelty detection and single class classification is a specific SVM algorithm. Assuming that a set of training vectors x = {x1 , ..., xm } is available in an input space denoted X , the aim of SV level set estimation is to find a region Rx of X where most of the data xi , i = 1, . . . , m lie. The region Rx must also have minimum volume. A good insight about the theory of level set estimation can be found in [13] and [14]. In the SV level set approach, the estimation of Rx is equivalently addressed by estimating a decision function fx (x) such that fx (x) > 0 if x ∈ Rx and fx (x) < 0 otherwise. In order to present the SV approach, a mapping φ from X to a so-called feature space F is defined: φ
: χ → x
→
F φ(x)
(3)
It is assumed that F is endowed with a dot product h· , ·i in F. This dot product, together with the mapping φ(·) define a kernel k(., .) over X × X by: ∀(xi , xj ) ∈ X × X , k(xi , xj ) = hφ(xi ), φ(xj )i
(4)
Furthermore, we assume that k(., .) is normalized such that for any x in X , k(x, x) = 1. Hence for all x ∈ X , kφ(x)k2 = hφ(x), φ(x)i = k(x, x) = 1. In other words, the mapped input space φ(X ) is a subset of the hypersphere S with radius one centered at the origin of F, denoted O. The training vectors are mapped in F and lie in S as shown in Fig. 7. The SV approach to single-class classification consists of positioning a hyperplane W in F such that the origin O is located on one side of W whereas most of the training vectors are located on the opposite side. The equation of a hyperplane in F is given by hw, xi − b = 0 where w and x are elements of F and b ≥ 0.
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Fig. 7.
The training vectors mapped by φ lie on a hypersphere of radius 1 in feature space F.
Choosing W is equivalent to choosing the corresponding decision function fx (x) = hw, xi − b with w ∈ F and b ≥ 0. fx (x) defines the segment of the hypersphere in F where fx (x) is positive, that is to say the level set of x. We do not require that all training vectors lie in the segment of the hypersphere S where hw, xi − b ≥ 0, because some of the training vectors might be outliers that are not representative of the data considered, [13]. In standard SV level set estimation, it is shown that the above geometrical problem in F can be formulated as the following optimization problem:
m
1 X 1 ξi + b max − kwk2 − w,ξ,b 2 νm i=1
(5)
subject to hw, φ(xi )i ≥ b − ξi and ξi ≥ 0 where ν is a positive parameter (0 < ν ≤ 1) that tunes the possible amount of outliers and ξi are the so-called slack variables, which allow some outliers. This constrained optimization problem admits the following dual formulation in terms of Lagrange multipliers [13]:
m
min α,b
m
1 XX αi αj hφ(xi ), φ(xj )i 2 i=1 j=1
subject to 0 ≤ αi ≤
1 νm
for i = 1, ..., m and
(6)
Pm i=1
αi = 1
The hyperplane decision function can be written as: fX (x) =
m X
αi hφ(x), φ(xi )i − b =
i=1
m X
αi k(x, xi ) − b
(7)
i=1
The amount of outliers in the training set x is controlled by the parameter ν. It is shown in [13] that ν is an upper bound on the fraction of outliers in the training set x. In practice, we do not explicitly define the mapping φ; we define instead the kernel k(·, ·). Provided k(·, ·) is positive definite (i.e., it verifies Mercer conditions [13]), it implicitly defines a mapping φ, a feature space F and its dot product. Here we consider the Gaussian kernel with parameter σ: k(xi , xj ) = exp(−
kxi − xj k ) 2σ 2
(8)
The following subsection builts a change detection algorithm on SV level set estimation. 29th August 2005
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C. Online kernel change detection algorithm Consider, at analysis point xa , the two training sets x1 = {xa−m1 , ..., xa−1 } and x2 = {xa , ..., xa+m2 −1 } of size m1 and m2 . Then, train a SV level set estimator from the training set x1 and train independently another SV level set estimator from the training set x2 . Therefore, two optimal hyperplanes W1 and W2 parametered respectively by w1 , b1 and w2 , b2 are derived. Going back to X , W1 and W2 define the region Rx1 and Rx2 . If an abrupt change occurs at index a, it is expected that the region Rx1 and Rx2 do not strongly overlap. In order to measure the overlap of Rx1 and Rx2 , a contrast measure I(a) is computed at each index a . I(a) reflects the dissimilarity between the sets x1 and x2 via a dissimilarity measure computed between Rx1 and Rx2 , see [15].
