## 4 Fire detection algorithms
### Selection of background pixels  
If the pixel has been identified as a potential fire pixel, the radiant statistical information of its neighboring pixels will be adopted to estimate the brightness temperatures of the fire-free proportion in it. A valid background pixel should meet the following conditions: (1) it is not covered by clouds, which are identified with an external cloud mask; (2) It is not itself a potential fire pixel; (3) it was not classified as water, sun glint, fire scar or data gap. At first a 5\(\times\)5 window (1.5\(\times\)1.5 km) centered on the potential fire pixel is selected to collect the background information. If the valid background pixels in this window are less than 25%, it can be increased grow up to 30\(\times\)30 pixels (9\(\times\)9 km) until 25% valid pixels are found and the number of valid background pixels is at least eight. If a sufficient number of valid background pixels can be identified, several statistical values will be computed for fire detection; otherwise the pixel is classified as an \"unknown\" pixel which will be not analyzed in the following tests [10, 18]. These computed statistics mainly include:  
\(\overline{T_{3B}}\), the mean of \(T_{3}\)  for the valid neighboring pixels  
\(\delta_{3B}\), the mean absolute deviation of \(T_{3}\)  for the valid neighboring pixels  
\(\overline{T_{34B}}\), the mean of \(T_{3}-T_{4}\)  for the valid neighboring pixels  
\(\delta_{34B}\), the mean absolute deviation of \(T_{3}-T_{4}\)  for the valid neighboring pixels  
The mean absolute deviation is employed as a measure of statistic properties of the background  
Figure 2: The difference of brightness temperature between MIR and TIR channel of HJ-1B data.  
window rather than the standard deviation since it is more efficient to the normal and some non-normal distributions [30].  
_4.6. Identification of fire pixels_  
In summary, a pixel will be recognized as a fire pixel after the following steps:  
1) It is thought as a potential hot pixel if \(T_{3}>308\) K, \(T_{34}>8\) K, and \(\rho_{2}<0.3\);  
2) A pixel is assumed to be cloud if \(\rho_{1}+\rho_{2}>0.8\)_or_\(T_{4}<265\) K or  
\(\rho_{1}+\rho_{2}>0.6\)_and_\(T_{4}<285\) K  
3) A pixel is assumed to be water if \(\rho_{1}<0.1\)_and_\(\rho_{2}<0.1\)_and_ NDVI \(<0\)  
4) It is recognized as strong sun glints if \(\left|\rho_{1}-\rho_{2}\right|<0.01\). [6]  
5) It is recognized as the highly reflective clouds if \(\rho_{2}>0.6\) ;  
6) If one of the following tests (equation (5) or (6)) can be satisfied, it will be classified as a fire pixel:  
\[T_{3}>360K \tag{5}\]  
\[T_{3}>\overline{T_{3B}}+3.5\times\delta_{3B} \tag{6}\]  
Equation (5) has been described in 4.3. The first expression of equation (6) means that if the brightness temperature of MIR channel is higher enough, compared with the mean background brightness temperature of the same channel, the pixel may be a fire pixel.  
The second expression of equation (6), which is restricted to daytime pixels, is primarily used to reject small convective cloud pixels that can appear warm in the MIR channel (due to reflected sunlight) yet cool in the TIR channel [10, 28]. It can also help reduce coastal false alarms that sometimes occur when cooler water pixels are unknowingly included in the background window [10]. The last expression of equation (6) is that the difference of brightness temperature of MIR and TIR  
Figure 3: An illustration of the histogram of \(\delta_{34B}\)  
channel should be larger enough. The histogram of \(\delta_{34\delta}\), shown in Figure 3, indicates that the mean absolute deviation is far less than 8 K. The detailed flow chart of fire detection is shown in Figure 4: