1.5.1. Sensors

For this research, we used two hyperspectral imaging sensors. The first was a Specim ImSpector V9 (see Figure 2), a hyperspectral prism-grating-prism imaging spectrograph [37] which has a spectral range of 430–900 nm, a spectral resolution of 7 nm, sampling 5 nm, and 95 channels (product specifications). The second was a Cubert UHD-185 snapshot camera (see Figure 3), with a spectral range of 450–950 nm, spectral resolution of 8 nm, 125 channels, sampling at 4 nm, and spatial resolution of 1000 × 1000 pixels for panchromatic or 50 × 50 pixels for spectral (product specifications). The third sensor was a point measuring FieldSpec3 Spectroradiometer, from Analytical Spectral Devices, Inc., Boulder, CO, USA (ASD), ranging from 350 to 2500 nm, resolution from 3 to 10 nm, and 512 channels (product specifications); which was used for point measurements of targets and materials

**Figure 2.** Hyperspectral push-broom sensor provides real hyperspectral data, while complex processing is needed to produce a calibrated hyperspectral cube: (**a**) Hyperspectral line scanner; (**b**) data are collected in scan lines, which need parametric geocoding; and (**c**) hyperspectral cube needed calibration.

**Figure 3.** (**a**) Hyperspectral snapshot camera UHD-185; (**b**) panchromatic image of the scene (1000 × 1000 pixels); and (**c**) hyperspectral cube obtained by sharpening real hyperspectral recording of 50 × 50 pixels with 1000 × 1000 panchromatic pixels.

#### 1.5.2. Ground-Based and Aerial Platforms

We have previously used the hyperspectral line scanner V9 to study minefields, landmines, and unexploded ordnances, initially through a ground-based mechanical scanner on a gantry [9,18,38]. We have used the V9 on several aerial platforms, such as the helicopters Mi-8c [39] and Bell-206. Note that the V9 was also used onboard the helicopter Mi-8 for detection of ship-sourced oil pollution on the sea [40].

Since 2012, we have applied the true spectral scanner V9 on UAVs, along with the pan-sharpening snapshot imaging scanner UHD-185 [17,41]. The helicopter Mi-8 platform was skipped in this research, as the spatial resolution was too low for the sake of target detection (due to blurring). Besides this primary purpose, the same mechanical scanner with V9 has been applied for archeological research [42] and in vineyards [43].

#### 1.5.3. Portable Carry-on and Handheld Hyperspectral Cameras

Portable carry-on (or handheld) hyperspectral cameras are novel technological devices, one appearing around 2015–2018 and subsequently disappearing (Headwall Hyperspec® SNAPSHOT VNIR, Headwall Photonics, Inc., Bolton, MA, USA), while the second appeared in 2020 (Specim IQ). The Hyperspec® SNAPSHOT VNIR Sensor can quickly render a high-resolution hyperspectral scene at distances of 1.5 km in the VNIR spectral range (380–1000 nm; Headwall 2014). This makes it an excellent sensor for military hyperspectral reconnaissance. In 2017, the authors asked Headwall to offer this sensor; however, the answer was that it is not in production.

Specim IQ is a portable carry-on hyperspectral camera that contains the features needed for hyperspectral data capturing, data processing, and visualization of results. It has a wavelength band of 400–1000 nm, 204 spectral bands, an image resolution of

512 × 512 pixels, spectral resolution of 7 nm, and 12-bit data output. A full field of view (FOV) is 31 × 31 degrees; at 1 m, it covers 0.55 × 0.55 m. It is equipped with WiFi, GPS, and a 32 GB SD memory card. This camera can serve as an excellent tool for collecting hyperspectral data about explosive targets, landmines, unexploded ordnances, cluster munitions, improvised explosive devices, and neighborhood terrain.

#### **2. Materials and Methods**

After the war in 1991–1995, Croatia had become contaminated with minefields, scattered landmines, and unexploded ordnances, cluster munitions, and other explosive remnants of war. When we proposed to apply airborne multi-sensor minefield detection in 2001 [44], the reaction was prompt and productive [45,46]. Our interest in the detection of unexploded ordnances (UXOs) was initiated after an unplanned explosion in 2011 at the ammunition depot at Padjene, Croatia, and the survey of UXOs was included in the project TIRAMISU [18,38,41]. Fifteen different kinds of scattered UXO samples have been measured by V9 in imaging mode. Hyperspectral cubes have been produced and Johnson parameters calculated for each type [47]. The UXO samples appear in different conditions (e.g., intact, damaged, burned, covered by rust, covered by soil, original paint), orientation, and on similar soil types. This set of true hyperspectral cubes is our source for further research on UXOs. While radiance data were collected, we converted them into reflectance using the atmospheric correction QUAC (Quick Atmospheric Correction, ENVI).

