Accurately measuring the spatial extension distance of nerve bundles in completing a split/merge is impossible because no clear mathematical definition exists for the starting and ending positions in nerve-bundle splitting/merging. We manually count the number of nerve-bundle splits/merges in long nerve segments, which is labor-intensive, inefficient, and prone to counting errors. Currently, the mathematics are unclear for the nerve-bundle diameter before and after splitting/merging. This paper explores these problems and proposes nerve-bundle splitting/merging rules. Based on the method of defining the beginning and ending positions of nerve-bundle splitting/merging, we explored the mathematical law of equivalent diameter of nerve bundles before and after splitting/merging. The experimental results revealed that the moving average of circularity of nerve bundle accurately defines the beginning and ending positions of nerve-bundle splitting/merging. The diameter of the nerve bundles before and after split/merge approximately conforms to the principles of the Da Vinci formula. The proposed automatic counting algorithm based on centroid offset matching obtains the number of split/merged nerve bundles in the sequence scan images with 100 % accuracy. The mathematical definition of the starting and ending positions of nerve-bundle splitting/merging proposed in this paper is accurate and strict and is the foundation of subsequent research. The proposed automatic counting algorithm based on centroid offset matching (ACA-COM) can accurately and efficiently count the number of times the nerve bundles split and merge in sequential images. The mathematical law satisfied by the diameter of the nerve bundles before and after splitting/merging reflects that the nerve bundles tend to have better capability to resist breaking.

中文翻译：

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人周围神经节段束分裂/合并模式的数学定义和规则

准确测量神经束在完成分裂/合并时的空间延伸距离是不可能的，因为对于神经束分裂/合并的起始和结束位置不存在明确的数学定义。我们手动计算长神经段中神经束分裂/合并的数量，这是劳动密集型、低效的，并且容易出现计数错误。目前，分裂/合并前后神经束直径的数学计算尚不清楚。本文探讨了这些问题并提出了神经束分裂/合并规则。基于定义神经束分裂/合并起始和结束位置的方法，我们探索了神经束分裂/合并前后等效直径的数学规律。实验结果表明，神经束圆度的移动平均值准确地定义了神经束分裂/合并的开始和结束位置。分裂/合并前后神经束的直径大致符合达芬奇公式的原理。所提出的基于质心偏移匹配的自动计数算法以100%的准确度获得序列扫描图像中分裂/合并神经束的数量。本文提出的神经束分裂/合并起始和终止位置的数学定义准确、严格，为后续研究奠定了基础。所提出的基于质心偏移匹配的自动计数算法（ACA-COM）可以准确有效地计数序列图像中神经束分裂和合并的次数。神经束分裂/合并前后的直径所满足的数学规律反映了神经束往往具有更好的抗断裂能力。