Geometric shape classification of vector polygons remains a non-trivial learning task in spatial analysis. Previous studies mainly focus on devising deep learning approaches for representation learning of rasterized vector polygons, whereas the study of discrete representations of polygons and subsequent deep learning approaches have not been fully investigated. In this study, we investigate a graph representation of vector polygons and propose a novel graph message-passing neural network (PolyMP) to learn the geometric-invariant features for shape classification of polygons. Through extensive experiments, we show that the graph representation of polygons combined with a permutation-invariant graph message-passing neural network achieves highly robust performances on benchmark datasets (i.e., synthetic glyph and real-world building footprint datasets) as compared to baseline methods. We demonstrate that the proposed graph-based PolyMP network enables the learning of expressive geometric features invariant to geometric transformations of polygons (i.e., translation, rotation, scaling and shearing) and is robust to trivial vertex removals of polygons. We further show the strong generalizability of PolyMP, which enables generalizing the learned geometric features from the synthetic glyph polygons to the real-world building footprints.

翻译：矢量多边形的几何形状分类在空间分析中仍是一项重要的学习任务。先前研究主要集中于设计深度学习方法来学习栅格化矢量多边形的表示，而对多边形的离散表示及其后续深度学习方法的研究尚未充分展开。本研究探索了矢量多边形的图表示方法，并提出了一种新颖的图消息传递神经网络（PolyMP）来学习多边形形状分类所需的几何不变特征。通过大量实验，我们证明与基线方法相比，多边形图表示结合置换不变的图消息传递神经网络在基准数据集（即合成字形和真实世界建筑轮廓数据集）上实现了高度鲁棒的性能。我们论证了所提出的基于图的PolyMP网络能够学习对多边形几何变换（即平移、旋转、缩放和剪切）保持不变的表达性几何特征，并对多边形的冗余顶点删除具有鲁棒性。我们进一步展示了PolyMP强大的泛化能力，该能力使得从合成字形多边形学习到的几何特征能够有效迁移到真实世界建筑轮廓数据中。