Fig. 8.
Feature space representation of the regions Rx1 and Rx2 . They are represented as segments of hypersphere Σ1 and Σ2 . The index
I(a) is computed as darc (c1 , c2 )/(r1 + r2 ) where darc is the arc distance on the hypersphere.
In feature space F, the hyperplane W1 defines a segment of the hypersphere S denoted Σ1 , and similarly, the hyperplane W2 defines Σ2 , see Fig. 8. I(a) is a measure of the distance in F between Σ1 and Σ2 , computed as the arc distance between the center of Σ1 and Σ2 , divided by the sum of the radii of Σ1 and Σ2 . The contrast measure I(a) is computed in feature space, but it informs about the similarity of Rx1 and Rx2 in X . It is computed thanks to the kernel k(., .) described in III-B, see [15]. Abrupt changes are finally detected whenever the index I(a) is larger than a threshold ηa . This means that x1 and x2 are significantly different as proved in [12]. Once I(a) is computed, the training sets x1 and x2 are updated at analysis point a + 1. An important remark is that the SV level set estimator training is trained twice at each analysis point xa , as level set estimation is performed over both x1 and x2 training sets. A non-computationally efficient procedure would consist in recomputing the parameters (wi , bi ) (i=1,2) from scratch using the optimization problem of equation (6). Instead, the parameters w1 , b1 and w2 , b2 are also updated using the online ν-SV novelty detection technique presented in [16]. This makes the computational cost of the algorithm low. The following section presents the full landmine detection and localization method.
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IV. L ANDMINES DETECTION METHOD As explained in Section II clutter appears in Bscans as horizontal stripes and a buried object appear as an hyperbolic spreading function resulting from the imperfect directivity of the GPR antenna, see Fig. 2. Hence, the two hyperbola branches resulting from a buried object are much more energetic than the background (response of the soil without buried objects). It is thus quite natural to adopt an abrupt change framework when moving along the horizontal or vertical axis of a Bscan. The landmines detection method proposed consists of detecting all abrupt changes in Bscan data, along both the time and spatial dimensions. The following step consists of finding those coming from the responses of buried landmines. Informations relative to the depth and the position of landmines can therefore be extracted. More precisely the two steps of our procedure are: • Step 1: Spatial abrupt changes are searched in order to detect the possible horizontal landmines position. Clutter reduction is not necessary here as it is constant along the horizontal Bscan axis. • Step 2: The time abrupt changes are searched in order to detect the buried objects response times. Clutter has to be removed beforehand in order to avoid detecting clutter bands instead of real landmines. The precise description of these steps is given in Subsections IV-A and IV-B below. A. Description of step 1 Data used in the abrupt change detection algorithm to form the training sets are extracted from a Bscan as follows. Each vector xa is made of one Ascan. At each horizontal position l (thus a ≡ l), two training sets x1 and x2 made of respectively m1 and m2 Ascans are built (typical values are m1 = m2 = 5, see Subsection V-A). Note that the abrupt changes detection algorithm can be implemented online along the spatial coordinates l. (In other words, it is not necessary to have the entire Bscan to search the abrupt changes.) The contrast measure I1 (l) is computed as explained in Subsection III-C. Spatial abrupt changes are detected whenever the index I1 (l) is larger than a threshold ηl which is determined heuristically (this means that the two training sets differ significantly and that there might be a buried object or a landmine). Once I1 (l) is computed, the training sets x1 and x2 are updated at spatial coordinate l + 1 by incorporating the next Ascan in x2 , removing the oldest Ascan from x1 and so forth. A bloc diagram of Step 1 is represented in Fig. 9. A buried object is characterized by two near abrupt changes which indicate the boundaries of the object in a Bscan and thus their horizontal positions. It is important to notice that step 2 is only applied if at least one buried object is detected on a Bscan at step 1. B. Description of step 2 Let consider a sub-Bscan made of consecutive Ascans taken from a Bscan containing the response of one buried object detected at step 1. The sub-Bscan is first preprocessed by the clutter reduction method described in Section II. Then, a time-varying gain (TVG) is applied to the filtered Bscan in order to compensate the spreading losses and the losses due to the propagation through a lossy soil, see [17].
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Fig. 9.
