## 3 Results and Discussion
### Remote Sensing and IR Camera  
The experiment was designed such that one IR video could be captured every twenty minutes over a pipeline. The experiment was run for three hours, producing nine thermograms. It took around sixty minutes for IR detection of water leakage. The experimental setup is shadowed by surrounding buildings, so the temperature of the soil was anticipated to decrease with time. The images shown in Figures 9-11 are the acquired thermograms of the model WDN shown in Figure 4b. Figure 9 shows the captured grayscale RGB format, and Figure 10 shows the false-color IR images, which are used for better visualization of the leak locations. Figure 10: Multitemporal false-color IR images. Figure 9: Multitemporal raw IR images. The temperature ranges have been set automatically by the camera. The white circles indicates potential leakage location. The leakage areas and shadows shown in the IR images have overlapped luminance values, so temporal-based techniques are required to distinguish them. In addition, a decrease in the field temperature would reduce the soil's temperature. As such, the dynamic ranges of the luminance of all the thermograms are transformed to remove the effects of the field temperature using the following equation:  
\[\mathcal{L}_{s}(t_{i})=\mathcal{L}(t_{-}i)-min\{\mathcal{L}(t_{i})\} \tag{1}\]  
where \(\mathcal{L}(t_{i})\) is the luminance of the IR images and \(\mathcal{L}_{s}(t_{i})\) represents the shift-transformed luminance at a particular time \(t_{i}\). The method proposed in this paper is to quantify the time variation of the transformed luminance \(\mathcal{L}_{s}(t_{i})\). Figure 11 has the best illustration of leaks captured on the IR camera as it shows the log-ratio images. One of the variables that can affect the readings shown on the thermograms is whether the temperature of the leaked water is higher or lower than the soil's temperature. In order to highlight the temperature changes in either case and improve the visual detection of the leakage spots, the following log-ratio equation was used:  
\[R_{l}(t_{i})=\left|log\frac{\mathcal{L}_{s}(t_{i}+1)}{\mathcal{L}_{s}(t_{i})} \right|=\left|log\frac{\mathcal{L}_{s}(t_{i})}{\mathcal{L}_{s}(t_{i}+1)}\right| \tag{2}\]  
where \(R_{l}\) represents the log-ratio image. The log-ratio resulted in the best images for visual detection, as the equation focuses on only one source of leakage. As such, this method allows for the identification of leakage areas and negates non-leakage and shadowed areas. The log-ratio image is derived from the ratio image that is defined by:  
\[R(t_{i})=\frac{\mathcal{L}_{s}(t_{i}+1)}{\mathcal{L}_{s}(t_{i})}+\quad\frac{ \mathcal{L}_{s}(t_{i})}{\mathcal{L}_{s}(t_{i+1})} \tag{3}\]  
where \(R\) represents the ratio image. While ratio images are capable of distinguishing leakage areas from non-leakage areas [23], they do not offer the best visuals to display the locations of leaks. Therefore, the log-ratio method is best at detecting the temporal variation of the temperature due to leakage. Moreover, hot spot analysis of the IR images has been employed to detect the leaks. As observed in Figure 11, there is a clear formation of light blue spots over time in the IR images. The light blue spots indicate the locations where the temperature was reduced due to increased moisture in the soil from the leak. IR images with higher resolutions may be able to capture more distinct temperature contrasts between the soil and the water leak. It is important to note that the general moisture of the soil can drastically affect the readings of the IR camera. That is, it can be more difficult to detect leaks if the soil has an initially high percentage of moisture [4]. Previous studies conducting water leak and oil spill detection  
Figure 11: Analysis of IR images, white circles indicating the potential leak location and blue areas indicating the surrounding. also observed it to be a suitable technology [4; 34].