## 3 Methodology
### Seeded Region Growing for Labeling Water Points  
Seeded region growing is a pixel-based image segmentation algorithm [19; 46; 47; 48]. In this research, the seeded region growing algorithm was applied on the 3D LiDAR points. The algorithm is divided into two main steps: selection of seed points and criterion for region growing (Figure 3). Previous studies mainly relied on manually selecting seed points or applying data-driven threshold values on the LiDAR data. Also, in region growing criteria, threshold values were manually selected to fit the tested data. We aimed to present a fully automated and unsupervised method for labeling water points based on seeded region growing using the automated extracted point features \(NOR\) and \(HV\).  
In seed points selection, the point feature _\"\(NOR\)\"_ was used to find the possible seed points. As mentioned previously, the water points have single and double returns when the data are collected at the infrared and green wavelengths, respectively. First, the points that have single returns (_points_single_) at the infrared wavelengths (e.g., 1064 nm) were extracted, which included points from built-up areas (building roofs and road surfaces) and vegetation as well as water surfaces. Second, the first points of the double returns (_points_first_of_double_) at the green wavelength (i.e., 532 nm) were extracted. These points included points from vegetation and may represent built-up areas (from power lines or fences) as well as water surfaces. For each point in _points_single_, the nearest point within the footprint of the green wavelength from _points_first_of_double_ was found. For simplicity's sake, the footprint was assumed to be a circle with radius \"\(r_{\text{G}}\)\", where \(r_{\text{G}}\) = 0.5 \(\times\) altitude \(\times\) beam divergence (\(\beta\)). The footprint was used to ensure that the point belonged to the same object. This step is essential for removing points that belong to built-up areas and vegetation with single returns. Thus, all points in _points_single_ that have nearest points from _points_first_of_double_ were considered as the possible seed points.  
It should be pointed out that vegetation could be recorded with single or more returns at various wavelengths due to different interaction between vegetation and those wavelengths as well as the change of the scan angles. Therefore, the point feature _\"\(HV\)\"_ was used to refine the possible seed points.  
The height difference within a searching radius for each point was checked against the variations in the point's elevations at the infrared wavelengths in C1 or C2. These variations are because of the presence of waves on the water surface and the fact that the Titan channels scan a given area in slightly different time periods. A threshold of 0.5 m was used in order to preserve horizontal surfaces and, hence, filter out non-water points. Thus, the remaining points were considered as water seed points. In the region growing criterion, all points in the scene were considered as neighboring points of each water seed point. Then, points within the neighborhood of each seed point were arranged according to their distance to the seed point. The \(HV\) was subsequently tested point by point against the variations in the point's' elevations in order to label all water points in the scene.