Thermal Infrared Identification of Buried Landmines - CiteSeerX

Preprint Proc. SPIE Vol. 5794, Det. and Rem. Techn. for Mines and Minelike Targets X, Orlando FL, USA, Mar. 2005 1

Thermal Infrared Identification of Buried Landmines Thành Trung Nguyen1 , Dinh Nho Hào1 , Paula Lopez2 , Frank Cremer3 and Hichem Sahli1,3 1

Vrije Universiteit Brussel, ETRO Department, Pleinlaan 2, B-1050 Brussel, Belgium Universidad de Santiago de Compostela, Departamento de Electrónica y Computación, E-15782, Santiago de Compostela, Spain 3 Interuniversity Micro Electronics Centre, ETRO Department, Pleinlaan 2, B-1050 Brussel, Belgium 2

ABSTRACT This paper deals with a three-dimensional thermal model for landmine detection problems and an inverse problem for reconstructing the physical parameters of buried objects. Moreover, solutions are given for the estimation of the soil thermal diffusivity and meteorological parameters, needed for solving the inverse problem. The paper describes the main fundamental principles of thermal modelling for buried object identification and illustrates the results on data acquired from a real minefield, together with qualitative and quantitative results illustrating the validity of the model. Keywords: Thermal model, infrared technique, heat equations, inverse problems

1. INTRODUCTION During the last decade, research in landmines detection received a growing interest in finding structured and reliable solutions for solving the problem of the detection and subsequent removal of mines and unexploded ordonnance. Several ’new’ technologies, based on different physical principles, e.g. electromagnetic detection, vapor/builk detection, and optoelectronic imaging, have been investigated. Among the used technologies, dynamic thermal infrared (IR) technique seems to be effective to detect non-metallic landmines for which metal detectors cannot be applied14. Dynamic thermal IR technique has been used since the 80s for nondestructive evaluation3 with the wellknown paper of K. Watson25 for geologic applications of IR images. The use of thermal IR technique is based on the thermal radiation contrast of objects, with respect to their background. All objects at temperatures greater than absolute zero emit electromagnatic radiations at all wavelengths in which the radiations corresponding to the wavelengths from 3 µm to 100 µm is referred to be the thermal IR radiations. The magnitude of spectral radiations of an object depends on its temperature. The total energy radiated by a blackbody is given by Stefan-Boltzmann’s formula9, 13, 26. According to Wien’s displacement Law 9, almost all objects on the earth emit electromagnatic radiation mainly in the range of longwave infrared (8 µm to 14 µm). The difference of thermal characteristics, i.e., heat capacity c, thermal conductivity k and thermal diffusivity α, between buried objects and the background is the base of using IR technique for detecting landmines. Indeed, the presence of a buried object affects the heat conduction inside the soil during natural heating conditions. Consequently, the temperature of the soil surface, above the buried object, may be different from that of the surrounding area. This temperature contrast is measured by an IR imaging system. In the case of surface laid landmines, the thermal radiation, measured by the IR camera, may be different for the landmines and the surrounding. This high contrast is due to the difference in radiant characteristics (emissivity, absorptivity and Email addresses: {ntthanh, dnhohao, hsahli, fcremer}@etro.vub.ac.be, [email protected] Copyright 2005 Society of Photo-Optical instrumentaion Engineers This paper was published in Proc. of SPIE 5794 and is made available as an electronic preprint with the permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.


