# An Efficient Numerical Approach for Field Infrared Smoke Transmittance Based on Grayscale Images
## 4 Results and Discussion  
With the field experiment setup and grayscale smoke transmittance model introduced above, a field trial example is illustrated and discussed in this section. A flow chart of the approach is shown in Figure 5 below.  
First of all, a video of the target scene is input into the Matlab computer software (R2012a, Mathworks, Natick, MA, USA); secondly, the grayscale image is converted into a binary image for the convenience of target positioning; thirdly, the motion path of dynamic smoke is tracked and recorded in the image; lastly, the smoke transmittance of each target is calculated based on the grayscale smoke transmittance model, and an \(n\times m\) smoke transmittance matrix can be output at each image frame. Thus, a smoke transmittance matrix cube containing a smoke transmittance matrix of each frame is formed in the end. Combined with the transmittance threshold, we can demonstrate whether the target is efficiently obscured by a smoke screen during anytime of the smoke diffusion process.  
In order to observe the variation trend of smoke transmittance, we chose 8 targets that were exactly within the smoke transport and diffusion path as study objects according to the video. In Figure 6, targets circled in red are the selected study objects to output its smoke transmittance variation graph. By using the three value computing methods mentioned in Section 3, smoke transmittance curves were obtained and are shown in Figure 7.  
Figure 4: Schematic picture of three value computing methods.  
Figure 5: Field smoke transmittance trial flow chart.  
Figure 6: Study objects in infrared target array.  
Figure 7: Smoke transmittance curves of eight study objects shown in Figure 6 during the smoke diffusion process. \(\mathrm{T_{a}}\), \(\mathrm{T_{b}}\), and \(\mathrm{T_{c}}\) represent transmittance results from three different methods mentioned in Section 3.  
In Figure 7, calculation curves are almost consistent with the theory analysis. The smoke transmittance remains 1 at first, when there is no block of radiation in line of sight. After the release of smoke, smoke transmittance gradually drops to nearly 0 due to the obscuration effect of the smoke cloud. When the smoke cloud continues to drift out of the target area with the wind, the transmittance finally recovers to 1 again.  
In theory, the true value of transmittance should be between 0 and 1. According to the three value computing methods shown in Figure 7, methods (a) and (b) have large relative errors compared with method (c). For example, in (5) and (8) of Figure 7, the value of transmittance by method (a) even reaches \(-0.3\) and 1.3 at 5 s, respectively. This is because a smoke cloud forms and has very intense infrared radiance. Since method (c) extracts more samples adjacent to the target, the value it calculates is closer to the true value of the background condition. Thus, it is suggested that method (c) be applied to calculate the background condition of targets.  
Based on the infrared images and grayscale smoke transmittance model, the smoke transmittance of the study objects can be calculated at any time. Figure 8 below is the image of the target scene at 9.72 s, and Table 1 below describes the smoke transmittance at each target.