Bloc diagram of Step 1
Data made of one Bscan line are extracted from the preprocessed sub-Bscan. At each time instant t (thus a ≡ t), two training sets x1 and x2 made of respectively m1 and m2 Bscan lines are built (typical values are m1 = m2 = 5, see Subsection V-A). The contrast measure I2 (t) is computed by the abrupt change detection algorithm. Time abrupt changes are detected whenever the index I2 (t) is larger than a threshold ηt which is determined heuristically. Once I2 (t) is computed, the two training sets are updated at time instant t + 1. Numerous abrupt changes are likely to be detected due to the multiple reflections between buried objects and GPR antenna and also due to clutter reduction residues. Therefore, it can be difficult to determine automatically the response time of the landmines. This is the reason why the contrast measure I2 (t) is replaced by I˜2 (t) in order to introduce a weight on each abrupt change. At each time instant t, I˜2 (t) is expressed as the product of the contrast measure I2 (t) by the weight function Im (t) as follows: I˜2 (t) = Im (t)I2 (t)
(9)
The weight function Im (t) is built as follows. The preprocessed sub-Bscan is normalized and a thresholding on the magnitude is applied. (Thresholding is often used to suppress noise in situations where the signal to noise ratio is large, i.e. after a good clutter reduction.) All magnitudes below the chosen threshold are set to zero. Then the first order time derivative of each Ascan of a Bscan is computed. The weight function, denoted Im (t), is expressed as the mean over all these time derivatives. It indicates how the magnitude of the signal varies with respect to time. Hence, by multiplying I2 (t) by Im (t) at each time instant, this leads in enhancing significantly the magnitude of the abrupt changes due to landmines in comparison with those coming from clutter residuals. A bloc diagram of 29th August 2005
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Step 2 is represented in Fig. 10.
Fig. 10.
Bloc diagram of Step 2
C. Tuning the algorithm The tuning of m1 and m2 is generally imposed by the dynamics of the signal. Small m1 and m2 make the algorithm detect frequent, small changes, whereas large m1 and m2 enable the detection of long-term changes. In the landmine detection framework, the emitted pulse is of short duration (few nanoseconds) therefore we need to detect small changes in the return signal. Here, we choose m1 = m2 = 5. The kernel parameter σ influences the location of the vectors on the hypersphere S. σ should be chosen greater than one. The rate of outliers ν is tuned according to detection requirements: for values about 0.2 to 0.8, the influence of outliers is limited, which reduces the rate of false alarms. Finally, there is no automatic tuning for the thresholds ηl and ηt . An analysis of simulation results on a Bscan containing a landmine response is used to select ηl and ηt . For more details on the tuning of the algorithm parameters, see [12].
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V. S IMULATIONS A. Simulated data The method described previously is applied to the simulated Bscan shown in Fig. 11. The split step 2D method presented in [18] is used to generate this Bscan. An electromagnetic (EM) pulse, modeled by a gaussian function, is sent at a height of 11cm above an homogeneous ground in which two objects have been placed. The central frequency of the pulse spectrum is 900MHz. To apply the split step method the relative dielectric permittivity (εr ) and the quality factor (Q) of the soil and objects must be known. The coupling effects between antennas that arise for bistatic GPR are not taken into account. The simulation parameters are given in table I. TABLE I S IMULATION PARAMETERS
Object 1
Object 2
soil
(εr , Q)
(5,500)
(5,500)
(9,100)
horizontal positions
{0.6,0.9}
{2.1,2.4}
-
depth
8cm
3cm
-
response time tr
2.33ns
1.33ns
0.73ns
As the objects positions and their physical parameters are known, their response times can be computed by: tr =
2 hr 2 z0 εrs + c c
where c is the EM wave propagation speed in the air, hr the radar height, z0 the object depth and εrs the soil relative dielectric permittivity. Hence the real horizontal positions and response times of the buried objects are known and can be compared with the one found by applying the landmines detection method proposed in Section IV. Step 1: the detection of the objects horizontal positions is carried out. Data made of 1 Ascan are extracted from the Bscan. The training sets sizes are m1 = m2 = 5. The Gaussian kernel parameter σ equals 10 and the amount of outliers which is tuned by ν equals 0.5. Fig. 12 displays the index I1 (l) which is computed by applying the abrupt changes detection algorithm. By choosing heuristically, the threshold ηl = 0.5, the horizontal abrupt changes due to the returns from the two objects are correctly detected, see Fig. 12. The first object is situated between the two first abrupt changes detected, at horizontal positions l = {0.63, ..., 0.85} and the second object is situated between the two next abrupt changes detected, at horizontal positions l = {2.1, ..., 2.37} of the Bscan. Step 2: the responses time of the two detected objects are searched. The interest is given to the detection of the response time of the object situated at horizontal positions l = {0.63, ..., 0.85}. As a consequence the algorithm is not applied to the entire Bscan but to the sub-Bscan which is made of the Ascans data recorded at positions l = {0, ..., 1.4}. This sub-bscan is preprocessed as explained in Subsection IV-B, see Fig. 13. The data extracted from the preprocessed sub-Bscan are made of 1 line of this sub-Bscan. The training sets sizes are m1 = m2 = 5.
