Learning Geometric Invariant Features for Classification of Vector Polygons with Graph Message-passing Neural Network

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.

LMSeg: A deep graph message-passing network for efficient and accurate semantic segmentation of large-scale 3D landscape meshes

Semantic segmentation of large-scale 3D landscape meshes is pivotal for various geospatial applications, including spatial analysis, automatic mapping and localization of target objects, and urban planning and development. This requires an efficient and accurate 3D perception system to understand and analyze real-world environments. However, traditional mesh segmentation methods face challenges in accurately segmenting small objects and maintaining computational efficiency due to the complexity and large size of 3D landscape mesh datasets. This paper presents an end-to-end deep graph message-passing network, LMSeg, designed to efficiently and accurately perform semantic segmentation on large-scale 3D landscape meshes. The proposed approach takes the barycentric dual graph of meshes as inputs and applies deep message-passing neural networks to hierarchically capture the geometric and spatial features from the barycentric graph structures and learn intricate semantic information from textured meshes. The hierarchical and local pooling of the barycentric graph, along with the effective geometry aggregation modules of LMSeg, enable fast inference and accurate segmentation of small-sized and irregular mesh objects in various complex landscapes. Extensive experiments on two benchmark datasets (natural and urban landscapes) demonstrate that LMSeg significantly outperforms existing learning-based segmentation methods in terms of object segmentation accuracy and computational efficiency. Furthermore, our method exhibits strong generalization capabilities across diverse landscapes and demonstrates robust resilience against varying mesh densities and landscape topologies.