# Detecting Green Mold Pathogens on Lemons Using Hyperspectral Images
## 3 Results and Discussion  
For the normalization, the intensity distribution of each spectral image from all infected states is averaged by adding up the intensities of all pixels making up the lemon image and then dividing it by the added number of pixels. These averaged intensities are divided by that of corresponding wavelength spectral image of the fresh lemon to normalize the intensities. This normalization eliminates the calibration problem incurred by the spectral intensity differences between different spectral ranges of the illumination lamp. The averaged spectral intensity \(I_{\lambda_{k}}^{j}\) of \(j\)th infected image at the spectral wavelength \(\lambda_{k}\), where \(j=1,\ 2,\ 3,\ 4,\ \cdot\ \cdot\ \cdot,\ 17\), including the fresh lemon, \(k=1,\ 2,\ 3,\ 4,\ \cdot\ \cdot\ \cdot,\ 16\), can be expressed as  
\[I_{\lambda_{k}}^{j}=\frac{\sum\limits_{i=1}^{n_{\lambda_{k}}^{j}}P_{i}}{n_{ \lambda_{k}}^{j}} \tag{1}\]  
where \(P_{i}\) and \(n_{\lambda_{k}}^{j}\) represent \(i\)th pixel intensity and the number of pixels making up each gray scale lemon image of \(j\)th infected image at the spectral wavelength \(\lambda_{k}\), respectively. The normalization can be expressed as  
\[\alpha_{\lambda_{k}}^{j}=\frac{I_{\lambda_{k}}^{j}}{I_{\lambda_{k}}^{0}} \tag{2}\]  
where, \(\alpha_{\lambda_{k}}^{j}\) and \(I_{\lambda_{k}}^{j}\) are the normalized coefficient and averaged intensity of \(j\)th infected image at the spectral wavelength \(\lambda_{k}\), respectively, and \(I_{\lambda_{k}}^{0}\) the averaged intensity of not damaged lemon image at \(\lambda_{k}\). When the holds taken from the completely infected lemon, as in image 20 of Figure 1, are grafted on the skin surface of healthy lemons, the grafted area is hardly identified for the spectral filter of 540 nm, 550 nm, and 560 nm, as shown in Figure 12. Figure 12 presents photographic images of the grafted area taken with 16 spectral filters used for Figures 5-8. The numbers in this figure represent the central wavelengths of the spectral filters. The grafted area appears to be of a gray color with no filter as shown in the leftmost image of Figure 12. This means that the molds are probably having RGB color components with almost the same intensity. When the spectral filters are used, the molds are hardly identified in the spectral range of 540 nm to 560 nm. This means that the spectral wavelength of the green molds is in the range of 540 nm to 560 nm. For the case of red color, the molds are still  
Figure 11: Intensity distribution of Figure 7b. identified up to 650 nm. Therefore, a spectral filter in the range of 535 nm to 565 nm will be enough for the accurate detection of the green mold pathogen because the spectral range is the most sensitive to the pathogens. The averaged spectral intensities of the 20 spectral images, as shown in Figure 1, are plotted in Figure 13 at each of the spectral wavelengths. The number of each curve corresponds to that of each sample in Figure 1. The intensity has the same relative scale as in Figures 8-11. Figure 13 shows that the spectral intensities at 570 nm have the minimum difference between samples. This is expected because the dominant wavelengths of the green molds and the fresh lemon are in the range of 535 nm to 565 nm and 580 nm, respectively. As sample 1 has the highest spectral intensity at 580 nm and very low spectral intensities at below 570 nm, the spectral intensity at 570 nm has an intermediate value between these two values. Sample 2 behaves the same way as sample 1. However, starting from sample 3, the intensity at 570 nm becomes lower than that of samples 1 and 2 and then increases as the sample number increase. For a few samples, the values can slightly exceed those of samples 1 and 2. Along with this feature, Figure 13 also shows other features: (1) the fresh lemon has the lowest spectral intensity at 550 nm, and (2) the intensity increases with sample numbers increase in the spectral ranges 510 nm to 560 nm though the increment between adjacent numbers is not the same.