reflectivity) between the landmines and the background soil. From the measured images, one can easily detect the presence of abnormal objects. However, to detect and identify buried objects, a thorough analysis of the thermal behaviour of the surveyed area, by considering the thermal parameters of both background and buried objects, is needed. This is achieved in two steps. • The first step, referred to as forward thermal model, aims at modelling the temporal behaviour of the soil temperature, under natural heating conditions, with the presence of buried landmines. This is based on the solution of an initial boundary value problem for a three-dimensional heat transfer equation. Although heat transfer processes in solids have been analysed thoroughly6, 20, only few thermal models have been proposed for landmine detection problems. Among the existing models, I. K. Sendur and B. A. Baertlein21 proposed a three-dimensional thermal model for homogeneous soil containing a buried anti-tank mine modelled as TNT object. The authors considered smooth and Gaussian distributed rough surfaces, and proposed a radiometric model for thermal signatures released from the soil surface and from other sources. The considered radiometric model, instead of using apparent temperature, allows approximating the real temperature of the surface from measured IR images. The same radiometric model has been also studied by P. Pregowski et al.19. A three-dimensional model, for homogeneous soil containing buried landmines and considering both the explosive (TNT) and the casing of the landmine, has been introduced by K. Khanafer and K. Vafai11. In their paper, the authors analysed the effect of the casing on the temporal behaviour of the soil temperature distribution taking into account rough soil surfaces and diurnal cycle. These models helped understanding the effect of buried landmines on the soil temperature. However, their validity, by comparing the simulated and experimental results, have not been studied. This has been done in our early works14, 16, where we proposed and validated, using indoor and outdoor experiments, a 3D thermal model for homogeneous soil and buried landmines characterised by their TNT and considering flat soil surface. A 2D thermal model has been also investigated by S. Sjokvist et al.22–24. • The second step, referred to as inverse problem setting for landmine detection, consists of using these thermal models for the detection and identification of the buried objects, i.e., estimate the position, (c1 , c2 ), the sectional radius r, the height h, the depth d, and the thermal diffusivity αt of the buried object (see figure 1). Here, we are faced with an ill-posed inverse problem of determining the location (position, depth and height), size and the physical properties of buried objects from diurnal thermal observations on the soil surface. Although inverse problems in heat conduction have been intensively studied1, 2, 4, 5, 8, 12, to our knowledge, only our previous work, P. Lopez et al.14, 15, applied them for landmine detection. In14, 15 the depth (of burial) and the thermal diffusivity, of a buried object have been estimated, when its location in the soil volume is known. Moreover, in the later work, we considered known the soil characteristics and the incoming heat flux parameters. To apply thermal modelling for detecting landmines in a real minefield7, several parameters, such as specific heat, thermal conductivity, thermal diffusivity, emissivity, solar absorptivity, etc. have to be estimated. Moreover, one should take into account the relationship between the real soil surface temperature and the ’intensity’ of the acquired IR images. This relationship is not straightforward, indeed, the measured thermal ’intensity’ is affected by the solar radiation, the emission of the air, as well as the soil roughness. Finally, the ill-posedness of the inverse problem may cause large errors, in the estimated parameters, with small errors in the input data. All these aspects are considered in this paper. The paper is organised as follows. In Section 2, we first state mathematically the full process of detecting landmines using thermal modelling. This model requires, among other parameters, the soil thermal diffusivity, the soil thermal emissivity, the solar absorption, the sky absorption, and the convective heat transfer coefficients. These parameters depend on the local soil characteristics and the meteorological (weather) conditions during the thermal observations. From measured soil temperatures at different locations and depths, in Section 3, we present a method of estimating the soil thermal diffusivity and the derivation of the soil temperature (in the vertical direction) proportionally to the heat flux on the soil surface. The other parameters such as solar absorptivity, the soil emissivity, etc. are estimated as described in Section 4 using weather data. The model given by Lopez14


is used for the estimation of the thermal diffusivity of the buried objects and their depths of burial. In Section 5, we present some results of the inverse problems for the estimation of the physical parameters of soil and buried objects, using data acquired in a real minefield within the United Nations Buffer Zone in Cyprus. The operated stand-off thermal IR survey system and the anomaly detection algorithm are described in Cremer et al.7

2. MATHEMATICAL FORMULATION In this section, we describe the mathematical equations governing the heat transfer process inside the soil and the buried objects, as well as the necessary boundary conditions. Moreover, the formulation of the inverse problems for buried object detection is given.

2.1. Governing equation Consider a rectangular parallelepiped domain Ω within the three-dimensional soil volume containing a possibly buried target (see figure 1). We denote by Γ1 and Γ2 the top and bottom surfaces of the domain, respectively. Γ1 , being the soil surface and the only portion of the volume accessible for measurements. We assume that the soil and the target are isotropic solids with specific heat c(x, y, z) (J/(kg K)), density ρ(x, y, z) (kg/m3 ) and thermal conductivity k(x, y, z) (W/(m K)). We also assume that the soil moisture content variation is negligible. Then, the temperature distribution, T (x, y, z, t), (x, y, z, t) ∈ Ω × [0, te ], of the considered volume (the soil and the possibly buried object) under natural heating conditions, satisfies the following partial differential equation µ ¶ µ ¶ µ ¶ ∂T ∂ ∂T ∂ ∂T ∂ ∂T cρ = k + k + k . (1) ∂t ∂x ∂x ∂y ∂y ∂z ∂z In the case of homogeneous or piecewise homogeneous solid, equation (1) has the form ∂T = α(x, y, z)∆T, ∂t

(2)

where α = k/(cρ) (m2 /s) is the thermal diffusivity of the solid.