We measured several other UXOs with the imaging hyperspectral sensor V9; this is also a set of true hyperspectral data, Figures 4–9. The mean values of measured reflectance of UXOs are shown at Figure 10. The conditions of measuring were controlled, Figures 11 and 12. Several landmines and one plastic object were measured using the point measuring spectroradiometer ASD. This data set provides only one value of reflectance for each wavelength, Figures 13–17. Both sets are used in the current article.

**Figure 4.** (**a**) Spectralon (on the right side) and UXO targets (artillery shell, bullet, and mortar mine); (**b**) The geometry of the measured data of Figure 4a are corrected by interpolation, with the new GRD being 0.945 mm.

**Figure 5.** Artillery shell (**a**) photography by handheld camera; (**b**) color-visualized hyperspectral cube (red = 650 nm, green = 550 nm, blue = 450 nm). The ground resolving distance (GRD) is 0.945 mm.

**Figure 6.** Bullet: (**a**) photography; and (**b**) color-visualized hyperspectral cube (red = 650 nm, green = 550 nm, blue = 450 nm). The ground resolving distance (GRD) is 0.945 mm.

**Figure 7.** Mortar mine: (**a**) photography; and (**b**) color-visualized hyperspectral cube (red = 650 nm, green = 550 nm, blue = 450 nm). The ground resolving distance (GRD) is 0.945 mm.

**Figure 8.** Cluster munition: (**a**) photography; and (**b**) color-visualized hyperspectral cube (red = 650 nm, green = 550 nm, blue = 450 nm). The ground resolving distance (GRD) is 0.945 mm.

**Figure 9.** UXO: (**a**) photography; and (**b**) color-visualized hyperspectral cube (red = 650 nm, green = 550 nm, blue = 450 nm). The ground resolving distance (GRD) is 0.945 mm.

**Figure 10.** Mean spectra of five UXO targets. Legend: AS—artillery shell, B—bullet, CM—cluster munition, MM—mortar mine, and UXO\_X—UXO of unknown type.

**Figure 11.** Irradiance counts were measured in the morning and the afternoon, using the UHD-185 imaging sensor onboard the UAV. This is the raw, uncalibrated Sun irradiance. The deep minimum of the irradiance (e.g., ~760 nm) must be corrected by interpolating irradiances at lower and higher wavelengths.

**Figure 12.** Absolute (calibrated) spectral irradiance, measured in the test area when hyperspectral data acquisition was carried out with the UAV.

The main obstacle was to provide hyperspectral cubes of the terrain ground surface, which should have pixel area smaller than the area of the considered UXO and landmines. The solution could be to use hyperspectral imaging of the minefields, which has been done using the V9 and UHD-185, onboard a Bell-206 helicopter or UAVs [17]. In the current article, we use only the terrain ground surface hyperspectral cubes collected by UHD-185 onboard a UAV.

#### *2.1. The True Hyperspectral Data Cubes of UXO on the Ground*

UXO samples have been measured by V9 in imaging mode, using the first, small version of the mechanic gantry [18]. The geometry of the acquisition mode is presented in Figure 4b.

The spectral radiance was measured, with vertical length A = 1.1 m, number of pixels M = 1164, and ground resolving distance of 0.945 mm. The horizontal length between Spectralon and the white-black-white panel is B = 2.0 m, the number of pixels is N = 556, and the ground resolving distance is 3.597 mm. The next step was geometric transformation and interpolation. For the interpolation, we tested the nearest neighbor, bilinear, and cubic methods and, as a result, decided to apply the nearest-neighbor method. The mean reflectance spectra values were below 0.280; see Figure 10.

The HR400 Spectrometer was used for irradiance measurements, both relative and absolute μW/(m2nm) to the Sun in the periods when the hyperspectral missions were carried out; see Figures 11 and 12. Its role was to understand the dynamics of the absolute irradiance and to select times which are suitable for hyperspectral measurements.

