## 3 Results  
The edge points were compared with the ground truth case based on the manual detection of key boundary points by 15 volunteers. All results are presented in Figure 6, which confirms that the proposed approach shows results similar to the crowdsourcing-based approach.  
Table 1 summarizes the differences between the active contour method and the local gradient estimation method for a single image, for points of interest (highest point, left equator point, right equator point, left contact point, right contact point) as shown in Figure 7, and compare the two methods with the ground truth, which is the average value of the results obtained by volunteers. The comparison is made between the coordinates of the points of interest, i.e., the row and column of each point of interest for the three methods. The table shows that the coordinate values of the edge points obtained from the proposed method are very similar to the ground truth, unlike the edge point obtained from the active contour method, which proves that the proposed method is more accurate than the active contour method.  
The results in Table 1 show that the method based on local gradient estimation method and ground truth (crowdsourcing method) is similar with slight differences in a few pixels and closer to the droplet boundary at points of interest, compared to the active contour method. These differences significantly increase in the contact area between the droplet and the base.  
Figure 6: Comparison between the 3 methods. (**a**) Active contour (continuous line), ground truth (blue points), the proposed method (yellow points). (**b**) Superposition of points from the ground truth and the proposed method on the original image.  
Figure 8 shows a comparison of three different images of the same specimen taken at different temperatures at 1175 \({}^{\circ}\)C, 1133 \({}^{\circ}\)C, and 1234 \({}^{\circ}\)C for images 1, 2, and 3, respectively. The images in the upper part show the edge points on the original images, and the images in the lower part show the edge points obtained from the gradient method and the active contour line.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Active Contour** & **Local Gradient Estimation Edge Detection** & **Ground Truth (Mean Value)** \\ \hline
**Highest point** & P1 [646, 535] & P1 [661, 538] & P1 [653, 537] \\
**Left equator point** & P2 [412, 757] & P2 [418, 755] & P2 [415, 752] \\
**Right equator point** & P3 [903, 757] & P3 [899, 749] & P3 [901, 749] \\
**Left contact point** & P4 [466, 904] & P4 [483, 908] & P4 [487, 911] \\
**Right contact point** & P5 [853, 905] & P5 [838, 908] & P5 [835, 911] \\ \hline \hline \end{tabular}
\end{table}
Table 1: The coordinate values of the three methods for the points of interest (highest point, left equator point, right equator point, left contact point, and right contact point).  
Figure 7: The points of interest: P1 (highest point), P2 (left equator point), P3 (right equator point), P4 (left contact point), and P5 (right contact point).  
The results presented above indicate that the proposed method can be implemented on more than one image and gives accurate localization of the edge points of the droplet. The proposed approach could be developed in the future for a large range of images. Moreover, the extracted point set can be used to measure the contact angle based on the ellipse approximation method proposed in [18] and check whether it improves the calculated values significantly. This work is in progress.