2.2. Initial and boundary conditions In order to solve (1) or (2), one should know the initial distribution of temperature (T (x, y, z, t = 0)), as well as the boundary conditions, e.g., the incoming or outgoing heat flows on the boundary, ∂Ω, of the domain. These conditions are described as follows 1. The initial condition expresses the soil temperature at the initial time instant t = 0 T (x, y, z, t = 0) = g(x, y, z), ∀(x, y, z) ∈ Ω.

(3)

2. The sufficient deep depth condition, assumes that the soil temperature at sufficient deep depth, z0 , does not depend on the diurnal heat transfer process. T (x, y, z0 , t) = T∞ , ∀(x, y, z0 , t) ∈ Γ2 × [0, te ].

(4)

From our experimental observations, z0 is set to 50 cm (see section 5). 3. The surface heat flux, establishes the incoming heat flux, qnet , through the portion of the soil volume accessible for measurements, i.e. the air-soil interface (soil surface) Γ1 −k

∂T = qnet for (x, y, z) ∈ Γ1 , ∂z

The estimation of qnet will be considered in detail in Section 4.

(5)

Preprint Proc. SPIE Vol. 5794, Det. and Rem. Techn. for Mines and Minelike Targets X, Orlando FL, USA, Mar. 2005 4 y Γ 1 c2 d r x c

1

Ω 1

h

Γ 2 z

Figure 1. Model of the soil domain containing a buried object

4. The domain is assumed to insulate the outgoing as well as the incoming heat flows from surrounding areas of the soil, i.e., there is no heat flowing in the horizontal direction on the boundary of Ω. This hypothesis is reasonable if the soil is homogeneous and the considered domain is large enough so that we can neglect the effect of the buried objects to the boundary of the domain. In this case, the heat balance takes place on the surrounding boundary of the domain during the analysis period. This condition is given by ∂T = 0 for (x, y, z) ∈ ∂Ω \ (Γ1 ∪ Γ2 ), ∂~n

(6)

where ~n is the outward unit normal vector of ∂Ω. Equation (1) or (2) with the initial and boundary conditions (3)–(6) define the forward thermal model for landmine detection.

2.3. Inverse problems for buried landmines detection As mentioned before, the aim of the inverse problem setting for landmine detection is to detect (locate) the presence of an abnormal object and characterise it as being mine or not, i.e. estimate it’s physical thermal characteristics. In this problem, we aim at reconstructing the internal characteristics of the soil based on measured temperatures on the surface. This problem is stated as follows. Let αs being the thermal diffusivity of the bare soil, and suppose the existence of a buried object with thermal diffusivity αt occupying a sub-domain Ω1 of Ω. Moreover, the sub-domain is assumed to be a cylinder with sectional center (c1 , c2 ) in the horizontal plane, height h, sectional radius r and is located at depth d (see figure 1). The soil temperature distribution T (x, y, z, t) is described by the boundary value problem (2)–(6) with piecewise constant thermal diffusivity ( αt in Ω1 α= (7) αs in Ω \ Ω1 The aim of the inverse problem is to reconstruct the parameters αt , r, h, d, c1 , c2 from measured soil surface temperatures, T (x, y, z = 0, t) = θ(x, y, t), at t = t1 , t2 , . . . , tn . This problem can be written in the form of an optimization problem: tn Z 1X 2 |T (x, y, 0, t) − θ(x, y, t)| dxdy, (8) min αt ,r,h,d,c1 ,c2 2 t=t 1

Γ1

where T (x, y, z, t) is the solution of the forward model (2)–(6) with piecewise constant thermal diffusivity α. In section 5 we will consider numerical methods for solving the forward problem (2)–(6) and inverse problem (8).


3. SOIL THERMAL DIFFUSIVITY ESTIMATION In order to model the heat transfer process in a given soil, it is necessary to know its specific heat, density, thermal conductivity and thermal diffusivity characteristics. Although the characteristics of different materials, including soil types, have been given in the literature, they can not be used directly. Indeed, soil characteristics are dependent on the location and moisture content of the soil. In this section, we propose a simple method to estimate the soil diffusivity from soil temperature profiles measured by thermocouples placed at different depths. We consider a domain of homogeneous soil without buried objects. In this domain, the three-dimensional equation (1), with the given temperature on the domain boundary, can be simplified to a one-dimensional problem describing the soil diurnal temperature distribution in depth:  ∂T ∂2T   ∂t = α ∂x2 , a ≤ x ≤ b, 0 ≤ t ≤ te ,  T (x, 0) = g(x), a ≤ x ≤ b, (9) T (a, t) = fa (t), 0 ≤ t ≤ te ,    T (b, t) = fb (t), 0 ≤ t ≤ te , where α is a constant (the soil is considered homogeneous), and T = T (x, t; α) is the soil temperature at depth x and time t. The functions fa (t) and fb (t) are temperature profiles at given depths a and b, respectively, while g(x) is the initial distribution of the soil temperature in depth. Consistent estimates of the coefficient α is obtained by least squares minimization, i.e., find the coefficient α such that the difference between the simulated solution of (9) and the measured data is minimal: 1 min α>0 2

