Multi-spectral Image Acquisition and Spectral Reconstruction using a Trichromatic Digital Camera System associated with absorption filters PART VIII General Discussion

This part describes the results obtained in the simulations and experiments reported in the previous sessions of this report. A) Statistical comparison of the principal component analysis in various spaces The cumulative contributions of the eigenvectors in each space are summarized for multiple-of-three numbers of eigenvectors in Tables I to III. Table I. Cumulative contribution of the eigenvectors in reflectance space. Number of eigenvectors Cumulative Contribution (%) for Macbeth Color Checker Cumulative Contribution (%) for 147 painted patches Cumulative Contribution (%) for 105 painted patches 3 98.34 98.50 96.69 6 99.80 99.83 99.60 9 99.97 99.98 99.97 12 100.00 100.00 100.00 Table II. Cumulative contribution of the eigenvectors in K/S space. Number of eigenvectors Cumulative Contribution (%) for Macbeth Color Checker Cumulative Contribution (%) for 147 painted patches Cumulative Contribution (%) for 105 painted patches 3 98.86 99.18 98.42 6 99.92 99.92 99.98 9 99.99 99.99 100.00 12 100.00 100.00 100.00 Table III. Cumulative contribution of the eigenvectors in the new empirical space. Number of Cumulative Contribution Cumulative Contribution Cumulative Contribution eigenvectors (%) for Macbeth Color Checker (%) for 147 painted patches (%) for 105 painted patches 3 98.49 98.57 97.48 6 99.84 99.85 99.70 9 99.97 99.98 99.98 12 100.00 100.00 100.00 From Table I to III we can observe that by statistical point of view, the eigenvectors in reflectance, K/S and new empirical spaces presented very similar performances. But, for the purpose of this study, spectral and colorimetric accuracy is required. Table IV to VI show the influence of the number of eigenvectors on the colorimetric and spectral accuracy of the spectral reconstruction of each patch, respectively, for reflectance, K/S and new empirical spaces. The colorimetric accuracy is calculated using CIE94 under D50 and 2° observer. Table IV. Influence of the number of eigenvectors in reflectance space used in the spectral reconstruction on the colorimetric and spectral error. Macbeth ColorChecker 147 painted patches 105 painted patches Number of eigenvectors Mean E*94 reflectance factor rms error Mean E*94 reflectance factor rms error Mean E*94 reflectance factor rms error 3 3.1 0.032 4.1 0.027 3.1 0.036 6 0.3 0.013 0.4 0.009 1.0 0.012 9 0.2 0.007 0.1 0.004 0.08 0.003 12 0.002 0.002 0.01 0.001 0.06 0.002 Table V. Influence of the number of eigenvectors in K/S space used in the spectral reconstruction on the colorimetric and spectral error. Macbeth ColorChecker 147 painted patches 105 painted patches Number of eigenvectors Mean E*94 reflectance factor rms error Mean E*94 reflectance factor rms error Mean E*94 reflectance factor rms error 3 4.1 0.010 1.9 0.050 2.8 0.011 6 1.4 0.039 0.9 0.022 0.5 0.012 9 0.3 0.027 0.2 0.016 0.1 0.008 12 0.2 0.017 0.2 0.014 0.02 0.001 Table VI. Influence of the number of eigenvectors in the new empirical space used in the spectral reconstruction on the colorimetric and spectral error. Macbeth ColorChecker 147 painted patches 105 painted patches Number of eigenvectors Mean E*94 reflectance factor rms error Mean E*94 reflectance factor rms error Mean E*94 reflectance factor rms error 3 2.5 0.025 3.3 0.025 1.8 0.022 6 0.2 0.009 0.3 0.007 0.5 0.007 9 0.1 0.004 0.03 0.003 0.05 0.002 12 0.01 0.001 0.00 0.001 0.01 0.000 Comparing Tables IV to VI, it is possible to see that the best overall result was produced in the new empirical space, followed by reflectance and K/S spaces. Particularly, the results in K/S space were not satisfactory because the influence of errors caused by low dimensionality on the inherent problems of K/S equations, for low reflectance factors. If we establish that a reproduction is acceptable if ∆E*94 is less than a unity and spectral reflectance rms error less than 1%, while 6 eigenvectors are enough to reconstruct spectra in the new empirical space, 9 eigenvectors are required in reflectance space and more than 12 necessary in K/S space. It is also possible to notice that the performance depends on the samples used to perform principal component analysis. B) Spectral reconstruction using simulated camera digital counts in various spaces, targets and trichromatic signal combinations Influence of combination of trichromatic signals in reflectance space Target I: GretagMacbeth ColorChecker Table VII summarizes the result obtained for various combinations of signals. Table VII. Spectral reconstruction using 6 eigenvectors and 6 signals Patch E*94 reflectance factor rms error Metameric Index 6 eigenvectors and 6 signals: R,G,B without filter and with light-blue