Hexagonal Convolutional Neural Networks for Hexagonal Grids

Hexagonal grids use a hierarchical subdivision tessellation to cover the entire plane or sphere. Due to the 6-fold rotational symmetry, hexagonal grids have some advantages (e.g. isoperimetry, equidistant neighbors, and uniform connectivity) over quadrangular and triangular girds, which makes them suitable to tackle tasks of geospatial information processing and intelligent decision-making. In this paper, we first introduce some applications based on the hexagonal grids. Then, we introduce the planer and spherical hexagonal grids and analyze the group representations for them, we review geometric deep learning, some Convolutional Neural Networks (CNNs) for hexagonal grids, and group-based equivariant convolution. Next in importance, we propose the HexagonNet for hexagonal grids, and define a new convolution operator and pooling operator. Finally, in order to evaluate the effectiveness of the proposed HexagonNet, we perform experiments on two tasks: aerial scene classification on the aerial image dataset (AID), and 3D shape classification on the ModelNet40 dataset. The experimental results verify the practical applicability of the HexagonNet given some fixed parameter budgets.