# Reconstructing Nerve Structures from Unorganized Points
## 5 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subject** & **Total No. of Fascicles** & **No. of Branchings** & **No. of Complex Fascicles (\%)** \\ \hline Subject 1 & 49 & 20 & \(\approx\)33\% \\ Subject 2 & 47 & 21 & \(\approx\)28\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical details concerning two realistic nerve models used in this study. different dataset. Further details regarding the values of these parameters will be provided in the subsequent paragraphs. The parameter \(k\) is defined in Equation (9). It is worth noting that, for future parameter selection, a value of 5 was suitable in roughly 93% of cases examined in this study. However, values of 4 and 6 reflect special cases and should be considered when setting up this method with initial values. The parameter \(\alpha\), as introduced in Equation (30), plays a vital role in defining the area where omitted points will be sought. Achieving an optimal value for \(\alpha\) must be balanced due to the reasons and logic explained in Section 4.3. In our experimentation, we explored a range of values from \(2^{\circ}\) to \(90^{\circ}\), as these values align with the intended purpose; values below \(2^{\circ}\) result in a region that is too narrow, while values exceeding \(90^{\circ}\) yield regions that are excessively wide. It is noteworthy that, for nearly 97% of cases, any value within this range yields satisfactory reconstructions. However, in special cases, such as the one illustrated in the lower row of Figure 15, an angle between \(5^{\circ}\) and \(25^{\circ}\) proves necessary. In the context of nerve contour reconstruction, we determined that the optimal value for \(\alpha\) is \(8^{\circ}\). The parameter \(\theta\), as outlined in Equation (31), plays a pivotal role in consolidating clusters to formulate the final contour. When deliberating on the suitable value for this parameter, there was no predefined rationale regarding its permissible range. Unlike \(\alpha\), which intuitively had a \"forward\" direction, \(\theta\) possessed greater flexibility in its potential values. Consequently, we conducted experiments involving both the lower and upper limits of the angles that permit successful reconstruction. We systematically recorded the values that resulted in successful reconstructions, and these findings are summarized in Table 3, which presents statistical information regarding the range, i.e., the minimum and maximum angle values. As a practical rule of thumb, we identified the optimal value for \(\theta\) to be \(45^{\circ}\). Figure 16: Certain points (marked with arrows) that the algorithm deems redundant are omitted during the reconstruction process. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Minimum Angles for** & **Maximum Angles for** \\  & **Successful Reconstruction** & **Successful Reconstruction** \\ \hline Mean value & \(17.34^{\circ}\) & \(252.5^{\circ}\) \\ Standard deviation & \(13.55^{\circ}\) & \(115.97^{\circ}\) \\ Minimum & \(5^{\circ}\) & \(110^{\circ}\) \\ Maximum & \(45^{\circ}\) & \(360^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of minimum and maximum angle ranges for successful reconstruction with parameter \(\theta\).