Zte [T (c, t; α) − fc (t)]2 dt,

(10)

0

where T (x, t; α) is the solution of the Dirichlet problem (9). For which, (i) fa and fb are approximated from the measured data, (ii) the initial condition g is approximated by interpolating the measured temperatures at different depths at time t = 0, and (iii) c, (a < c < b), a depth for which soil temperature profile fc is measured. For solving the inverse problem (10), we refer the reader to the paper of Kravaris and Seinfeld12 and the references therein for different numerical methods. For the forward model (9) we used the well-known Crank-Nicolson scheme17 for heat equations. Figure 2 illustrates the obtained results using data acquired during minefield trials7. Figure 2 (left) shows the measured soil temperature profiles at different depths. Figure 2 (right) shows the error evolution when solving equation (9); the minimum is obtained with α = 5.3 × 10−7 (m2 /s). Figure 2 (middle) shows a good agreement between the measured and the simulated (using the estimated soil thermal diffusivity) soil temperature. Measured soil temperature and simulation at diffusivity = 5.3e−007(m2/s)

Soil temperature at different depths 20

2 measured at 3cm simulated at 3cm measured at 8cm simulated at 8cm measured at 18cm simulated at 18cm

14 12

10

5

1.8 1.6 1.4

10 Error (0C)

Soil temperature (oC)

15 Soil temperature (0C)

Evolution of error of soil diffusivity estimation

16 Surface 3cm 8cm 18cm 48cm

8

1.2 1 0.8

6

0.6 4 0

0.4 2

−5

0

5

10

15

20 Time (hour)

25

30

35

40

0

0.2 0

5

10

15

20 25 Time (hour)

30

35

40

0

1

2

3

4

5

6

Soil diffusivity (m2/s)

7

8

9

10 −7

x 10

Figure 2. Soil thermal diffusivity estimation; Left: Measured soil temperature profile; Middle: Measured soil temperatures versus simulated soil temperatures; Right: Error Evolution


4. BOUNDARY PARAMETERS ESTIMATION As mentioned in Section 2.2, the boundary conditions (3)-(5) are estimated using soil temperature data at different depths and locations (see Figure 4 (left)), and meteorological data, namely, air temperature, solar irradiance, sky irradiance, and wind speed (Figure 3), measured near the suspected minefield during the thermal IR image acquisition7. Air temperature

Solar and sky irradiance on the earth surface

288

4.5 Solar irradiance Sky irradiance

600

286

4 3.5

Irradiance (W/m2)

282

280

Wind speed (m/s)

500

284 Air temperature (C)

Wind speed

700

400 300 200

3 2.5 2 1.5

278

100

276

0

274

−100

8

10

12

14

16 18 Time (hour)

20

22

24

1 0.5

8

10

12

14

16 18 Time (hour)

20

22

24

0

8

10

12

14

16 18 Time (hour)

20

22

24

Figure 3. Measured meteorological data by the weather station; Left: Air temperature; Middle: Solar and sky irradiances; Right: Wind speed

Assuming that the soil is homogeneous, the initial condition (3) could be approximated from the measured soil temperatures. Figure 4 (left), shows the approximated initial soil temperature for both linear and fourth order polynomial interpolations of the data of Figure 2 (left). The sufficient deep depth condition (4), can be estimated from the measured soil temperature at a depth where the temperature is invariant for a diurnal cycle, and it is not effected by the presence of buried objects. This condition is reasonable as we are dealing with the detection of shallowly buried objects. From Figure 2 (left) one can notice that the soil temperature at the depth of 48 cm is almost constant over time. The surface heat flux (5) can be approximated as follows11, 16, 21, 25 qnet (x, y, t) = qsun (x, y, t) + qsky (x, y, t) + qconv (x, y, t) − qemis (x, y, t),