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Fig. 11. Simulated Bscan containing the responses of two buried
Fig. 12.
objects. One is situated at horizontal positions {0.6,0.9} and buried
buried objects are detected. One is situated between horizontal
at 8cm from the air-ground interface. The other is situated at
positions l =
horizontal positions {2.1,2.4} and buried at 3cm.
l = 2.1 and l = 2.37.
0.63 and l = 0.85 and the other one between
The Gaussian kernel parameter is σ = 10 and the amount of outliers is tuned by ν = 0.5. It can be seen in Fig. 14 that all the abrupt changes occurring in time are correctly identified. However it is almost impossible to detect −9
0
x 10
0.9
Time (s)
2
0.8
4
0.7
6
0.6
8
0.5
10
0.4
12
0.3 0.2
14
0.1
16
0 0
0.2
0.4
0.6
0.8
1
1.2
2
1.4
Fig. 13.
Preprocessed sub-Bscan containing the response of the
object detected at horizontal positions l = {0.63, ..., 0.85}.
4
6
8
10
Time (s)
Spatial coordinates (m)
12
14
16 −9
x 10
Fig. 14. Normalized contrast measure I2 (t) for the sub-Bscan of Fig. 13.
automatically the one coming from the object. This is the reason why a new index I˜2 (t) has been built in order to add a weight on each abrupt change. Fig. 15 displays the index I˜2 (t) with ηt = 0.7, the abrupt change detected is the one due to the returns of the object. Hence the response time is determined: tr = 2.4ns. The real buried object response time is tr = 2.33ns this leads to an error on the depth of 3.5mm which is acceptable. The same procedure is applied to the preprocessed sub-Bscan displayed in Fig. 16 to determine the time response of the object situated at lateral positions l = {2.1, ..., 2.37}. As shown in Fig. 17 the peak of maximum amplitude is detecting at time instant tr = 1.32ns and it corresponds to the time response of this object which is theoretically equal to 1.33ns. The error on depth is of 0.5mm and thus can be neglected. The proposed detection method is efficient to detect the response times and the horizontal positions of buried objects on simulated Bscan. The method can now be tested on real data recorded in the frame of landmines detection.
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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.5
1
1.5
Fig. 15.
2 −8
Time (s)
x 10
Normalized contrast measure I˜2 (t) for the sub-Bscan of Fig. 13.
−9
0
x 10
1 0.9
2
0.8 4
0.7 6
Time (s)
0.6 8
0.5
10
0.4
12
0.3
14
0.2 0.1
16 1.6
1.8
2
2.2
2.4
2.6
0 0
2.8
0.2
0.4
0.6
Fig. 16.
0.8
1
1.2
1.4
1.6
Time (s)
Spatial coordinates (m)
Preprocessed sub-Bscan containing the response of the
object detected at horizontal positions l = {2.1, ..., 2.37}.
1.8 −8
x 10
Fig. 17. Normalized contrast measure I˜2 (t) for the sub-Bscan of Fig. 16.
B. Real data The landmines detection method is applied to the real Bscan shown in Fig. 18. It results from the recording of a GPR moved along a survey line above an earthy soil in which two MAUS1 landmines of metallic content were buried. One was buried at a depth of 5 cm and the other one was laid down on the ground surface. The pulse GPR used operates at 1GHz. 8
−9
0
x 10
7 2
Time (s)
6 4
5
6
4 3
8
2 10
1 12 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0
0.8
0.1
Fig. 18.
Bscan recorded above an earthy soil. Two MAUS1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Spatial coordinates (m)
Spatial coordinates (m)
Fig. 19.
Contrast measure I1 (l) for the Bscan of Fig. 18. Two
landmines responses are recorded. One is coming from a MAUS1
buried objects are detected. One is situated between horizontal
landmine buried at a depth of 5 cm (left arrow) and the other one
positions l =
from a MAUS1 landmine laid down on the ground surface (right
l = 0.54 and l = 0.66.
