25.4 Real Image Experiments

Two real image data sets, the Cuprite data of Figure 1.12 and the 15-panel HYDICE image scene in Figure 1.15, have been used for experiments in previous chapters. Since the experiments in Sections 25.2 and 25.3 have used the AIVRIS data of Figure 1.9 that are derived from the scene in Figure 1.12, this section will only focus on the 15 panels in Figure 1.15(b) and use the 5 panel signatures in Figure 1.16 for experiments. It should be noted that despite that the panel signatures are obtained from real image pixel vectors, the following experiments are performed on the five panel signatures as signature vectors not pixel vectors. Therefore, no sample spectral correlation among pixels is considered in signature coding.

25.4.1 SDFC

Figure 25.24 shows the results of spectral similarity values produced by SPAM, SFBC, HD-SDFC, and AVD-SDFC.

Figure 25.24 Spectral similarity values among p1, p2, p3, p4, and p5 produced by SPAM, SFBC, HD-SDFC, and AVD-SDFC.

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Figure 25.25(a) plots comparative results of spectral similarity values of p1, p2, p3, p4, and p5 produced by the four different coding methods, SPAM, SFBC, HD-SDFC, and AVD-SDFC. Once again, there was no clear visual assessment to determine how one coding method performed better than another. RSDPW was calculated for this purpose to further evaluate discriminatory power.

Experiment 25.4.1.1 (R = Average of Five Signatures in Figure 1.16)

Figure 25.25(b) plots RSDPW values calculated by (25.19) using pave obtained by averaging all the five panel signature vectors as the reference signature vector and pi designated as the signature vector of interest s1 and other four signature vectors pj with img chosen to be s2 to be compared against s1. As can be seen from the experiments, SDFC also outperformed SPAM and SBFC in discriminatory power and AVD-SDFC seemed to perform slightly better than HD-SDFC in general. For other cases where signature s1 was selected to be a different panel signature, the conclusion was very similar. Their results are not included here.

Experiment 25.4.1.2 (R = Individual Signature)

In this case, we choose each of the five signature vectors as a reference signature, that is, r = p1, p2, p3, p4, and p5. In the mean time, these five panel signature vectors are also set to the signature vector of interest s1 = r for calculation of the RSDPW via (25.19). Figure 25.26(a)–(e) plots RSDPW values and shows the results of spectral similarity values between s1 = r and s2 = other four signature vectors produced by SPAM, SFBC, HD-SDFC, and AVD-SDFC along with plots of their corresponding RSDPW values.

Figure 25.25 Comparative plots of spectral similarity values of the panel data produced by SPAM, SFBC, HD-SDFC, and AVD-SDFC along with plots of RSDPW values.

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According to Figure 25.26, both versions of SDFC also performed better than SPAM and SFBC in terms of RSDPW. As noted, unlike the simulation results where AVD-SDFC performed better than the HD-SDFC, the performance of HD-SDFC was slightly better than AVD-SDFC.

25.4.2 SFPC

Similar experriments conducted in Section 25.4.1 were also performed by SFPC on the five panel signature vectors. Figure 25.27 shows the spectral similarity values among p1, p2, p3, p4, and p5 produced by SPAM, SFBC, 2-bit C-SFPC, 2-bit S-SFPC, 3-bit C-SFPC, 3-bit S-SFPC, 4-bit C-SFPC, and 4-bit S-SFPC, where the best performance seemed was produced by 4 bit S-SFPC followed by 4-bit C-SFPC.

Figure 25.26 Comparative plots of spectral similarity values produced by SPAM, SFBC, HD-SDFC, and AVD-SDFC along with their corresponding plots of RSDPW values.

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In order to further quantitatively measure discriminatory powers of SPAM, SFBC, C-SFPC, and S-SFPC with variable bit rates, RSDPW via (25.19) was once again used for performance evaluation.

Experiment 25.4.2.1 (R = Average of the Five Panel Signatures in Figure 1.16)

Using the average of five signature vectors as the reference signature vector, Figure 25.28 shows comparative graphic plots of spectral similarity values of p1, p2, p3, p4, and p5 produced by 2-bit SPAM, 2-bit C-SFPC, and 2-bit S-SFPC and comparative plots of spectral similarity values produced by 3-bit SFBC, 3-bit C-SFPC, and 3-bit S-SFPC. In the mean time, Figure 25.28 also plots their corresponding RSDPW values using pave obtained by averaging all the five panel signature vectors as the reference signature vector and each panel signature vector pi designated as the signature vector of interest s1 and other four signature vectors pj with img chosen to be s2 to be compared against s1.