#### *2.2. Landmines and Plastic Objects, Whose Spectra Are Provided by Point-Like Measurements with ASD*

The figures in the following section represent some of the targets that were measured by Point-Like Measurements with ASD. These sensor measures only one position where it is pointed. If we sample 10 or 15 points on target, they do not provide as much information variability as imaging sensor, covering entire target. When we created simulated targets by using ASD, we had available couple of points and simulation was not as realistic as from imaging sensor.

**Figure 13.** TMA-4 landmine.

**Figure 14.** VTMRP-6 landmine.

**Figure 15.** PMR-2A landmine.

**Figure 16.** Plastic bottle.

**Figure 17.** The reflectance of PMR-2A, TMA-4, and VTMRP-6 landmines, as well as that of a plastic bottle, measured by a point measuring unit ASD.

#### *2.3. Hyperspectral Cubes of the Terrain Acquired by UHD-185*

The hyperspectral cubes of terrain were acquired by the snapshot camera UHD-185, with 50 × 50 spectral pixels sharpened by 1000 × 1000 panchromatic pixels. The aerial platforms were UAVs at low altitude (Figures 18 and 19) and a Bell-206 helicopter at high altitude (Figure 20).

**Figure 18.** Hyperspectral scene 147. Dimensions 18.681 × 18.681 m, 1000 × 1000 pixels. Visualized with r = 650 nm, g = 550 nm, b = 460 nm.

**Figure 19.** Hyperspectral scene 227. Dimensions 18.681 × 18.681 m, 1000 × 1000 pixels. Visualized with r = 650 nm, g = 550 nm, b = 460 nm.

**Figure 20.** Calibration area acquired from Bell-206 helicopter: (**a**) color-visualized hyperspectral cube (red = 650 nm, green = 550 nm, blue = 450 nm). Area ~ 72 × 72 m, GRD = 7.19 cm; and (**b**) Handheld oblique photography.

Note that the ground resolving distance (GRD) in Figures 18 and 19 of the pansharpened pixels is 1.868 cm, while the real spectral GRD was 37.36 cm. The consequences of pan-sharpening for spectral discrimination are generally qualitatively known, but we do not analyze them herein.

#### *2.4. Simulation of the Spatial Distribution of the Explosive Objects*

Data of the spatial distribution of threat-causing explosive objects are limited and, for IEDs, are classified. One possible solution is predicting their distribution by simulation, using the public sources considered in Section 1.3; we consider this in the current section. Once the spatial distribution is solved, the problem of how to implant the spectral data of targets in the hyperspectral data of terrain arises, which is considered in Section 2.5.

One older minefield simulation system [48] considers and models factors of airborne detection, including the type of background, time of day, swath width, number of steps, overlapping, minefield scenarios, false alarms, and landmine statistics.

Predicting the distribution of improvised explosive devices, in [49], had the purpose of examining how IED placement can be predicted using related historical data processed by artificial neural networks. Monte Carlo simulation and a logic-based examination of publicly available IED sources were performed, in order to simulate a population resembling the real world in relevant respects. Two cases were analyzed: flat terrain features and objects, and mountainous terrain features and objects [49].

The modeling and simulation of the detection of landmines and improvised explosive devices with multiple automatic target detection loops, as presented in [50], provided an example of a military approaches. In [51], the authors stated that a fully automatic target recognition process still fails to satisfy the operational requirements of minefield detection. This necessitates human interaction for verification and decision-making. It has been found that the operator would not be able to handle the number of segments to process effectively when the percentage of minefield segments in ground truth is more than 1% and when the false alarm rate for non-minefield segments is more than 1.5%.

From several promising detection technologies, we only consider passive hyperspectral data in this study. The crucial factor is the lack of civilian (or public military) data regarding explosive devices in a realistic, non-laboratory environment. The hyperspectral imaging sensors used on UAVs can provide pixels smaller than explosive devices on the ground surface, which simplifies the processing of collected hyperspectral data. The positive consequence is that the problems of target detection with sub-pixel dimensions are avoided. Two groups of hyperspectral target detection methods use only spectral information; not the size, shape, or texture of the target [52,53] (p. 066403-1). These are spectral matching detection algorithms and spectral anomaly detection algorithms. More information about both groups can be found in [54,55], and more about anomaly detection in [56], about deep learning classification in [57], and about the application of neural networks for landmine detection in [58]; we will not consider these further.