0.15 and l = 0.25 and the other one between
arrow).
The parameters for the abrupt changes detection algorithm are the same than for step 1 of Section V-A. Fig. 19 29th August 2005
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displays the contrast measure I1 (l) with a threshold ηl = 3, the horizontal abrupt changes due to the returns from the two mines are correctly detected. The first mine is situated at horizontal positions l = {0.15, ..., 0.25} and the second mine is situated at horizontal positions l = {0.54, ..., 0.66} of the Bscan. The Bscan is divided into two sub-Bscans which are both preprocessed. Each sub-Bscan contains the response of a landmine, see respectively Fig. 20 and Fig. 22. The abrupt change detection algorithm, with the same parameters than for step 2 of Section V-A, is applied to each sub-Bscan independently and a contrast measure I˜2 (t) is computed for each of them. Results are displayed in Fig. 21 and Fig. 23. −9
0
1
x 10
0.9 0.8
2
0.7 4
Time (s)
0.6 0.5
6
0.4 8
0.3 0.2
10
0.1 12 0
0.05
0.1
0.15
0.2
0.25
0.3
0 0
0.35
0.2
0.4
Fig. 20.
0.6
0.8
1
1.2
Preprocessed sub-Bscan containing the response of the
landmine detected at horizontal positions l = {0.15, ..., 0.25}.
Fig. 21.
1.4 −8
x 10
Time (s)
Spatial coordinates (m)
Normalized contrast measure I˜2 (t) for the sub-Bscan
of Fig. 20. The time response tr of the landmine is detected at 3.25ns.
−9
0
x 10
1 0.9
2
0.8 0.7
4
Time (s)
0.6 6
0.5 0.4
8
0.3 0.2
10
0.1 12 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0 0
0.75
Fig. 22.
Preprocessed sub-Bscan containing the response of the
landmine detected at horizontal positions l = {0.54, ..., 0.66}.
0.2
0.4
0.6
0.8
1
1.2
Time (s)
Spatial coordinates (m)
Fig. 23.
1.4 −8
x 10
Normalized contrast measure I˜2 (t) for the sub-Bscan
of Fig. 22. The time response tr of the landmine is detected at 2.35ns.
As it can be seen on the Bscan displayed in Fig. 20, there is residual clutter. However the abrupt changes detected using the new index I˜2 (t) with a threshold ηt = 0.7, corresponds to the landmine. Its time response equals tr = 3.25ns, see Fig. 21. In Fig. 22, multiple reflections between the radar antennas and the landmine laid on the ground are recorded. The response time of the landmine is however well detected and is equal to tr = 2.35ns, see Fig. 23. The proposed detection method is now tested on the Bscan displayed in Fig. 24. It results from the recording of a GPR moved along a survey line above an earthy soil in which an AUPS landmine of very low metal content was buried at a depth of 1 cm and a MAUS1 one of metal content was buried at the same depth.
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−9
0
x 10
5 4.5
2
4 3.5
4
Time (s)
3 6
2.5 2
8
1.5 1
10
0.5 12 0
0.1
0.2
0.3
0.4
0.5
0.6
0 0
0.7
0.1
Fig. 24.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Spatial coordinates (m)
Spacial coordinates (m)
Bscan recorded above an earthy soil. The responses
Fig. 25.
Contrast measure I1 (l) for the Bscan of Fig. 24. Two
coming from an AUPS landmine (left arrow) and from a MAUS1
buried objects are detected. One is situated between horizontal
landmine (right arrow) buried both at 1cm are recorded.
positions l = 0.08 and l =
0.55 and the other one between
l = 0.3 and l = 0.65.
Fig. 25 displays the index I1 (l), the horizontal abrupt changes due to the returns from the two mines are correctly detected. The first mine is situated at horizontal positions l = {0.08, ..., 0.55} and the second mine is situated at horizontal positions l = {0.3, ..., 0.65} of the Bscan. The Bscan is then preprocessed and divided into two subimages each of them containing the response of a landmine. The abrupt change detection algorithm is then applied to each sub-image and the contrast measure I˜2 (t) is computed at each time. 1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2 0.1
0.1 0 0
0.2
0.4
0.6
0.8
Time (s)
Fig. 26.
1
1.2
0 0
1.4 −8
x 10
Normalized contrast measure I˜2 (t) for the AUPS
Fig. 27.
