Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is known to be $\mathcal{NP}$-hard, the distance measure proves an impractical choice for applications. As a computationally tractable alternative, we propose in this paper the Graph Mover's Distance (GMD), which has been formulated as an instance of the earth mover's distance. The computation of the GMD between two geometric graphs with at most $n$ vertices takes only $O(n^3)$-time. Alongside studying the metric properties of the GMD, we investigate the stability of the GGD and GMD. The GMD also demonstrates extremely promising empirical evidence at recognizing letter drawings from the {\tt LETTER} dataset \cite{da_vitoria_lobo_iam_2008}.

翻译：许多模式识别应用将模式表示为几何图。几何图距离（GGD）近期被研究作为衡量两个几何图相似性的有意义指标。由于已知计算GGD是$\mathcal{NP}$-难的，该距离度量在实践中难以应用于实际场景。作为一种计算上可行的替代方案，本文提出图迁移距离（GMD），并将其形式化为地球迁移距离的一个实例。计算最多包含$n$个顶点的两个几何图之间的GMD仅需$O(n^3)$时间。除研究GMD的度量性质外，我们还探讨了GGD与GMD的稳定性。在{\tt LETTER}数据集 \cite{da_vitoria_lobo_iam_2008}上的字母图形识别实验中，GMD呈现出极具前景的经验证据。