Consequently, we consider the modeling and simulation of explosive devices (targets) on a ground surface using their hyperspectral data obtained by hyperspectral measurement and their implanting in terrain hyperspectral cubes. We consider the effects of this process by assessing the outcomes of classification by the spectral angle mapping (SAM) method [59].

#### *2.5. The Implanting Spectral Data of Explosive Targets in the Hyperspectral Scene of the Terrain*

The analysis [60] by Basener et al., verified that "the utility of a hyperspectral image for target detection can be measured by synthetically implanting target spectra in the image and applying detection algorithms." Our aim is to implant spectral data of explosive targets, which was done in the following way: We implanted the true hyperspectral data of UXOs and landmines, measured with a ground resolving distance GRDUXO = 0.945 mm, into hyperspectral scenes of terrain surface (GRDterrain = 18.68 mm), after spatial transformation and processing. Note that the ratio of the ground resolving distances, UXO/Terrain, is

0.05058 (or 5.058%). The dimensions of each UXO target are decreased and matched for implanting into pixels of the terrain hyperspectral data, such as in the example presented in Figure 21b.

**Figure 21.** Artillery shell (**a**) extracted from its neighborhood (Figure 8b); (**b**) small targets, of decreased dimensions, in this figure are presented not in exact scale, in order to be recognizable. Small targets can be implanted with any orientation. This small target image is named nameR, where the suffix R means the decrease to 5.058%.

All operations were done with arrays (stacks) of images having MxNxL pixels, where M = number columns, N = number of rows, and L = number of wavelengths (channels). For processing, we used the ENVI and ImageJ software; see Table 1 and Figure 22. The format of spectral data was floating point 32 bits. The extracted targets contained all real hyperspectral data obtained by measurements, while the decreased targets contained from 0.23% to 0.27% of the data only; see Table 2. The following examples were used: hyperspectral scenes 147 and 227 of terrain (Figures 18 and 19; each 1000 × 1000 × 90 spectral data, 32-bit float); arrays with the same dimensions but zeroed data, named "blackboard"; and arrays of small targets (100 × 100 × 90 spectral data, 32-bit float), named AS-artillery shell, B-bullet, C-cluster munition, MM-mortar mine, UXOX-UXOX, TMA-4, VTMRP-6, PMR-2A, and Plastic bottle.

**Table 1.** Implanting spectral data of targets in the hyperspectral scene of the terrain.


The targets can be implanted in the hyperspectral data of the terrain in one or two of the following combinations: 1. Without interaction with its neighborhood—the whole area of the target is visible to the imaging hyperspectral sensor. 2. The area of the target is partially hidden, obscured, or covered by terrain. In the following text, we use the term obscured. 3. The spectrum of a target is mixed or overlaid by spectra of the terrain surface (e.g., partially by soil, sand, gravel, or vegetation). In the following text, we use the term overlaid.

**Figure 22.** Main steps for implanting targets onto the hyperspectral scene of the terrain. Figure A9 is an example for terrain 147, Figure A10 is terrain 227: (**a**) Targets inserted on blackboard (1000 × 1000 pixels, 90 channels, floating point 32-bit, stack, tif). Red: AS, B, CN, MM, UXOX, Plastic bottle, mines PMR-2a, TMA-4, VTMRP-6; Yellow: False alarm objects; Green: Random uniform spectral values inside the minimum–maximum interval; (**b**) locations of targets: black—0, white—1, 90 channels, 32-bit; (**c**) hyperspectral terrain scene 227 (1000 × 1000 pixels, 90 channels, 32 bits, tif) multiplied by (**b**). One channel is shown; (**d**) Adding (**a**) to (**c**) in 90 channels, giving implanted targets on hyperspectral terrain scene 227. Color visualization (r = 650 nm, g = 550 nm, b = 460 nm).



