PAI-GCN: Permutable Anisotropic Graph Convolutional Networks for 3D Shape Representation Learning

Demand for efficient 3D shape representation learning is increasing in many 3D computer vision applications. The recent success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to 3D shapes. However, unlike images that are Euclidean structured, 3D shape data are irregular since each node's neighbors are inconsistent. Various convolutional graph neural networks for 3D shapes have been developed using isotropic filters or using anisotropic filters with predefined local coordinate systems to overcome the node inconsistency on graphs. However, isotropic filters or predefined local coordinate systems limit the representation power. In this paper, we propose a permutable anisotropic convolutional operation (PAI-Conv) that learns adaptive soft-permutation matrices for each node according to the geometric shape of its neighbors and performs shared anisotropic filters as CNN does. Comprehensive experiments demonstrate that our model produces significant improvement in 3D shape reconstruction compared to state-of-the-art methods.