String Tightening as a Self-Organizing Phenomenon: Computation of Shortest Homotopic Path, Smooth Path, and Convex Hull

TL;DR

This paper introduces STON, a neural network model that simulates string self-organization to compute shortest paths, smooth paths, and convex hulls, with applications in computational geometry and robotics.

Contribution

The paper presents a novel neural network variant, STON, for solving geometric problems through self-organizing string tightening, demonstrating correctness and practical effectiveness.

Findings

Successfully computes shortest homotopic paths.

Effectively smooths paths to avoid sharp turns.

Converges to minimal string length in practical experiments.

Abstract

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.