Noisy Road Network Matching

Abstract

Let $\mathcal{N}$ and $\mathcal{M}$ be two road networks represented in vector form and covering rectangular areas R and R′, respectively, not necessarily parallel to each other, but with R′ ⊂ R. We assume that $\mathcal{N}$ and $\mathcal{M}$ use different coordinate systems at (possibly) different, but known scales. Let $\mathcal{B}$ and $\mathcal{A}$ denote sets of ”prominent” road points (e.g., intersections) associated with $\mathcal{N}$ and $\mathcal{M}$, respectively. The positions of road points on both sets may contain a certain amount of ”noise” due to errors and the finite precision of measurements. We propose an algorithm for determining approximate matches, in terms of the bottleneck distance, between $\mathcal{A}$ and a subset $\mathcal{B}'$ of $\mathcal{B}$. We consider the characteristics of the problem in order to achieve a high degree of efficiency. At the same time, so as not to compromise the usability of the algorithm, we keep the complexity required for the data as low as possible. As the algorithm that guarantees to find a possible match is expensive due to the inherent complexity of the problem, we propose a lossless filtering algorithm that yields a collection of candidate regions that contain a subset S of $\mathcal{B}$ such that $\mathcal{A}$ may match a subset $\mathcal{B}'$ of S. Then we find possible approximate matchings between $\mathcal{A}$ and subsets of S using the matching algorithm. We have implemented the proposed algorithm and report results that show the efficiency of our approach.