(11)

where • qsun = ²sun Esun is the solar irradiance absorbed by the soil; ²sun is the solar absorption coefficient or solar absorptivity of the soil, and Esun (W/m2 ) the solar irradiance on the earth surface. In practice, Esun is either measured (see Figure 3(middle)) or approximated using equation (12)25 Esun (t) = S0 (1 − C)H(t),

(12)

with S0 = 1353(W/m2 ) the solar constant, C is a factor that accounts for the reduction in the solar irradiation due to cloud cover, and H(t) a local insolation function. In our approach, we use the measured solar irradiance. • qsky = ²sky Esky is the sky irradiance absorbed by the soil; ²sky is the sky absorption coefficient or sky absorptivity of the soil, and Esky (W/m2 ) the sky irradiance on the earth surface. Esky can be formulated by Stefan-Boltzmann’s law9, 21 4 Esky = σTsky , (13) with Tsky the sky temperature, and σ the Stefan-Boltzman constant (σ = 5.67 × 10−8 W/(m2 K4 )). The sky temperature can be approximated by21 √ Tsky = Tair (0.61 + 0.05 ω)0.25 ,


with ω the water vapour pressure in the atmosphere, expressed in mmHg, and Tair the air temperature. Combining the two above equations, we get: √ 4 4 Esky = σTair (0.61 + 0.05 ω) ≈ 0.61σTair . (14) The sky irradiance can also be measured as shown in Figure 3 (middle), from which, one can notice the correlation between the solar and sky irradiances. • qconv (W/m2 ) is the heat transfer, by convection, between the soil and the air. It refers to the transport of heat between the surface and the atmosphere by motion of the air. In 1701, Isaac Newton considered the convective process and suggested that the cooling would be such that13 dTs ∼ (Ts − Tair ). dt So the net heat flux by convection can be written as, qconv = h(Tair − Tsoil ), where h is the convective heat transfer coefficient; it depends on the wind speed. In practice, Kahle10 approximated it by qconv (x, y, t) = ρa cpa Cd (W (t) + 2)(Tair (t) − Tsoil (x, y, t)), (15) with ρa the density of the air, cpa the specific heat of the air, Cd the wind drag coefficient (normally chosen to be 0.002) and W (t) the wind speed. • qemis (W/m2 ) is the thermal emittance of the soil. It corresponds to the thermal radiation emitted by the soil: 4 qemis = ²soil σTsoil , (16) where ²soil is the thermal emissivity of the soil, and Tsoil the temperature at the soil surface. From Kirchoff’s Law9, the thermal emissivity of the soil is equal to the sky absorptivity ²sky . In summary, equation (11) can be rewritten as: qnet (x, y, t) = ²sun Esun (t) + ²conv (W (t) + 2)(Tair (t) − Tsoil (x, y, t)) 4 + ²sky Esky (t) − ²soil σ Tsoil (x, y, t)

(17)

with, Tair (t), Esun (t), Esky (t), and W (t) measured, with the help of a weather station, as illustrated in Figure 3. To estimate the the boundary condition (5), using equation (17), one should estimate the unknown coefficients ²sun , ²sky , ²conv and ²soil . This is done by solving the following minimization problem min

²sun ,²sky ,²conv ,²soil

1 2

Zte |− 0

−

∂T ²sun ²conv (t) − Esun (t) − (W (t) + 2)(Tair (t) − Tsoil (x, y, t)) ∂z k k

(18)

²soil ²sky 4 Esky (t) + σ Tsoil (x, y, t)|2 dt. k k

where − ∂T ∂z (t) is an approximation of the heat flux in the bare soil area, calculated as the derivative of the solution of the problem (9) using the estimated soil diffusivity (equation (10)). Note that, from equation (5), − ∂T ∂z (t) = qnet (t)/k, k being the unknown soil conductivity, so in (18), we estimate ²sun /k, ²sky /k, ²conv /k and ²soil /k instead of the coefficients ²sun , ²sky , ²conv and ²soil . Figure 4 (right) shows the approximation of the surface heat flux. Solving the above minimization problem, we obtain ²sun /k = 0.4574 (m K/W), ²sky /k = 0.5416 (m K/W), ²soil /k = 0.6725 (m K/W), ²conv /k = 1.8634 (m K/W).