0.2
0.4
0.6 0.8 Time (s)
1
1.2
1.4 −8
x 10
Normalized contrast measure I˜2 (t) for the MAUS1
landmine. The time response tr of the landmine is detected at
landmine. The time response tr of the landmine is detected at
3.7ns.
3.8ns
As shown in Fig. 26, the time response of the AUPS landmine is correctly detected and equals tr = 3.7ns. The time response of the MAUS1 landmine is also correctly determined: tr = 3.8ns, see Fig. 27. C. Performances analysis of the landmines detection method The performances of our landmines detection method are studied in terms of detection probability and false alarm probability with the help of Receiver-Operating Characteristic (ROC) curves. For this, a set of real Bscan data that have been collected by a bench arc is used. The bench allows scanning, line by line in the abscisse (l) direction, of a 1 × 1.5 − m area of the ground with a 2-cm step in both directions. That is, an amount of Nl = 50 by Ny = 75 Ascans for the scanned area. By concatenating all the Ascans in the l direction, we obtain a set of Ny = 75 Bscan data. The laying configuration of the landmines is shown in Fig. 28. 29th August 2005
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Five MAUS1 landmines and one AUPS landmine have been buried at different depths in an agricultural soil without any potential other objects such as twigs or rocks.
Fig. 28.
Laying configurations of the landmines.
For each Bscan, we apply Step 1 of our detection method. A buried object is characterized by two near abrupt changes which indicate the boundaries of the object in a Bscan and thus their horizontal positions. For each detected horizontal position, if it is a theoretical position of a landmine, the detection is true, otherwise it is considered as a false alarm. Then, the probability of detection and the probability of false alarm are computed for different values of the threshold ηl (ηl ∈ [3, 8]). The corresponding ROC curve is plotted in Fig. 29. For ηl = 3, the probability of detection is maximum and is equal to 0.8 while the probability of false alarm is equal to 0.25. Hence, the horizontal positions of the buried landmines are not all detected. Indeed, most of the horizontal positions of the AUPS landmine are not detected. This can be explained by the fact that this landmine has a very low metal content and that its response on a Bscan is not characterized by a hyperbola but by a thin horizontal stripe (see Fig. 24). Hence, few abrupt changes due to this landmine are likely to occur in the set of Bscans data. 1 0.9
Detection probability
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.05
0.1
0.15
0.2
False alarm probability
Fig. 29.
ROC curve for Step 1.
Then, for each Bscan of Step 1 where buried landmines have been detected we apply Step 2 of our landmines detection method. After clutter reduction, each of these Bscans is split into two sub-Bscans so as to find the response times of the landmines. For each sub-Bscan, made of the Ascans recorded at positions l = [0, 0.5], abrupt changes 29th August 2005
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in the time direction are searched. A buried object is characterized by two near abrupt changes in the time direction which are relative to the response times of the top and bottom of the object. Hence, for each detected response time, if it corresponds to a theoretical response time of a landmine, the detection is true, otherwise it is considered as a false alarm. Then, the probability of detection and the probability of false alarm are computed for different values of the threshold ηt (ηt ∈ [0, 12]). The corresponding ROC curve is plotted in Fig. 30. For ηt = 0, the probability of detection is maximum and is equal to 0.99 while the probability of false alarm is equal to 0.19. Finally, the same method is applied to each sub-Bscan, made of the Ascans recorded at positions l = [0.5, 1]. The corresponding ROC curve is plotted in Fig. 31. For ηt = 0, the probability of detection is maximum and is equal to 0.95 while the probability of false alarm is equal to 0.07. It can be seen that the probability of false alarm is 1
1
0.9
0.9 0.8
0.7
Detection probability
Detection probability
0.8
0.6 0.5 0.4 0.3 0.2
0.6 0.5 0.4 0.3 0.2
0.1 0 0
0.7
0.1
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0
0.18
0.01
0.02
False alarm probability
Fig. 30.
ROC curve for Step 2 for landmines whose horizontal
positions are inside [0, 0.5].
0.03
0.04
0.05
0.06
0.07
False alarm probability
Fig. 31.
