# Identification of Industrial Heat Source Production Areas Based on SDGSAT-1 Thermal Infrared Imager
## 2 Materials and Methods
### Method
#### 2.3.2 Multi-Feature Extraction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Feature Type** & **Name** & **Notes** & **Original data** \\ \hline
1 & & \(\mathrm{T_{1}}\) & Satellite brightness temperature of Band 1 & SDSGSAT-1 TIS data \\
2 & & \(\mathrm{T_{2}}\) & Satellite brightness temperature of Band 2 & SDSGSAT-1 TIS data \\
3 & & \(\mathrm{T_{3}}\) & Satellite brightness temperature of Band 3 & SDSGSAT-1 TIS data \\
4 & Thermal features & \(\mathrm{RI_{1}}\) & Thermal radiation index features (\(\mathrm{RI_{1}}\), \(\mathrm{RI_{2}}\), \(\mathrm{RI_{3}}\) and \(\mathrm{RI_{4}}\)), and 3 optical features (NDVI, NDBI, and NDWI). & \\ \hline
5 & & \(\mathrm{RI_{2}}\) & Thermal radiation indices & SDSGSAT-1 TIS data and \\
6 & & \(\mathrm{RI_{3}}\) & \(\mathrm{RI_{3}}=\frac{\mathrm{T_{2}-T_{1}}}{\mathrm{\rho_{NIR}}}\) & Landsat-8 OLI data \\
7 & & \(\mathrm{RI_{4}}\) & Thermal radiation indices & SDSGSAT-1 TIS data and \\  & & & \(\mathrm{RI_{4}}=\frac{\mathrm{T_{3}-T_{1}}}{\mathrm{\rho_{NIR}}}\) & Landsat-8 OLI data \\ \hline
8 & & \(\mathrm{NDVI}\) & Normalized difference vegetation index & Landsat-8 OLI data \\  & Optical features & \(\mathrm{NDVI}=\frac{\mathrm{\rho_{NIR}-\rho_{NIR}}}{\mathrm{\rho_{NIR}+\rho_{ IR}}+\mathrm{\rho_{IR}}}\) & Landsat-8 OLI data \\  & & & \(\mathrm{NDBI}=\frac{\mathrm{\rho_{NIR}-\rho_{NIR}}}{\mathrm{\rho_{NIR}+\rho_{ NIR}}+\mathrm{\rho_{NIR}}}\) & Landsat-8 OLI data \\
9 & & \(\mathrm{NDWI}\) & Normalized difference water index & Landsat-8 OLI data \\  & & & \(\mathrm{NDWI}=\frac{\mathrm{\rho_{NIR}-\rho_{NIR}}}{\mathrm{\rho_{C}+\rho_{ NIR}}}\) & Landsat-8 OLI data \\ \hline \hline \end{tabular} Notes: \(\mathrm{\rho_{NIR}}\) is the reflection value in the NIR band, \(\mathrm{\rho_{B}}\) is the reflection value in the red band, \(\mathrm{\rho_{SWB}}\) is the reflection value in the mid-wave IR, and \(\mathrm{\rho_{C}}\) is the reflection value in the green band.  
\end{table} 
Table 3: The description of multi-features based on thermal features and optical features. Ten features were obtained by our method from SDGSAT-1 TIS and Landsat-8 OLI data. They include 3 brightness temperature features \(\mathrm{T_{1}}\), \(\mathrm{T_{2}}\), and \(\mathrm{T_{3}}\)), 4 thermal radiation index features (\(\mathrm{RI_{1}}\), \(\mathrm{RI_{2}}\), \(\mathrm{RI_{3}}\) and \(\mathrm{RI_{4}}\)), and 3 optical features (NDVI, NDBI, and NDWI). \[\text{RI}_{\text{4}}=\frac{\text{T}_{\text{3}}-\text{T}_{\text{1}}}{\rho_{\text{NIR}}} \tag{6}\]  
where T\({}_{\text{1}}\), T\({}_{\text{2}}\), and T\({}_{\text{3}}\) are the satellite brightness temperatures of SDGSAT-1 TIS Band 1, Band 2, and Band 3. \(\rho_{\text{NIR}}\) represents the reflectance value on the near-infrared band of the Landsat-8 OIL data. Optical features are extracted from optical remote sensing images by sensors that detect electromagnetic radiation in the visible, near-infrared, and sometimes shortwave infrared regions of the electromagnetic spectrum [44]. They provide valuable information about the Earth's surface, especially land cover information [45]. They are essential in various remote sensing applications, including land cover classification, vegetation health monitoring, and the detection of land use and land cover changes [46; 47; 48]. The normalized difference vegetation index (NDVI) [49], building index (NDBI) [18], and water index (NDWI) [50] are three important and widely applied optical feature indices used to analyze and monitor different aspects of the Earth's surface. Therefore, the above three indices were introduced to distinguish IHSPAs from other land covers in this study. Considering the absence of the medium infrared band of the SDGSAT-1-MII data, which is essential to extract the NDBI, Landsat-8 OLI data with stable data quality and the same spatial resolution as the SDGSAT-1 TIS data were used to extract the NDVI, NDBI, and NDWI. These optical indices were calculated from Landsat-8 OLI data by using the corresponding spectral bands [51].