**3. Results**

The results of our research were methods for modeling and simulating explosive targets in a real hyperspectral data scene. We considered improvised explosive devices (IED), unexploded ordnances (UXOs), and landmines. Spectral data of these objects are limited and, for IEDs, are classified. Our approach included spectral data of UXOs and landmines, measured by hyperspectral imaging sensors (line scanner and a snapshot camera) onboard a ground-based mechanic gentry, a helicopter, and a UAV. The spectral data of the terrain were acquired with a snapshot hyperspectral camera onboard a UAV and a Bell-206 helicopter. The measured spectral data of the explosive targets had a very fine spatial resolution of 0.945 × 0.945 mm, while the spectral data of the terrain had a resolution of 1.868 × 1.868 cm. The dimensions of each UXO target were, thus, decreased to 5.0588% (see Figure 21) and, after this step, they could be implanted into the pixels of hyperspectral data of the terrain (see Figures 18 and 19).

A key concept in our research is a combination of tests and analyses, in which several factors appear. The factors were UXO targets (artillery shell—AS, bullet—B, cluster munition—CM, mortar mine—MM, unexploded ordnances of unknown type—UXOX), landmines—PMR-2a, TMA-4, VTMRP-6—and plastic bottles) and the spectral angle mapping classifier (detector). The independent variable was the spectral angle (from 0.055 to 0.150 radians). A detector was tested with each UXO target in two situations: Spectra of targets overlaid with 10% of terrain spectra, or targets obscured by 25.7%. The overlaid and obscured UXO targets were implanted into the terrain hyperspectral cubes 147 and 227, which introduced additional variability; an example with terrain 227 is shown in Figure 22d. Figures 13–16, several targets had only one spectral value for each wavelength (see Table 2, Figure 25c,d), and were excluded from the following analysis. The histogram of the spectra in all channels of one considered UXO target showed rich variability, while the randomly simulated spectra were also very variable (see Figure 26c). In contrast to the discussed cases, where only the mean value per channel was known, spectral values were uniformly distributed in the majority of channels (see Figure 26b). We are aware that such cases appear often; therefore, we initially tested simulation with random spectral values, if besides mean values, the minimum and maximum values of the reflectance spectra were known (Figure 25e,f).

#### *3.1. Probability of Target Detection POD, Confidence Intervals*

The SAM classification outputs (an example is shown in Figure 28c) were used as the detector outputs. At the same time, the estimated probability of detection for a particular factor level combination is the ratio of the number of detected targets to the total number of opportunities to detect a target. The examples for ASR are shown in Figure 24b,c. While we assumed a binomial distribution for the number of correct positive indications, we also found the 95% confidence limits for the probability of detection, as indicated by relations in Equations (4) and (5).

The considered SAM class raster data models (Figure 24) of the explosive targets ASR, BR, CMR, MMR, and UXOXR were used, after normalizing each to its maximum value. For each target, the POD was derived, as well as the detection probability (see Figures 29 and 30 target 10% overlayed spectra; Figures 31 and 32 target obscured by 25.7%). As the POD and confidence interval data were non-monotonic, we applied a polynomial approximation (see Figures 30 and 32, as well as Appendices A and B).

**Figure 29.** Probability of detection POD of ASR, BR, CMR, MMR, and UXOR targets, with their spectra overlaid with 10% of terrain 147 spectra.

**Figure 30.** Probability of detection (POD), the confidence limits (PODupper, PODlower), and polynomial approximations (Poly) of ASR 147 overlaid spectra.

**Figure 31.** The probability of detection (POD) of ASR, BR, CMR, MMR, and UXOR in terrain scene 227; targets obscured by 25.7%.

**Figure 32.** Probability of detection (POD), confidence limits (PODupper, PODlower), and polynomial approximations (Poly) of ASR 227, targets obscured by 25.7%.

The POD functions of targets with overlayed spectra (Figures 29 and 30, Appendix A) were smoother than the POD functions of obstructed targets (Figures 31 and 32, Appendix B).

#### *3.2. Polynomial Approximations of POD, PODupper, and PODlower*

The functions of the probability of detection (POD) and the associated confidence limits (PODupper and PODlower) were derived from empirical (measured) reflectance spectra. They are intended for use in civilian security applications, where they should be simulated and processed. Hence, we derived polynomial approximations for the considered targets (see Tables 3 and 4) Through approximation, we can avoid the need to read empirical POD, PODupper, and PODlower data, by using the corresponding functions.


**Table 3.** Polynomial approximation functions of targets overlayed with 10% of terrain 147.

**Table 4.** Polynomial approximation functions of targets 25,7% obscured in scene 227.


#### *3.3. Simulation of Target Placement*

The placement of targets in the terrain hyperspectral scene is defined in Figure 31, with futher examples given in Appendices A–C. We created three sets of fused scenes with targets. The first set contained targets, as described earlier. The second had a 10% overlay of spectral information from the position of target placement. The third set had an obscured, partially randomly hidden 25.7% area of targets (Figure 27). In the second case—where targets were overlaid with the scene—we were able to test whether and how different terrain would influence the outcomes. In the third case, we could see how the spectral footprint was changed by hiding randomly chosen different parts of 5 targets at 10 locations. The locations of targets in the scenes were picked to match as much variety as possible, and different positions were picked for each scene.

#### *3.4. SAM Detection Endmembers and Results*

We tested the detection results with endmembers from full-scale targets vs. targets decreased to 5.058% (to match scene resolution). Less accurate results were achieved with endmembers of the full-size targets and, so, we continued with the endmember collection containing all the pixels of the reduced-size targets. The use of true spectral data of explosive targets, measured by a hyperspectral imaging scanner and processed as described in Table 1 and Figure 22, led to reliable outcomes and is suitable for civilian security applications (see Figure 25a,b). The average spectral data produced a strong constant response (Figure 25c,d), and should not be used.