ROC curve for Step 2 for landmines whose horizontal
positions are inside [0.5, 1].
greater for the landmines buried in area 1 (l = [0, 0.5],∀y) than for the one situated in area 2 (l = [0.5, 1],∀y). This can be explained by the fact that in area 1 the three landmines are buried at greater depths than the ones situated in area 2. Hence, their responses are more attenuated and might even be sometimes less energetic than the ones from clutter residues. Moreover, in area 1 there is an AUPS landmine whose signature is not an hyperbola but a thin horizontal band. The digital filter we use for clutter reduction is built in order to filter the horizontal stripes that represent the clutter in a Bscan. As a consequence, a part of this landmine response is filtered. VI. C ONCLUSION The abrupt change detection algorithm is a very promising tool in the frame of landmines detection. The different simulation results on simulated and real data show its abilities to detect automatically the horizontal positions and the time responses of buried objects whose signatures are hyperbolic. It has been shown thanks to the simulations that this algorithm is able to detect landmines buried at different depths and whose metal content can be low. However its performances are related to the efficiency of the clutter reduction method used as the signal to noise ratio must be large. The digital filter used herein for the clutter reduction is efficient as it reduces significantly the clutter without bringing distortions to the hyperbolic signatures of the buried objects. The advantage of the proposed landmine detection method on others ([3]-[9]), is that it does not require a physical or a statistical model of a landmine signal. Moreover this method is robust since the SV level set estimators used in order to build the contrast measure I(a) allows outliers in the training sets, see Subsection III-B. The disadvantage 29th August 2005
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of our approach is that buried objects are detected but no information on their nature is given. Other sensors such as metal detectors and infrared cameras can help to discriminate the detected objects. Multisensor fusion methods for landmines detection, such as the ones proposed in ([19], [20]), can then be used. The performances of our landmines detection method have been evaluated thanks to the computation of ROC curves on a set of real Bscan data. This study shows the good potential of our detection method. We are currently working at collecting simulated data as well as real data, for different laying configurations of the landmines, in order to deepen the performances study of the proposed landmines detection method. ACKNOWLEDGMENT The authors would like to thank the reviewers for their comments and suggestions to improve the quality of this paper. The authors are grateful to the Fondation Norbert Ségard for its financial contribution. R EFERENCES [1] Adopt-A-Minefield, “Global landmines crises,” www.landmines.org, Tech. Rep., 2005. [2] D. J. Daniels, “Surface - penetrating radar,” Institution of Electrical Engineers, 1996. [3] P. D. Gader, J. M. Keller, and B. Nelson, “Recognition technology for the detection of buried landmines,” IEEE trans. on Fuzzy Systems, vol. 9, no. 1, pp. 31–43, Feb 2001. [4] Q. Zhu and L. M. Collins, “Application of feature extraction methods for landmine detection using the wichmann/niitek ground penetrating radar,” IEEE trans. on Geoscience and Remote Sensing, vol. 43, no. 1, pp. 81–85, Jan 2005. [5] P. D. Gader, M. Mystkowski, and Y. Zhao, “Landmine detection with ground penetrating radar using hidden markov models,” IEEE trans. on Geoscience and Remote Sensing, vol. 39, pp. 1231–1244, jun 2001. [6] E. Bermani, A. Boni, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE trans. on Geoscience and Remote Sensing, vol. 41, no. 4, pp. 927–931, Apr 2003. [7] K. C. HO and P. D. Gader, “A linear prediction landmine detection algorithm for hand held ground penetrating radar,” IEEE trans. on Geoscience and Remote Sensing, vol. 40, no. 6, pp. 1374–1384, Jun 2002. [8] S. Yu, K. Mehra, and T. R. Witten, “Automatic mine detection based on ground penetrating radar,” Proc. SPIE, vol. 3710, pp. 961–972, Apr 1999. [9] X. Xu, E. L. Miller, C. M. Rappaport, and G. D. Sower, “Statistical method to detect subsurface objects using array ground-penetrating radar data,” IEEE trans. on Geoscience and Remote Sensing, vol. 40, no. 4, pp. 963–976, April 2002. [10] M. Basseville and I. Nikiforov, Detection of Abrupt Changes - Theory and Application. Prentice-Hall, 1993. [11] P. Vanheeghe, E. Duflos, and D. Potin, “Landmines ground penetrating radar signal enhancement by digital filtering,” Submitted to IEEE trans. on Geoscience and Remote Sensing, Jan 2005. [12] F. Desobry and M. Davy, “An online kernel change detection algorithm,” IEEE trans. Sig. Proc., 2005, to be published. [13] A. Smola and B. Schölkopf, “Learning with kernels,” MIT press, 2002. [14] S. Mika, K. S. Müller, G. Rätsch, K. Tsuda, and B. Schölkopf, “An introduction to kernel-based learning algorithms,” IEEE transactions on Neural Networks, vol. 12, no. 2, Mar. 2001. [15] F. Desobry and M. Davy, “Dissimilarity measures in feature space,” IEEE ICASSP Montreal Canada, 2004. [16] A. Gretton and F. Desobry, “Online one-class nu-svm, an application to signal segmentation,” IEEE ICASSP, Hong-Kong, China, Apr. 2003. [17] N. Milisavljevic, “Analyse et fusion par la méthode des fonctions de croyances et données multi-sensorielles pour la détection de mines antipersonnel,” PhD thesis, Ecole Nationale Supérieure des Télécommunications, 2001. [18] A. Bitri and G. Grandjean, “Frequency-wavenumber modeling and migration of 2d gpr data in moderately heterogenous dispersive media,” Geophysics, vol. 46, pp. 287–301, 1998.