Preprint Proc. SPIE Vol. 5794, Det. and Rem. Techn. for Mines and Minelike Targets X, Orlando FL, USA, Mar. 2005 8 Approximation of initial condition

Incoming heat flux on the soil surface

18

150 4th poly. inter. Linear inter. Data

16

From simulation With estimated parameters 100

12

Heat flux (W/m2)

Soil temperature (0C)

14

10 8 6

50

0

−50

4 −100 2 0

0

0.1

0.2

0.3

0.4

−150

0.5

8

10

12

14

Depth (m)

16 18 Time (hour)

20

22

24

Figure 4. Initial and boundary conditions estimation; Left: initial temperature condition; Right: Approximated surface heat flux Detected anomaly

An IR image at 0:5

An IR image at 9:58

5

5

5

10

10

10

15

15

15

20

20

20

25

25

25

30

30

30

35

35

35

40

40 5

10

15

20

25

30

35

40 5

10

15

20

25

30

35

5

10

15

20

25

30

35

Figure 5. IR images of a suspected target; Left: Detected anomaly; Middle: Image acquired at 0:05 , Right: Image acquired at 9:58

5. NUMERICAL RESULTS AND COMPARISON TO EXPERIMENTS In this section, we present some numerical results of the forward model (2)–(6) and the inverse problem (8), using data acquired in a real minefield within the United Nations Buffer Zone in Cyprus. The operated stand-off thermal IR survey system, the acquired data, and the image processing steps, are described in Cremer et al.7. However, to help the reader understanding the full process of diurnal thermal IR landmines detection using the developed system, we outline here after the main system components and data processing approaches. The system allows (i) a stand-off observation of hazardous area, (ii) acquiring thermal IR data during a diurnal cycle, (iii) measuring meteorological data (solar irradiance, sky irradiance, air temperature, etc.), and soil temperatures at different depths, (iv) estimating the soil thermal diffusivity as described in Section 3, and the meteorological coefficients, ²sun , ²sky , ²conv and ²soil , as described in Section 4, (v) temporally calibrating and co-registering the IR images, (vi) detecting anomalies, i.e. locating and searching for targets which are thermally and spectrally distinct from their surroundings; Figure 5 shows two IR images of a suspected target and the results of the anomaly detection procedure, and (vii) finally estimating the depth of burial and thermal diffusivity of the detected anomaly. In the following we illustrate the forward model (2)–(6) and the inverse problem (8), using the data of Figure 2(left), Figure 3 and Figure 5, the estimated soil diffusivity α = 5.3 × 10−7 (m2 /s) (see Section 3), the initial condition as approximated in Figure 4 (left), and the meteorological coefficients ²sun /k = 0.4574 (m K/W), ²sky /k = 0.5416 (m K/W), ²soil /k = 0.6725 (m K/W), ²conv /k = 1.8634 (m K/W), as estimated in Section 4.


The forward thermal model (2)–(6), has been solved using a simple explicit finite difference scheme as described in Ozisik18, page 420. The numerical result of the simulation for the NR22C1, anti-personnel plastic, mine buried at 1 cm deep is plotted in Figure 6. In this simulation we assumed the mine as a TNT object with thermal diffusivity of 1.139 × 10−7 (m2 /s). Figure 6 (left) depicts the simulated soil surface temperatures above the mine and in the surrounding area, and the measured soil surface temperature. The figure shows a good agreement between the simulation and the measured soil surface temperature. Figure 6 (right) shows the thermal contrast between the soil temperature above the mine and the surrounding area. As it can be seen, during sun shine, the soil above the mine was hotter than the surrounding area and it became cooler during the night. Moreover, the highest thermal contrast took place around noon. This result can be explained from the fact that, when the sun was shining, there was an incoming heat flux through the soil surface. In this case, the mine blocked the heat flow from the surface due to its small thermal conductivity or thermal diffusivity. Consequently, the soil above the mine became hotter than the surrounding area. During the night, there was an outgoing heat flow from the bottom of the soil volume. The mine blocked the heat flow resulting in cooler temperature above the mine than the surrounding area. The same results have been obtained in the previous works of Sendur and Baertlein21, Khanafer and Vafai11 and Lopez et al.16. Evolution of soil temperature

Temperature contrast between mine and bare soil on the surface

20

2 Simulation at bare soil area Simulation on the top of mine Measured soil temperature

1.5

Temperature contrast (oC)

Temperature (oC)

15

10

5

1

0.5

0

−0.5

0 −1

−5

5

10

15

20 Time (hour)

25

30

35

−1.5

5

10

15

20 Time (hour)

25

30

35

Figure 6. Forward model; Left: Simulated and measured soil temperatures on the surface; Right: Thermal contrast

