14.5 Real Image Experiments

In this section, the 15-panel HYDICE image scene in Figure 1.15(a) was used for experiments. One major difference between the real HYDICE image scene in Figure 1.15(a) and the simulated synthetic image in Figure 14.1(c) was that very little knowledge of the image background in Figure 1.15(a) was known compared to the image background in Figure 14.1(b), which was simulated by complete knowledge. As we may expect, an AC-LSMA classifier may not perform as well as it did for the synthetic image if the image background in Figure 1.15(a) was not well characterized. In order to demonstrate this fact, two scenarios were used to characterize the image background as follows. In addition, we also assumed that knowledge of the 9 R pixels in the and 5 R pixels in the panels in Figure 1.15(b) was available a priori. This is because the panels in the 3rd column are subpixel panels which cannot be visualized to obtain as priori knowledge. Thus, the panel signatures in Figure 1.16 and 14 R pixels in both the and panels were considered to be prior knowledge.

By viewing the scene in Figure 14.2, a large portion of the image background is formed of one-fourth of a forest on the left and three-fourth of a large grass field. Using this supervised knowledge, we conducted two experiments to represent the image background. One experiment was to use the area A to characterize the image background. In this case, a single-background signature b_A was used for experiments and the training samples used for -weighted AC-LSMA were all the pixels in the area A for one background class, as done in Example 14.1. Another scenario was to use the automatic target generation process (ATGP) to produce necessary background knowledge in an unsupervised manner.

Example 14.3

(Scenario 1: Single-Background Signature)

Like Example 1, the signature matrix M used for experiments is formed by . The 14 R pixels in both the and panels and pixels in the area A provided training samples for -weighted AC-LSMA. Six methods labeled by five AC-LSMA methods, MD-weighted AC-LSMA, LCMV-weighted AC-LSMA, -weighted AC-LSMA, OSP-weighted AC-LSMA, FCLS, and unconstrained LSOSP were evaluated for comparative analysis. Figure 14.8 shows their respective abundance fraction results of the 15 panels in Figure 14.2(c) with full abundance constraints (i.e., ASC + ANC), respectively.

Figure 14.8 15-panel abundance fraction results of the supervised five AC-LSMA methods and unconstrained LSOSP.

Once again, the unconstrained LSOSP was the worst and the three weighted AC LSMA, MD-weighted AC-LSMA, LCMV-weighted AC-LSMA, and -weighted AC-LSMA seemed among the best. To further justify our conclusions, Table 14.4 tabulates the quantification results obtained for the abundance fractions of the 14 pure R panel pixels (i.e., p₁₁, p₁₂, p₂₁₁, p₂₂₁, p₂₂, p₃₁₁, p₃₁₂, p₃₂, p₄₁₁, p₄₁₂, p₄₂, p₅₁₁, p₅₂₁, p₅₂) and the 5 R panel subpixels (i.e., p₁₃, p₂₃, p₃₃, p₄₃, p₅₃) in Figure 14.8(a)–(f). The quantification results show that the -weighted AC-LSMA in Figure 14.8(c) was the best in the sense that it produced the most accurate abundance fractions of the 19 panel pixels.

Table 14.4 Quantitative results produced by the MD-weighted AC-LSMA, LCMV-weighted AC-LSMA, -weighted AC-LSMA, OSP-weighted AC-LSMA, FCLS, and unconstrained LSOSP with a single-background signature.

Figure 14.9 provides the graphical plots of quantification values in Table 14.4 for an easy visual assessment where the visual inspection of Figure 14.8 may not provide reliable quantification estimates of abundance fractions.

Figure 14.9 Graphical representation of abundance fractions of 19 R panel pixels in Figure 14.8 for visual assessment.

Example 14.4

(Scenario 2: Unsupervised Background Knowledge)

As demonstrated in Example 14.3, a single-background signature could not completely characterize the image background. As a result, AC-LSMA performance was not as good as it did for the synthetic image in Example 14.1, where only one signature was used to simulate the image background. In order to improve its performance, we need to find an appropriate set of background pixels that can well represent the image background. According to VD, the number of spectrally distinct signatures in the scene in Figure 14.1 is n_VD = 9, which was used as the number of endmembers for M. To determine additional background signatures, the number of total signatures in the scene was set to 2n_VD = 18. A reason for selecting 2n_VD will be explained and provided in Chapter 17 as well as Chapter 22. This implies that we need at least 13 spectrally distinct signatures to characterize the image background in addition to the five panel signatures in Figure 14.1. In this case, IN-FINDR was applied to find the 18 endmembers, , as shown in Figure 14.10 to form the desired signature matrix M, where the found pixels labeled by numbers 3, 5, 9, 15, and 17 in Figure 14.10 represented five panel signatures in five different rows in Figure 1.15(a) or Figure 14.1.