absorption filter Average 0.4 0.021 0.3 Std Dev 0.3 0.010 0.4 Max 1.1 0.053 1.8 Min 0.04 0.002 0.04 6 eigenvectors and 6 signals: R,G,B without filter and with very-light-green absorption filter Average 0.2 0.018 0.2 Std Dev 0.2 0.007 0.2 Max 0.8 0.038 0.9 Min 0.03 0.002 0.01 6 eigenvectors and 6 signals: R,G,B without filter and with didymium filter Average 0.5 0.021 0.8 Std Dev 0.4 0.009 0.9 Max 1.4 0.044 3.3 Min 0.05 0.002 0.02 6 eigenvectors and 6 signals: R,G,B with light-blue and with didymium filters Average 0.5 0.021 0.5 Std Dev 0.4 0.010 0.5 Max 1.8 0.051 1.8 Min 0.08 0.002 0.01 6 eigenvectors and 6 signals: R,G,B with light-blue and with very-light-green filters Average 0.4 0.022 0.2 Std Dev 0.5 0.009 0.2 Max 1.8 0.038 0.8 Min 0.06 0.002 0.02 6 eigenvectors and 6 signals: R,G,B with very-light-green and didymium filters Average 0.4 0.019 0.3 Std Dev 0.3 0.008 0.4 Max 1.1 0.037 1.9 Min 0.06 0.002 0.05 Effect of changing the number of eigenvectors to 9 channels and 9 eigenvectors Table VIII shows comparison of spectral reflectance performance in reflectance space for GretagMacbeth ColorChecker using various combination of 3 set of trichromatic signals. Table VIII. Spectral reconstruction using 9 eigenvectors; 9 signals. Patch E*94 reflectance factor rms error Metameric Index 9 eigenvectors and 9 signals: R,G,B without filter and with very-light-green and light-blue absorption filters Average 0.2 0.009 0.07 Std Dev 0.1 0.003 0.05 Max 0.4 0.019 0.2 Min 0.04 0.020 0.02 9 eigenvectors and 9 signals: R,G,B with didymium, very-light-green and light-blue absorption filters Average 0.3 0.009 0.08 Std Dev 0.2 0.003 0.04 Max 1.1 0.012 0.17 Min 0.06 0.002 0.01 9 eigenvectors and 9 signals: R,G,B without filter, with didymium and light-blue absorption filters Average 0.2 0.012 0.07 Std Dev 0.1 0.005 0.04 Max 0.5 0.027 0.2 Min 0.04 0.002 0.02 9 eigenvectors and 9 signals: R,G,B without filter, with didymium and very-light-green absorption filters Average 0.2 0.011 0.1 Std Dev 0.1 0.005 0.1 Max 0.5 0.022 0.6 Min 0.01 0.002 0.01 Looking the Table VII it is possible to see that the combination of R, G, B without filter and using very-light-green filter produced the best overall results. It is possible that these signal combinations give the best signal-to-noise ratio improving the performance. When 9 signals is used instead of 6 signals we can see improvement in reflectance factor rms error comparing Tables VII and VIII. However, the color difference did not improve dramatically. Moreover the various possible combinations of three signals did not affect the spectral reconstruction performance at all. Target II: Set of 147 painted patches Table IX summarizes the result of spectral reconstruction performance in reflectance space obtained for 147 painted patches using various combinations of signals. Table IX. Spectral reconstruction using 6 eigenvectors and 6 signals Patch E*94 reflectance factor rms error Metameric Index 6 eigenvectors and 6 signals: R,G,B without filter and with light-blue absorption filter Average 0.3 0.014 0.3 Std Dev 0.3 0.007 0.3 Max 1.3 0.031 1.4 Min 0.02 0.002 0.0 6 eigenvectors and 6 signals: R,G,B without filter and with very-light-green absorption filter Average 0.2 0.012 0.2 Std Dev 0.2 0.006 0.2 Max 0.7 0.030 1.0 Min 0.01 0.002 0.01 6 eigenvectors and 6 signals: R,G,B without filter and with didymium filter Average 0.6 0.015 0.9 Std Dev 0.5 0.009 0.8 Max 2.2 0.041 4.0 Min 0.04 0.002 0.01 6 eigenvectors and 6 signals: R,G,B with light-blue and with didymium filters Average 0.5 0.015 0.5 Std Dev 0.4 0.009 0.5 Max 1.6 0.046 2.2 Min 0.03 0.002 0.03 6 eigenvectors and 6 signals: R,G,B with light-blue and with very-light-green filters Average 0.3 0.017 0.3 Std Dev 0.2 0.011 0.2 Max 1.1 0.063 0.9 Min 0.04 0.003 0.01 6 eigenvectors and 6 signals: R,G,B with very-light-green and didymium filters Average 0.4 0.014 0.4 Std Dev 0.3 0.008 0.3 Max 1.4 0.047 1.3 Min 0.1 0.002 0.01 As in the spectral reconstruction of GretagMacbeth ColorChecker, the spectral reconstruction of 147 painted patches presented best performance for the combination of R, G, B signals without filter and using very-light-green filter. It is also possible to see that the spectral and colorimetric performances were not significantly different for various combinations of trichromatic signals. Target III: Set of 105 painted patches Table X summarizes the result of spectral reconstruction performance in reflectance space obtained for 105 painted patches using various combinations of signals. Table X. Spectral reconstruction using 6 eigenvectors and 6 signals Patch E*94 reflectance factor rms error Metameric Index 6 eigenvectors and 6 signals: R,G,B without filter and with light-blue absorption filter Average 0.8 0.019 0.4 Std Dev 0.5 0.006 0.3