作为自组织现象的弦收紧：最短同伦路径、光滑路径和凸包的计算
String Tightening as a Self-Organizing Phenomenon: Computation of Shortest Homotopic Path, Smooth Path, and Convex Hull
摘要：
几十年来，自组织现象一直是神经网络社区的特殊兴趣。在本文中，我们研究了自组织映射（SOM）的一个变体，它模拟了当弦从一端或两端收紧时，形成弦的粒子的自组织现象。所提出的变种，被称为字符串收紧自组织神经网络（STON），可以用来解决某些实际问题，如计算最短同伦路径，平滑路径，以避免急转弯，和计算的凸包。这些问题在计算几何、机器人路径规划、人工智能（图解推理）、超大规模集成电路布线和地理信息系统中具有相当大的意义。给定一组障碍物和一个在二维的空间中具有两个固定端点的字符串，STON模型不断收紧给定字符串，直到达到欧几里得度量的唯一最短配置。STON通过以竞争的方式动态地创建和选择特征向量来最小化收敛时字符串的总长度。文中给出了该算法的正确性证明和部署实验结果。
英文摘要：
The phenomenon of self-organization has been of special interest to the neural network community for decades. In this paper, we study a variant of the Self-Organizing Map (SOM) that models the phenomenon of self-organization of the particles forming a string when the string is tightened from one or both ends. The proposed variant, called the String Tightening Self-Organizing Neural Network (STON), can be used to solve certain practical problems, such as computation of shortest homotopic paths, smoothing paths to avoid sharp turns, and computation of convex hull. These problems are of considerable interest in computational geometry, robotics path planning, AI (diagrammatic reasoning), VLSI routing, and geographical information systems. Given a set of obstacles and a string with two fixed terminal points in a two dimensional space, the STON model continuously tightens the given string until the unique shortest configuration in terms of the Euclidean metric is reached. The STON minimizes the total length of a string on convergence by dynamically creating and selecting feature vectors in a competitive manner. Proof of correctness of this anytime algorithm and experimental results obtained by its deployment are presented in the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
