26.5 Real Image Hyperspectral Experiments

The second data set used for experiments was the 15-panel HYDICE image shown in Figure 1.15(a). Two scenarios were conducted for experiments based on this 15-panel HYDICE scene. One was spectral discrimination among the five panel signatures, p₁, p₂, p₃, p₄, and p₅. The other was to identify the 15 panels unsupervisedly using only knowledge obtained directly from the data.

Example 26.3

(spectral discrimination)

Like Example 26.1, spectral discrimination was performed by MPCM-PSSC where the number of stages required for MPCM-PSSC was calculated by (26.6) to be M = 13 and the stage levels were obtained by (26.7). To implement MPCM-PSSC algorithm, we also needed to determine an appropriate set of stage thresholds.

Using the same way conducted in Example 26.1, the desired set of stage thresholds were obtained in Table 26.10 by (26.12) using noise-corrupted signatures with SNR set to 30:1 as variation of signature tolerance.

Table 26.11 tabulates discrimination results obtained by MPCM-PSSC among the five panel signature vectors in Figure 1.16.

As shown in Table 26.11, p₁ and p₂ were more similar each other than other three panel signature vectors since the discrimination could be accomplished in stage 2 in terms of spectral variation compared to other signature discrimination that was already discriminated in stage 1.

Table 26.10 Stage thresholds for five panel signatures with SNR 30:1.

Table 26.11 Discrimination among five panel signature vectors using the stage thresholds in Table 26.10.

Example 26.4

(spectral identification)

The experiments conducted in this example were very interesting and offered several intriguing results and observations. It was designed to identify the 19 R panel pixels, p_ij in Figure 1.15(b) by MPCM-PSSC. Since the panel pixels p₁₃, p₂₃, p₃₃, p₄₃, p₅₃ have size of that is smaller than the pixel size, their abundance fractions present in single pixels can be at most that can be interpreted as approximately 50% of the pixel size. As a result, the performance in identification of these subpixel panels can be expected to be very challenging and difficult. On the other hand, due to its very high spatial and spectral resolution the spectral variations of image pixels in this HYDICE scene can be very subtle and sensitive. Therefore, using the five panel signatures in Figure 1.16 as a data base may not be appropriate. Instead, a more effective data base must be obtained in an unsupervised means directly form data. In doing so, the result of the 34 target pixels generated directly from the scene by an unsupervised fully constrained least squares (UFCLS) method developed in Heinz and Chang (2001) and Chang (2003a) were used to form a desired data base Δ. Among these 34 generated target pixels there were five panel pixels identified to correspond to the five distinct panel signatures . Table 26.12 tabulates the results produced by MPCM-PSSC using Algorithm 1 and Algorithm 2 for spectral identification along with the abundance fractions of the 19 R pixels estimated by FCLS where an identification error was highlighted by shade.

According to Table 26.12, Algorithm 1 yielded the best performance in the sense that it only missed identification when the panels pixel, p₁₃, p₂₁₂, p₃₃, p₄₁₂, p₄₃, p₅₃ with estimated abundance fractions less than 0.3821. Algorithm 2 also made six identification errors, but it seemed that these misidentifications had no clear tie to the abundance fractions as Algorithm 1 did. For example, it correctly identifies p₂₁₂ whose abundance was only 0.3141, but it misidentified the p₃₂ whose abundance was 0.5343. Compared to Algorithm 2, SAM and SID not only made the same 6 identification errors as did Algorithm 2, but also made two more additional errors, which were panel pixels p₅₁₁, p₅₂ with abundance fractions, 0.7203 and 0.7789.

This experiment shows that MPCM-PSSC performed more effectively than a pixel-based spectral similarity measure such as SAM and SID in Table 26.12. It should be noted that real target panel pixels in Table 26.12 are compared against the five panel signature vectors for analysis.

It is interesting to note that if the five panel signature vectors in Figure 1.16 were directly used for identification, the results are reported in Chang (2003a) and are not as good as the results in Table 26.12 that were produced by using the real target panel pixels in Table 26.12. This is primarily due to the fact that the panel signature vectors obtained by averaging R panel pixels are not real pixels. As a result, the signature variations of real target panel pixel vectors were compromised. MPCM-PSSC seemed to remedy such deficiency by capturing subtle spectral variations in multiple stages that were able to dictate changes in subtle difference encountered in real data as shown in Table 26.13.

Table 26.12 Identification of 19 R panel pixels in Figure 1.5(a).

Table 26.13(a) Identification of p₁₁.

Table 26.13(b) Identification of p₁₂.

Table 26.13(c) Identification of p₁₃.

Table 26.13(d) Identification of p₂₁₁.

Table 26.13(e) Identification of p₂₂₁.

Table 26.13(f) Identification of p₂₂.

Table 26.13(g) Identification of p₂₃.

Table 26.13(h) Identification of p₃₁₁.

Table 26.13(i) Identification of p₃₁₂.

Table 26.13(j) Identification of p₃₂.

Table 26.13(k) Identification of p₃₃.

Table 26.13(l) Identification of p₄₁₁.

Table 26.13(m) Identification of p₄₁₂.

Table 26.13(n) Identification of p₄₂.

Table 26.13(o) Identification of p₄₃.

Table 26.13(p) Identification of p₅₁₁.

Table 26.13(q) Identification of p₅₂₁.

Table 26.13(r) Identification of p₅₂.

Table 26.13(s) Identification of p₅₃.

As a final comment, it should be noted that the 34 target pixels used in this experiment were obtained according to Heinz and Chang (2001) that have shown to be sufficiently enough to represent the five distinct panel spectral signature vectors. However, it did not imply that it required at least 34 target pixel vectors to do so. There may have some unsupervised target detection and classification algorithms such as those developed in Chapter 17 that can generate a fewer number of target pixel vectors than 34 but still include pixels that can represent all the desired five panel signature vectors. In this case, these generated target pixel vectors can be used as a database as well. As expected, the conclusion drawn from Table 26.13 will remain unchanged.