# A Spatio-Temporal Model for Forest Fire Detection Using HJ-IRS Satellite Data
## 3 Methodology
### Overview of the Improved Algorithm
#### 3.2.4 Relative Fire Pixel Judgment Based on STM
In this study, the valid neighboring pixels were defined as those that: (i) contained usable observations; (ii) were not contaminated by clouds; and (iii) were not background fire pixels. Integration of Spatial and Temporal Information  
For single-date fire detection methods, a temperature anomaly is the variation between a particular temperature and the average temperature for its neighboring pixels (Equation (1)) because the fire  
Figure 9: Correlation coefficients between the inspected time series and the neighboring time series. produces a local increase in temperature above that of the neighboring pixels. However, it is hard to obtain enough valid neighboring pixels when there is a large fire, and the window size must be large enough for high-resolution images. For multi-temporal images, a pixel that has a BT significantly higher than the values in previous moments will also be regarded as a fire pixel (Figure 10). Therefore, to compare the inspected pixel's BT with its previous BTs, we added additional temporal information to STM by assigning different weights to multi-temporal images (Equation (12)). In addition, the mean absolute deviation varied tempestuously in different images, which resulted in instability in the forest fire detection results. To obtain a more robust result, we also added different weights to the calculation of the mean absolute deviation (Equation (13)). In summary, the approach was based on a change detection scheme that detects signal anomalies by utilizing the spatio-temporal domain of the HJ-IRS data. \[\mu_{n+1}=\rho_{2}\times T^{\prime}{}_{t_{n+1}}+(1-\rho_{2})\times\mu_{t_{n}} \tag{12}\]  
\[S_{t_{n+1}}=\rho_{2}\times\delta_{t_{n+1}}+(1-\rho_{2})\times S_{t_{n}}\ \ (0 \leqslant\rho_{2}\leqslant 1) \tag{13}\]  
where \(\delta_{t_{n+1}}\) is the mean absolute deviation of \(T_{t_{n+1}}(i,j)\in SC_{t_{n+1}}\), \(\mu_{t_{1}}=T^{\prime}_{t_{1}}\), and \(S_{t_{1}}=\delta_{t_{1}}\). We used the mean absolute deviation instead of the standard deviation because the mean absolute deviation is more resistant to outliers than the standard deviation [8]. \(\rho_{2}\) is a learning parameter that controls the different weights of the multi-temporal images. This parameter should not be too small; reasonable values range from 0.85 to 0.95. In this paper, we choose \(\rho_{2}=0.9\). Relative Fire Pixel Judgment  
In this study, we used the BT from band 7 and the difference in the BTs from band 7 and band 8 to detect the forest fire. The background BTs from band 7 and band 8 were predicted using Equation (11), and the absolute deviation was calculated using Equation (13). For a potential pixel to be classified as a true fire pixel, it should satisfy the following Equations:  
\[T_{T_{T_{n}}}(lx,ly)>\mu_{T_{Ta}}+\lambda_{1}\times S_{T_{Ta}} \tag{14}\]  
Figure 8:0  
where \(\Delta T_{t_{n}}(lx,ly)=T_{T_{Ta}}(lx,ly)-T_{8t_{n}}(lx,ly)\); \(\Delta\mu_{t_{n}}=\mu_{T_{Ta}}-\mu_{8t_{Ta}}\), \(T_{T_{Ta}}(lx,ly)\) and \(T_{8t_{n}}(lx,ly)\) are the observed BTs from band 7 and band 8 for pixel \((lx,ly)\) in the image acquired at time \(t_{n}\), respectively; \(\mu_{T_{Ta}}\) and \(\mu_{8t_{n}}\) are the weighted background BTs calculated using Equations (11) and (12), respectively; \(S_{T_{Ta}}\) and \(\Delta S_{t_{n}}\) are calculated using Equation (13) with mean absolute deviations of \(T_{T_{Ta}}(i,j)\) and \(\Delta T_{t_{n}}(i,j)\), respectively; and \(\lambda_{1}\) and \(\lambda_{2}\) are learning parameters that can be calibrated to control the detection results. For comparison, we chose \(\lambda_{1}=3\) and \(\lambda_{2}=3.5\), as defined in [24]. Figure 8:1 Time series of fire pixels. The red marks represent fire points.