Figure 14.10 Eighteen endmembers produced by IN-FINDR.

In analogy with Example 14.2, ATGP was also implemented to find potential interferers until a warning sign of matrix singularity was flagged. In our experiments, there are 169 target pixels. Since some of such ATGP-generated target pixels may also be very similar or identical to the 18 IN-FINDR generated endmembers, these ATGP-generated target pixels could not be considered interferers. So, when OSP-weighted AC-LSMA was implemented, the unwanted signature matrix U would be formed of all the ATGP-generated target pixels, except those that were also IN-FINDR-generated endmembers. In this case, SAM was set to 0.06 to determine if an ATGP-target pixel was also an endmember. On the other hand, -weighted AC-LSMA required a set of training samples. In this case, SAM was set to 0.025 to find pixels that were similar to each of the 18 endmembers, , to form a set of training data for each of the 18 classes, , where the total number of found training samples was 3714. Then, the means of training samples in each of the 18 classes were further calculated, , to form the desired signature matrix M. Six methods, AC-LSMA methods, MD-weighted AC-LSMA, LCMV-weighted AC-LSMA, -weighted AC-LSMA, OSP-weighted AC-LSMA, FCLS, and unconstrained LSOSP labeled by (a-f) were evaluated for comparative analysis.

Figure 14.11 shows their respective abundance fraction results of the 15 panels in Figure 14.1 with full abundance constraints (i.e., ASC + ANC), where the -weighted AC-LSMA was the best compared to the unconstrained LSOSP that was the worst. Unlike Example 14.3 that only used one background signature, the use of additional 12 background signatures to find training samples made a significant difference for the -weighted AC-LSMA. As shown in Figure 14.11, the -weighted AC-LSMA labeled by (c) clearly outperformed all other five AC-LSMA methods. Interestingly, the FCLS seemed to perform well in detection of 19 R panel pixels visually shown in Figure 14.11 at the expense of many falsely alarmed pixels. However, their quantitative results tabulated in Table 14.5 show otherwise. Figure 14.12(a) and (b) plots quantified abundance fractions of 14 R pure panel pixels and 5 R panel subpixels in Figure 14.11, respectively, where the MD-weighted AC-LSMA and LCMV-weighted AC-LSMA labeled by (a) and (b) unmixed abundance fractions more accurately than FCLS for most panel pixels. Nevertheless, the -weighted AC-LSMA from Figure 14.11(c) was still the best according to Table 14.5 in terms of quantifying abundance fractions of panel pixels.

Figure 14.11 Unsupervised 15-panel abundance fraction results of five AC-LSMA methods and unconstrained LSOSP.

Figure 14.12 further provides the graphical plots of quantification values in Table 14.5 for a better visual assessment compared to the results in Figure 14.11.

Figure 14.12 Graphical representation of abundance fractions of 19 R panel pixels in Figure 1(b) for visual assessment.

Table 14.5 Quantitative results produced by the MD-weighted AC-LSMA, LCMV-weighted AC-LSMA, -weighted AC-LSMA, OSP-weighted AC-LSMA, FCLS, and unconstrained LSOSP with endmembers generated by N-FINDR.

A remark on the threshold used for SAM is noteworthy. This threshold was selected empirically for SAM in our experiments. It is based on our experience gained while working on laboratory and real data. Since laboratory data are generally used for simulations, its tolerance to the threshold is more robust than real data. Thus, the threshold selected for simulations can be higher than that chosen for real data. The interval of [0.02, 0.03] for simulated data and the interval of [0.03, 0.05] for real data seemed reasonable ranges from which a threshold can be selected. As for the threshold used by SAM to find undesired signatures for OSP-weighted LSMA, it was set to 0.06 that was a little bit higher than the thresholds used to find endmembers. This is because undesired signatures are not necessarily as subtle as endmembers are. Nonetheless, the threshold selection is generally sensitive to spectral characteristics of signatures to be analyzed. It is advised that several trial-and-errors of selecting different values in this range may be worthwhile.

As a concluding comment, despite the fact that -weighted AC-LSMA was shown to be the best among the six evaluated methods, it required a good set of training samples to produce the within-class matrix S_W. If the sample pool is not well representative like Example 14.3, it will not perform effectively. To the contrary, if the training samples are selected judiciously as the way was done in Example 14.4, -weighted AC-LSMA could be one of the best AC-LSMA methods. Finally, the threshold values used in our experiments for SAM were not optimal, but rather empirical selections.