# Reconstructing Nerve Structures from Unorganized Points
## 6 Conclusions  
In this paper, we present an algorithm designed to reconstruct realistic nerve cross-sectional contours from unsorted points. Our approach addresses the complex geometry of human nerves' internal structures, characterized by frequent fascicle crossings and branching, presenting the algorithm with challenges such as handling sharp corners and closely positioned individual contours that require precise differentiation.  
This innovative method has significant potential contributions to the field of neuro-prostheses, particularly in simulating natural sensations in amputated limbs. We recognize the ongoing advancements needed in this area. Additionally, this study built upon our previous work in modeling nerve geometry, as detailed in [29].  
Our newly developed method offers several key advantages when compared to existing approaches for curve reconstruction from unarranged points:  
* Handling nonuniform point sets: Our method excels in working with nonuniform sets of points and is capable of reconstructing one or more contours, even when they are not necessarily smooth.
* Reconstructing closely positioned contours: An essential advantage of our algorithm is its proficiency in reconstructing closely positioned contours, a task where many existing methods face challenges.
* Automation: Once the parameters are set for the input values and remain relatively consistent, our algorithm operates without the need for further manual input from the user.
* Dynamics and fascicle model: Unlike many existing methods that primarily focus on geometric considerations, our algorithm stands out by incorporating dynamics and implicitly integrating a fascicle model through an adaptive Kalman filter.
* Innovative combination: To our knowledge, there is currently no algorithm for curve reconstruction from randomized points that combines valley-seeking clustering with a Kalman filter and NN classification method.  
A comparative analysis with state-of-the-art methods demonstrates that our approach excels in cases involving intricate internal nerve structures, making it particularly suitable for such scenarios. While it may not be ideal for cases with a small number of input points, it outperforms other methods in situations similar to those presented here.  
In this paper, we primarily focused on reconstructing closed contours due to the nature of the contours examined. However, our method has the potential to reconstruct open lines with minor algorithm modifications. In future work, we plan on expanding the algorithm's capabilities to handle open curves and, potentially, make the parameters more robust to the input values.  
Beyond its primary purpose, this innovative method has broader potential applications and can serve as inspiration or a foundational technique in various fields. These encompass 2D and 3D image processing, target tracking (see Figure 6), and spatial analysis of linearly arranged points across diverse domains, including biomedicine. Its impact extends not only to the field of simulation planning in neuroprosthetics, but also to virtual surgeries and many other specialized domains.  
Conceptualization, J.K. and Z.D.; methodology, J.K. and Z.D.; software, J.K.; validation, J.K., G.K. and Z.D.; formal analysis, J.K.; investigation, J.K.; data curation, J.K.; writing--original draft preparation, J.K.; writing--review and editing, J.K., G.K. and Z.D.; visualization, J.K.; supervision, Z.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data Availability Statement: Data are available from the corresponding author upon request.  
The authors declare no conflict of interest.