# Auto-generation of a centerline graph from a geometrically complex roadmap of real-world traffic systems using a hierarchical quadtree for cellular automata simulations

## TL;DR

This paper introduces a hierarchical quadtree-based method to automatically generate centerline graphs from complex real-world traffic roadmaps, facilitating cellular automata traffic simulations and network analysis.

## Contribution

The paper presents a novel approach combining quadtree decomposition and space-filling curves to extract centerline graphs from complex roadmaps for traffic modeling.

## Key findings

- Successfully generated centerline graphs from real-world airport maps.
- Enabled effective network analysis using Dijkstra's algorithm.
- Demonstrated applicability to complex traffic systems.

## Abstract

This paper proposes a method of auto-generation of a centerline graph from a geometrically complex roadmap of real-world traffic systems by using a hierarchical quadtree for cellular automata simulations. Our method is summarized as follows. First, we store the binary values of the monochrome image of target roadmap (one and zero represent the road and the other areas, respectively) in the two-dimensional square map. Second, we recursively divide the square map into sub-leafs by a quadtree until the summed-up value of pixels included inside the leaf becomes equal to or less than one. Third, we gradually remove the distal leaves that are adjacent to the leaves whose depths are shallower than the distal leaf. After that, we trace the remaining distal leaves of the tree using Morton's space-filling curve, while selecting the leaves that keep a certain distance among the previously selected leaves as the nodes of the graph. Finally, each selected node searches the neighboring nodes and stores them as the edges of the graph. We demonstrate our method by generating a centerline graph from a complex roadmap of a real-world airport and by carrying out a typical network analysis using Dijkstra's method.