Figure 25.27 Spectral similarity values among p1, p2, p3, p4, and p5 produced by SPAM, SFBC, 2-bit C-SFPC, 2-bit S-SFPC, 3-bit C-SFPC, 3-bit S-SFPC, 4-bit C-SFPC, and 4-bit S-SFPC.

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As shown in Figure 25.28(a), SFPC did not perform well in the 2-bit case due to the close similarity of the panel spectral signature vectors. However, the performance of SFPC was significantly improved when the bit rate was increased from 2 to 3 bits in Figure 25.28(b) and it performed better than the 3-bit SFBC except the case between p4 and p5. As the bit rate was increased to 4 and 8 bits, the performance of SFPC was improved as shown in Figure 25.29(a) and (b).

Experiment 25.4.2.2 (R = Individual Signature)

In this case, we chose any of five signature vectors as a reference signature vector where each of the five panel signature vectors p1, p2, p3, p4, and p5 could be used as the signature vector of interest s1 for the calculation of the RSDPW via (25.19) while one of the remaining four panels signature vectors is designated as signature vector s2. Since the spectral similarity values of various coding methods are already plotted in Figure 25.29(a), Figure 25.30(a)–(e) only shows comparative graphical plots of RSDPW values produced by 2-bit SPAM, 2-bit C-SFPC, 2-bit S-SFPC, 3-bit SFBC, 3-bit C-SFPC, 3-bit S-SFPC, 4-bit C-SFPC, 4-bit S-SFPC, 8-bit C-SFPC, and 8-bit S-SFPC, where one panel signature vector was used as the reference signature vector r while the other four panel signature vectors were used to calculate RSDPW values.

Figure 25.28 Comparative plots of spectral similarity values produced by 2-bit SPAM, 2-bit C-SFPC, 2-bit S-SFPC, 3-bit SFBC, 3-bit C-SFPC, and 3-bit S-SFPC along with their corresponding graphical plots of RSDPW values using pave obtained by averaging all the five panel signatures as the reference signature and each panel signature vector pi designated as the signature vector of interest s1 and other four signature vectors pj with img chosen to be s2 to be compared against s1.

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Figure 25.29 (a) Comparative plots of spectral similarity values produced by 4-bit C-SFPC, 4-bit S-SFPC, 8-bit C-SFPC, and 8-bit S-SFPC. (b) Comparative graphical plots of RSDPW values among the four panel signature vectors p1, p3, p4, and p5 produced by 4-bit C-SFPC, 4-bit S-SFPC, 8-bit C-SFPC, and 8-bit S-SFPC using pave obtained by averaging all the five panel signature vectors as the reference signature and each panel signature pi designated as the signature vector of interest s1 and other four signature vectors pj with img chosen to be s2 to be compared against s1.

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Figure 25.30 Comparative plots of RSDPW values produced by SPAM, SFBC, 2-bit C-SFPC. 2-bit S-SFPC, 3-bit C-SFPC, 3-bit S-SFPC, 4-bit C-SFPC, 4-bit S-SFPC, 8-bit C-SFPC, and 8-bit S-SFPC.

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According to the above experiments, the best performance was produced by 4-bit S-SFPC. Several remarks are worth noting:

1. SFPC generally performed well and better than the SPAM and SFBC when spectral characteristics were sophisticated and required more bits for quantization such as the bit rate greater than 2 bits. On the other hand, it performed worse than SPAM and SFBC if the bit rate was low such as 1-bit or 2-bit coding. Therefore, SFPC generally performed better than SPAM and SFBC for signatures that were spectrally similar and required high bit rates for coding.
2. S-SFPC was usually better than C-SFPC because there was a lack of correlation between the first and last bands used in C-SFPC.
3. As for the reference signature vector, the following guideline is recommended. If the signature vectors to be encoded are relatively distinct in the sense of spectral similarity, the reference signature vector can be selected to their average. Otherwise, the reference signature vector can be selected as one of the signature vectors. This was demonstrated by the above experiments. For example, as p1, p2, and p3 are spectrally similar, using the averaged signature vector as a reference was less effective than using individual signature vectors as a reference signature vector.
4. Compared to SPAM and SFBC, SFPC has a generalization ability that can be extended to any arbitrary-bit coder, a major advantage that cannot be gained by the 2-bit coder, SPAM, and the 3-bit coder, SFBC.
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