# Reconstructing Nerve Structures from Unorganized Points
## 5 Results and Discussion  
The combination of methods and procedures reported in the previous section enables the reconstruction of one (Figure 9) or several contours (Figure 11). Figure 11: An example of a cross-section that belongs to a complex, branching fascicle. (**A**) Individual clusters generated by the algorithm. (**B**) The final contours result from the merging of these clusters. Notably, the algorithm achieves the successful reconstruction of sharp corners and effectively distinguishes between closely positioned contours. Figure 10: (**A**) Input points for one of the contours. (**B**) Inadequate area selection (G(X)) in the valley-seeking clustering step of the algorithm. When the chosen radius is too small, the algorithm struggles to create an adequate number of sufficiently large clusters, resulting in multiple clusters containing only one or two points. This leads to the “missing” segment of the contour on the right. Figure 9: An example of two clusters/lines (**A**), which the algorithm recognizes as one closed contour and merges into one cluster (**B**). A complete reconstruction of one complex (i.e., that has at least one branching along its length) nerve fascicle is shown in Figure 12. Fascicle shapes, dimensions, and branching locations differ across nerves and individuals. The example from Figure 12 shows a fascicle branching from a single section (in the lower part) into two sections (in the upper part of the figure). Indeed, nerve structures such as this one can present the biggest challenge to the algorithm, due to the complexity of nerve cross-sections at the branching points. This intricacy can lead to semi-connected contours with pronounced angles or contours in near proximity to one another, etc. Figure 13 displays a segment (due to the clarity of the representation) of the reconstructed fascicles from one of the two subjects. In the context of comparing our algorithm with existing state-of-the-art methods for contour reconstruction from 2D point sets, we primarily focused on analyzing two algorithms: HNN-Crust [28] and Vicur [24]. Our selection of these two was informed by a thorough review paper [11], where they particularly distinguished themselves from other methods in an experimental study. We also selected these two algorithms because, as highlighted in Section 2, they represent cutting-edge techniques within their respective algorithm categories. HNN-Crust is the latest iteration in the Crust algorithm lineage,  
Figure 12: Nerve fascicle reconstruction by cross-sectional levels. Each color represents a reconstructed contour. Fascicle branching is visible in the upper segment of the figure. Figure 13: A section of nerve fascicles is shown for one of the subjects. Visible on the far **left** and **right** are two complex fascicles with branching. introducing new enhancements to this widely used algorithm category. On the other hand, Vicur is an evolved version of the acclaimed Discur algorithm. Given that it was developed by authors previously involved with Discur, we opted to analyze this advanced iteration, Vicur. While HNN-Crust and Vicur adeptly handle a broad range of reconstruction scenarios, they encountered challenges with specific nerve contour cases presented in this study. Particularly in situations requiring the differentiation of two closely situated contours, our newly introduced algorithm demonstrated a higher success rate than Vicur (Figure 14) and HNN-Crust (Figure 15). Figure 14: A comparison of the Vicur algorithm and our method. (**A**) Input points; (**B**) reconstruction performed with our approach; (**C**) reconstruction carried out using the Vicur technique. Due to the closeness of the two contours to be reconstructed and the point distribution in the segment where those contours are in close proximity, the Vicur algorithm mistakenly skipped from one contour to another and fused them together. Figure 15: Two illustrative comparisons between the HNN-Crust algorithm and our approach.