The quality of the acquired images has been analysed before solving the inverse problem. As it can be seen from Figure 5 (middle), Figure 5 (right), and the size of the detected anomaly of Figure 5 (left), the temporal co-registration is not perfect. This explains the irregular in shape of the measured contrast of Figure 7 (right). However, from Figure 7 (left), depicting the measured soil surface temperature versus the apparent thermal IR temperature, one can notice that the two temperatures follow the same behaviour with a small shift. Figure 7 (right) shows the simulated thermal contrast, considering that the suspected target is a NR22C1 mine buried at 3 cm, versus the measured thermal contrast. As it can be seen, during the night, with reasonable co-registrated images, the measured and simulated thermal contrasts are similar in shape. For solving the inverse problem, we used an early work14, 15 to estimate the depth of burial and the thermal diffusivity of the detected object of Figure 5. The inputs to the inverse problem are the acquired thermal IR images, and the spatial position (center) and radius of the object, estimated from the image of Figure 5 (left). Figure 8 illustrates the error evolution of the thermal diffusivity and depth of burial estimation, respectively. As it can be seen, the depth is estimated at 6 cm and thermal diffusivity 2 × 10−7 (m2 /s).

6. CONCLUSIONS In this paper, we presented the full process for landmine detection using thermal modelling. The difficulty in estimating physical and meteorological parameters of the soil has been solved. The forward model, using these estimated parameters, showed a good agreement with the measured data. The inverse problem has been

Preprint Proc. SPIE Vol. 5794, Det. and Rem. Techn. for Mines and Minelike Targets X, Orlando FL, USA, Mar. 2005 10 Measured real and apparent temperature

Thermal behaviour of the soil temperature measured by an IR camera

20

Thermal contrast on the soil surface

20

2

Real temperature Apparent temperature

Above the mine Bare soil

Simulated Measured 1.5

15

15

10

5

Thermal contrast (0C)



1 10

5

0.5

0

−0.5 0

0 −1

−5 5

10

15

20 Time (hour)

1

6

11

−5 5

10

15

20 Time (hour)

1

6

−1.5 5

11

10

15

20 Time (hour)

1

6

11

Figure 7. Image quality analysis; left: measured soil surface temperature versus the apparent thermal IR temperature, Middle: Apparent thermal IR behaviour; Right: Thermal IR contrast versus simulated contrast Evolution of the eror of thermal diffusivity estimation

Evolution of the eror of depth estimation

0.62

1.05 1

0.61 0.95 0.9

0.59

Error (0C)

Error (0C)

0.6

0.58

0.85 0.8 0.75 0.7

0.57

0.65 0.56 0.6 0.55

0

5

10 Iteration

15

20

0.55

0

5

10

15

Depth (cm)

Figure 8. Evolution of error of depth and thermal diffusivity estimation; Left: Error of diffusivity estimation; Right: Error of depth of burial estimation

solved using a the model presented in early works14–16, where the location and radius of the buried object are considered known using several anomaly detection procedures7, 15, 16 we developed. Future work consists in developing efficient numerical methods for solving the forward problem and considering the full inverse problem i.e. augmenting the estimation for both the physical parameters and the location of the buried objects.

ACKNOWLEDGEMENTS This work has been partly funded by the European Commision, under the CLEARFAST project IST-2000-25173. The authors would like to thank the other project partners, namely, TAMAM, RLS, and BACTEC. Furthermore we would like to thank the UN (UMAS, UNDP), the MACC and Armour Group for their support and for giving us the opportunity to perform the field trial in Cyprus.

REFERENCES 1. O. M. Alifanov. Inverse Heat Transfer Problems. Springer-Verlag, Berlin, Germany, 1994. 2. O. M. Alifanov, E. Artyukhin, and S. Rumyantsev. Extreme Methods for Solving Ill-posed Problems with Applications to Inverse Heat Transfer Problems. Begell House Publisher, New York, 1995.