2.5.1. Spectral Angle Mapping

From several spectral matching detection algorithms, we selected the Spectral Angle Mapping (SAM) algorithm, introduced in 1993 by F.A. Kruse et al., in The Spectral Image Processing System (SIPS) Interactive Visualization and Analysis of Imaging Spectrometer Data [58]. SAM allows for mapping of the spectral similarity of image spectra *ti* to reference spectra ri by calculating the angle, γ, between the two spectra, treating them as vectors in a space with dimensionality equal to the number of channels (L); see Figure 23 and Equation (1).

$$\mathbf{y}^\* = \arccos\left[\sum\_{i=1}^L t\_i r\_i / \left(\sum\_{i=1}^L t\_i 2\_i\right) 1 / 2 \left(\sum\_{i=1}^L r\_i 2\_i\right) 1 / 2\right].\tag{1}$$

**Figure 23.** The reference spectrum *ri*, (*i* = 1, ... ,*L*), the test spectrum *ti* (*i* = 1, ... ,*L*), γ is the angle between them (in radians), and L is a number of channels [58] (p. 157).

This similarity measure is insensitive to gain factors, as the angle γ between the two vectors is invariant, concerning the lengths of the vectors. More information about SAM is available in many references (see, e.g., [56]).

The number of positive outcomes of SAM classification is a measure of detection success, which depends on the quality and quantity of spectral samples (endmembers) representing objects or materials and their areas; see Figure 24a, Table 2. The largest number of endmembers in the area belonged to Mortar mines (116; 0.040482 m2), while the smallest belonged to UXOX (52; 0.018147 m2). Figure 24a shows the mean SAM values of targets. Figure 24b shows the SAM values of 9 ASR targets obscured 25.7%. Obscured targets have larger dispersion and larger SAM angles. Figure 24c shows the SAM values of 10 ASR targets; their spectra are overlayed with 10% of terrain (scene 147). Targets overlayed with scene spectra have larger dispersion at smaller SAM angles. Similar behaviors appeared with other targets.

**Figure 24.** Results of spectral angle mapping processing: (**a**) SAM of targets calculated using their own endmembers; (**b**) SAM of 9 ASR targets with areas obscured by 25.7%; and (**c**) spectra of targets overlayed with 10% of scene 147 at locations of targets—SAM of 10 ASR targets.

#### 2.5.2. Target Simulation Options

Our research aims to develop modeling and simulation of the spectral data of explosive targets, implanting them into spectral terrain scenes for civilian applications. Several approaches were analyzed or tested and considered:


In our research, we analyzed options 1, 2, 3, and 4, while 5 was the only one tested. The following conclusions were derived: The use of true spectral data of explosive targets, measured by a hyperspectral imaging scanner (case 1), and processed as described in Table 1 and Figure 22, gave reliable outcomes (Figure 25a,b). The average spectral data, (case 2) produced a high constant response (Figure 25c,d) and, so, should not be used. Histograms of spectral data comparing cases 1 and 2 (see Figure 26) provided additional evidence for this statement. Note that this kind of data has been used in several references, despite its weakness.

**Figure 25.** Examples of Case1: (**<sup>a</sup>**,**b**) target artillery shell; (**<sup>c</sup>**,**d**) Case 2: target mine TMA-4; (**<sup>e</sup>**,**f**) case 3: case target, mine TMA-4, spectral data randomly generated, with uniform distribution, in the interval from minimum to maximum.

The explosive targets in Figure 25 show their views at 550 nm, in the grayscale and artificial color lookup table. Note that case in Figure 26b has a stable constant view, which is not realistic in the natural environment. Figure 25e,f shows the same target's spectral data, generated by a random data generator with uniform distribution in the interval from minimum to maximum.

**Figure 26.** Histograms of spectral data of all channels: (**a**) Mortar mine; (**b**) TMA-4; and (**c**) randomly generated TMA-4 spectral data. Note that histograms (**a**) and (**c**) show significant variability of spectral values. Histogram (**b**) shows that constant values dominate the spectrum, and only several deviations appear.

