Robust Mesh Representation Learning via Efficient Local Structure-Aware Anisotropic Convolution

Mesh is a type of data structure commonly used for 3-D shapes. Representation learning for 3-D meshes is essential in many computer vision and graphics applications. The recent success of convolutional neural networks (CNNs) for structured data (e.g., images) suggests the value of adapting insights from CNN for 3-D shapes. However, 3-D shape data are irregular since each node's neighbors are unordered. Various graph neural networks for 3-D shapes have been developed with isotropic filters or 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 article, we propose a local structure-aware anisotropic convolutional operation (LSA-Conv) that learns adaptive weighting matrices for each template's node according to its neighboring structure and performs shared anisotropic filters. In fact, the learnable weighting matrix is similar to the attention matrix in the random synthesizer-a new Transformer model for natural language processing (NLP). Since the learnable weighting matrices require large amounts of parameters for high-resolution 3-D shapes, we introduce a matrix factorization technique to notably reduce the parameter size, denoted as LSA-small. Furthermore, a residual connection with a linear transformation is introduced to improve the performance of our LSA-Conv. Comprehensive experiments demonstrate that our model produces significant improvement in 3-D shape reconstruction compared to state-of-the-art methods.