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[19] S. Perrin, E. Duflos, P. Vanheeghe, and A. Bibaut, “Multisensor fusion in the frame of evidence theory for landmines detection,” IEEE trans. on Systems, Man, and cybernetics, vol. 34, no. 4, pp. 485–498, Nov 2004. [20] N. Milisavljevic and I. Bloch, “Sensor fusion in anti-personnel mine detection using a two-level belief function model,” IEEE transactions on systems, man, and cybernetics-PART C: applocations and reviews, vol. 33, no. 2, pp. 269–283, May 2003.
Delphine Potin was born in Liévin, France on September 12, 1979. She received the engineer degree from the Institut Supérieur d’Electronique du Nord (ISEN), Lille, France, in 2002 and the M.Sc. degree from the University of Manchester Institute of Science and Technology, Manchester, England, in 2002. She is currently working toward the Ph.D. degree. Her current research activity deals with personnel landmines detection.
Philippe Vanheeghe (M’92-SM’97) was born in France on July 20, 1956. He received the M.S. degree in data processing, the Diploma of Advanced Study in data processing, the Ph.D. degree, and the Habilitation à Diriger des Recherches (HDR) from the University of Lille, Lille, France, in 1981, 1982, 1984, and 1996, respectively. Currently, he is a Professor at the Ecole Centrale de Lille, Lille, France. He was an Assistant Professor at Institut Supérieur d’Electronique du Nord, Lille, France, and was promoted to Head of the Signals and Systems Department of the same institution in 1990. He is the Head of the French CNRS laboratory "Laboratoire d’Automatique, Génie Informatique et Signal," (LAGISUMRCNRS). His research activities include multisensor management, signal processing, signals, and systems modeling. He is a coauthor with Prof. Duflos of several papers about guidance law modeling, multisensor management systems with application to radar sensor management, and personnel landmines detection. Prof. Vanheeghe has been a Member of the International Program Committee (IPC) of several international symposiums (IEEE, IMACS), and has acted as a session organizer for many international conferences.
Emmanuel Duflos (M’00) was born in Amiens, France, on June 20, 1968. He received the engineer degree from the Institut Supérieur d’Electronique du Nord (ISEN), Lille, France, in 1991, the Diploma of Advanced Study in automatic control and signal processing from the University of Paris XI, Orsay, France, in 1992, the Ph.D. degree in engineer sciences from the Université de Toulon et du Var, France, in 1995, and the Habilitation à Diriger des Recherches (HDR) from the University of Lille I, Lille, France, in 2003. Currently, he is a Professor with Ecole Centrale de Lille, Laboratoire d’Automatique, Génie Informatique et Signal, Villeneuve d’Ascq Cedex, France, after eight years at ISEN. His current research activity deals with multisensor systems from signal analysis for data fusion to multisensor management in moving multitarget environment. He is coauthor with Prof. Vanheeghe of several papers about guidance law modeling, multisensor management systems with application to radar sensor management, and personnel landmines detection. Dr. Duflos is a of member the French CNRS laboratory "Laboratoire dŠAutomatique, Genie Informatique et Signal," (LAGIS UMR CNRS).
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Manuel Davy Manuel Davy was born in Caen, France in 1972. He graduated in Engineering in 1996 at Ecole Centrale de Nantes and he obtained his Ph.D. in Signal Processing at the University of Nantes in 2000. He was a research associate at the University of Cambridge from 2000 to 2002, and he is currently a full time researcher at the French National Research Center (CNRS) in the LAGIS laboratory located in Lille, France. His research interests are Signal Processing, Bayesian statistics, Machine Learning and audio signals.
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