2.5.3. Modeling the Obscured Spectra of the Explosive Target and the Overlayed Target's Spectra and the Spectra of Background

The general model for analysis of the effects of partially obscuring an explosive target and partially mixing its spectra with those of the neighboring terrain is [53]:

$$\infty = \mathbf{a}\mathbf{S} + \mathbf{b}\mathbf{V},\tag{2}$$

where x is the spectrum of the observed pixel, S is the spectrum of the target, V is the spectrum of the background, a ≥ 0 is the fraction of the considered pixel which is filled by the target, and b ≥ 0 is the fraction of the considered pixel filled by the neighboring terrain. If the observed pixel is filled with the target (a = 1, b = 0), it is resolved or a full-pixel target. When part of the pixel is filled with the target (a = 0, b = 0), it is unresolved or a sub-pixel target. Although we mainly analyzed resolved (full-pixel) targets, we tested cases where part of the explosive target was randomly obscured (see Figure 27) and cases where its spectrum was overlaid with the spectrum of the background (i.e., b > 0).

**Figure 27.** Example of obscuring: (**a**) clear targets; and (**b**) areas of targets (obscured 25.7%).

The target and terrain (background) spectral combinations, defined by Equation (2), are indeed summations, although we often use the words "overlaid" and "mixed". Another combination is the partial obscuring of a target area by the terrain and its spectra (see Figure 27).

The obscuring 25.7% was applied to the areas of targets (ASR, BR, CMR, MMR, UXOXR) in scene 227 (Appendix C).

The mixing (overlaying) of the spectra in terrain scene 147 (Appendix C) with the spectra of the 10 targets (ASR, BR, CMR, MMR, UXOXR) was applied with a = 1.0, and b = 0.10, such that:

$$
\infty = \text{S} + 0.10 \text{ V.} \tag{3}
$$

#### *2.6. Model of Target Detection*

Our goal was to derive methods for modeling and simulating the explosive targets in a hyperspectral scene, using the real hyperspectral data of several types of explosive devices, where simulation should be suitable for application by civilians, which is narrower and less complex than the analysis of hyperspectral methods for target detection. Thus, we used, for the considered cases, the SAM algorithm as the detector, among several others (Cross-Correlation, Linear Unmixing, Matched Filtering). The outputs of SAM are a Spectral Angle raster, containing values of the spectral angle for each image cell, and a Class raster, in which cells are assigned to endmember classes based on the angle value set for the threshold value *γ* (see Figure 28).

**Figure 28.** Spectral angle mapping (SAM) outputs for a decreased mortar mine MM: (**a**) The source of spectral endmembers, MM, in terrain 147 environment, visualized in color (r = 650 nm, g = 550 nm, b = 460 nm); (**b**) Spectral Angle raster, containing spectral angle values for each image cell, obtained with the angle threshold value of *γ* = 0.0174532925 radians; and (**c**) Class raster, in which cells are assigned to endmember classes based on the angle threshold value *γ*.

For our analysis, we used SAM Class raster values. The computing resources of SAM are proportional to 1/γ and, so, the smaller the value of γ, the larger the computing time. Thus, we selected γ as the independent variable.

The detection of a target was modeled as a Bernoulli experiment, where the binary random variable y took a value ofy=1 ("detected") with probability p andy=0 ("not detected") with probability 1−*p* [60]. The parameter p was specific for each treatment and depends on the influence variables characterizing that treatment.

Let POD be the probability of target detection. If the number of opportunities to detect a target is n and the number of detections is y, the number of detections is binomially distributed with parameter p, where p = POD and q = 1−*p*. The basic model for the analysis of mine detection POD confidence limits has been developed in [61], although we applied confidence limits—POD-lower and POD-upper—by Exact Confidence Interval using the Clopper–Pearson method [62]:

$$\text{PODupp} = 1 - \text{BetaInv}(\text{x}/2, \text{n}-\text{k}, \text{k}+1), \tag{4}$$

$$\text{PODlow} = 1 - \text{BetaInv}(1 - \alpha/2, \mathbf{n} - \mathbf{k} + 1, \mathbf{k}), \tag{5}$$

where PODlow is the confidence interval lower limit, PODupp is the confidence interval upper limit, n is the number of trials, k is the number of successes in n trials, α is the percent chance to reject the true null hypothesis about detection incorrectly, and BetaInv has been defined in [63]. Usually, α = 0.05 (5%) and 1 − α is the 95% confidence.

The estimated false alarm rate (FAR) can be defined as the number of false alarms counted on an area divided by the size of that area (i.e., the average number of false alarms per square meter). The area calculated was the area of the terrain scene (147 or 227) minus the area of all detected targets. As we limited our concern only to models and simulations of explosive targets, the FAR was not considered.
