# Color Recognition of Transparent Plastic Based on Multi-Wavelength Transmission Spectrum
## 3 Results and Discussion
### Color Feature  
Based on the analysis in Section 3.1, the color feature \(F\) for each sample was set up using color parameters \(BG\), \(GR\) and \(RB\) that were obtained at 381 nm, 439 nm, 620 nm and white light sources, as described in Equation (4).  
\[\begin{array}{l}F=[\alpha BG_{381\text{nm}},\alpha BG_{439\text{nm}},\alpha BG _{620\text{mm}},\alpha BG_{white},\\ \beta GR_{381\text{mm}},\beta GR_{439\text{nm}},\beta GR_{620\text{mm}},\beta GR _{white},\\ \gamma RB_{381\text{mm}},\gamma RB_{439\text{nm}},\gamma RB_{620\text{mm}}, \gamma RB_{white}]\end{array} \tag{4}\]  
Figure 3: The mean values of the color parameters \(BG\), \(GR\) and \(RB\) of the colorless, light blue, light green and apple green plastic at 381 nm (**a**), 439 nm (**b**), 620 nm (**c**) and white (**d**) transmission light sources.  
where the subscript of \(BG\), \(GR\) and \(RB\) indicates that the parameter is calculated from the transmission spectrum acquired at the light source with that wavelength. \(\alpha\), \(\beta\) and \(\gamma\) are, respectively, the weights of the color parameters \(BG\), \(GR\) and \(RB\).  
The values of \(\alpha\), \(\beta\) and \(\gamma\) depend on the ability of the parameters \(BG\), \(GR\) and \(RB\) to reflect the color difference. As shown in Figure 4, the ability of the color parameters \(BG\), \(GR\) and \(RB\) to reflect the color difference is different, and the coefficient of variation was employed to evaluate the ability of the color parameters \(BG\), \(GR\) and \(RB\) to reflect color difference. For each color parameter, the coefficient of variation of the values at each transmission wavelength was calculated, and four coefficients of variation were obtained and then the mean of the four coefficients of variation was calculated, as shown in Table 2. The ratio of the mean values of the coefficients of variation of \(BG\), \(GR\) and \(RB\) was about 1:2:2:2.4, consequently, \(\alpha\):\(\beta\):\(\gamma\) was initially set to 1:2:2:2.4. However, further analysis showed that although the mean of the coefficient of variation of \(BG\) was small, the coefficients of variation at the wavelength of 381 nm and 439 nm were relatively large, which can reflect the color difference. Therefore, the proportion of \(\alpha\) should be appropriately increased. Multiple groups of \(\alpha\):\(\beta\):\(\gamma\) were analyzed by the experiment, and the results showed that the color recognition effect was the best when \(\alpha\):\(\beta\):\(\gamma\) was about 1:2:2. Generally, the sum of \(\alpha\), \(\beta\) and \(\gamma\) was set to 1, therefore, \(\alpha\) = 0.2, \(\beta\) = 0.4, \(\gamma\) = 0.4. It should be pointed out that the sum of \(\alpha\), \(\beta\) and \(\gamma\) can be set to other values as long as the ratio of the weights is not changed.  
As there were 40 samples, respectively, for the colorless, light blue, light green and apple green plastic, 40 sets of color features were obtained for each color category and were labeled by 1, 2, 3 and 4, respectively. Finally, a sample set containing 160 sets of color features was established.  
Figure 4: The color parameters \(BG\) (**a**), \(GR\) (**b**) and \(RB\) (**c**) of colorless, light blue, light green and apple green plastic.