# Characterization and Separation of Traditional and Bio-Plastics by Hyperspectral Devices
## 3 Results and Discussion
### Hyperspectral Index Validation  
The last phase consists in verifying whether hyperspectral indexes, calculated employing only samples of virgin materials, are suitable for separating the different polymers no matter the shape of the sample. The separation of two materials of unknown typology into two classes (for instance class 1 and class 2) is based on the comparison of the hyperspectral indices computed employed the spectral signature belonging to the polymer ROI with the given threshold value: if the value of the index is lower than the threshold value, the signature is assigned, for example, to class 1, vice versa if the value of the index is greater than the threshold it will be assigned to class 2. The separation accuracy is introduced to quantitatively evaluate the performance of the hyperspectral indices computed. It is defined as the ratio (expressed as a percentage) between spectral signatures correctly assigned to a class (class 1 or 2) and the total number of spectral signatures belonging to the same class. The pairs of polymers used for the separation accuracy computation are, consistently with the previous analysis, PET-PLA, PS-PLA and PET-PS and samples of virgin materials are considered for index validation, as well as samples in flakes, pieces and original shape. The separation accuracy results are reported as histograms in Figures 9 and 10, where the different hyperspectral indexes and their performances (expressed as a percentage) appear. Remarkable separation accuracies are achieved for entire set of hyperspectral indices provided by the correlation matrix analysis. The application of the CR procedure is in general useful to increase the separation accuracies. To strengthen the index validation, the separation accuracy is computed also for samples in flakes, pieces and with their original shape. For PET-PLA samples, the accuracy is higher than 83% with the best performance provided by the wavelength ration 1170 nm/1650 nm (100% accuracy for both polymers). For PLA-PS samples, the accuracy is 100% for wavelength ratios 1430 nm/1140 nm, 1160 nm/1140 nm and 1470 nm/1640 nm. Finally, for PET-PS samples, the index providing the best separation accuracy is 1120 nm/1150 nm, whereas accuracy higher than 85% are achieved for the other two ratios. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Spectral Indices** & **PET** & **PS** & \\ \(\mathbf{\mu_{1}}\) & \(\mathbf{\mu_{2}}\) & **Threshold** \\ \hline \multicolumn{4}{c}{**Reflectance of Primary Raw Materials**} \\ \hline \multicolumn{4}{c}{\(\mathbf{\lambda_{1}/\lambda_{2}}\)} \\ \hline
1120/1150 & 0.942 & 1.945 & 1.443 \\
1150/1660 & 2.571 & 1.213 & 1.892 \\
1210/1660 & 2.989 & 1.820 & 2.405 \\ \hline \multicolumn{4}{c}{**Reflectance of Primary Raw Materials after Continuum Removal**} \\ \hline \multicolumn{4}{c}{\(\mathbf{\lambda_{1}/\lambda_{2}}\)} \\ \hline
1120/1150 & 0.935 & 1.912 & 1.424 \\
1150/1660 & 1.713 & 0.800 & 1.257 \\
1210/1660 & 2.019 & 1.237 & 1.628 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: First set of spectral indices for the pair PET-PS. \(\mathbf{\lambda_{1}/\lambda_{2}}\) (\(\mathbf{\lambda_{1}-\lambda_{2}}\)) are computed as the ratio among reflectance values at wavelengths \(\mathbf{\lambda_{1}}\) and \(\mathbf{\lambda_{2}}\). Figure 9: Accuracy assessment of spectral indices computed employing the reflectance values without post-processing for pairs **(a)** PET-PLA; **(b)** PS-PLA; **(c)** PET-PS. Figure 10: Accuracy assessment of spectral indices computed employing the reflectance values after the continuum removal procedure was applied for pairs **(a)** PET-PLA; **(b)** PS-PLA; **(c)** PET-PS. The method proposed to separate PET, PS and PLA waste samples can be potentially employed in a mechanical recycling plant. It involves a sequential procedure sketched in Figure 11 ('tree procedure'). As clearly demonstrated above, the continuum removal operation is profitably applied to the spectral signatures to enhance the separation process performance.