3. D. L. Balageas, J. C. Krapez, and P. Ceilo. Pulsed photothermal modeling of layered materials. Journal of Applied Physis, 59(2):348–357, 1986. 4. J. Beck, B. Blackwell, and S. R. St-Clair, Jr. Inverse Heat Conduction. Ill-posed Problems. John Willey and Sons, New York, 1995. 5. H. D. Bui. Inverse Problems in the Mechanics of Materials: An Introduction. CRC Press, 1994. 6. H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Oxford University Press, Oxford, second edition, 1959. 7. F. Cremer, T. T. Nguyen, L. Yang, and H. Sahli. Stand-off thermal IR minefield survey, system concept and experimental results. In R. S. Harmon, J. T. Broach, and J. H. Holloway, Jr., editors, Proceedings of SPIE 5794, Detection and remediation technologies for mine and minelike targets X, 2005. 8. D. N. Hào. Methods for Inverse Heat Conduction Problems. Peter Lang, Frankfurt am Main, Bern, New York, Paris, 1998. 9. P. A. M. Jacobs. Thermal infrared characterization of ground targets and backgrounds. SPIE Optical Engineering Press, Bellingham (WA), USA, 1996. 10. A. B. Kahle. A simple thermal model of the earth’s surface for geologic mapping by remote sensing. Journal of Geophysical Research, 82:1673–1680, 1977. 11. K. Khanafer and K. Vafai. Thermal analysis of buried land mines over a diurnal cycle. IEEE Transactions on Geoscience and Remote Sensing, 40(2):461–473, February 2002. 12. C. Kravaris and J. H. Seinfeld. Identification of parameters in distributed parameter systems by regularization. SIAM Journal of Control and Optimization, 23(2):217–241, March 1985. 13. J. H. Lienhard IV and J. H. Lienhard V. A heat transfer textbook. Plogiston Press, Cambridge MA, third edition, 2004. 14. P. López. Detection of landmines from measured infrared images using thermal modelling of the soil. PhD thesis, University of Santiago de Compostela, 2003. 15. P. López, H. Sahli, D. L. Vilarino, and D. Cabello. Detection of pertubations in thermal IR signatures: an inverse problem for buried land mine detection. In A. L. Gyekenyesi and P. J. Shull, editors, Proc. of SPIE, vol. 5046, Nondestructive Evaluation and Health Monitoring of Aerospace Materials and Composites II, pages 242–252, Orlando (FL), USA, Apr. 2003. 16. P. López, L. Van Kempen, H. Sahli, and D. C. Ferrer. Improved thermal analysis of buried landmines. IEEE Transactions on Geoscience and Remote Sensing, 4(9):1965–1975, 2004. 17. G. I. Marchuk. Splitting and alternating direction methods. In P. G. Ciaglet and J. L. Lions, editors, Handbook of Numerical Mathematics, volume 1: Finite Difference Methods. Elsevier Science Publisher B.V., North-Holland, Amsterdam, The Netherlands, 1990. 18. M. N. Ozisik. Boundary value Problems of Heat Conduction. Dover Publication, INC, New York, USA, 1968. 19. P. Pregowski, W. Swiderski, W. T. Walczak, and B. Usowicz. Role of time and space variability of moisture and density of sand for thermal detection of buried objects - modeling and experiments. In D. H. LeMieux and J. R. Snell, Jr., editors, Proceeding of SPIE 3700, Thermosense XXI, pages 444–455, 1999. 20. A. A. Samarskii and P. N. Vabishchevich. Computational Heat Transfer, volume 1: Mathematical Modelling. John Wiley & Sons, Chichester, England, 1995. 21. I. K. Sendur and B. A. Baertlein. Numerical simulation of thermal signatures of buried mines over a diurnal cycle. In A. C. Dubey, J. F. Harvey, J. T. Broach, and R. E. Dugan, editors, Proceedings of SPIE 4038, Detection and Remediation Technologies for Mines and Minelike Targets V, pages 156–167, Aug 2000. 22. S. Sjökvist. Heat transfer modelling and simulation in order to predict thermal signatures - the case of buried land mines. PhD thesis, Linkopings university, SE-581 83 Linkopings, Sweden, 1999. 23. S. Sjökvist, R. Garcia-Padron, and D. Loyd. Heat transfer modelling of solar radiated soil, including moisture transfer. In Third Baltic Heat Transfer Conference, pages 707–714, Gdansk, Poland, 22-24 September 1999. IFFM Publishers, ISBN 8-3907-5269-7.


24. S. Sjökvist, M. Georgson, S. Ringberg, M. Uppsall, and D. Loyd. Thermal effects on solar radiated sand surfaces containing landmines - a heat transfer analysis. In Fifth international conference on advanced computational methods in heat transfer, pages 177–187, Cracow, Poland, 17-19 June 1998. Computational Mechanics Publications. 25. K. Watson. Geologic applications of thermal infared images. In Proceedings of the IEEE, volume 63, pages 128–137, 1975. 26. M. C. Wendl. Fundamental of heat transfer: Theory and application. Class note for ME 371, Washington University, 2003.