This paper presents new designs of graph convolutional neural networks (GCNs) on 3D meshes for 3D object segmentation and classification. We use the faces of the mesh as basic processing units and represent a 3D mesh as a graph where each node corresponds to a face. To enhance the descriptive power of the graph, we introduce a 1-ring face neighbourhood structure to derive novel multi-dimensional spatial and structure features to represent the graph nodes. Based on this new graph representation, we then design a densely connected graph convolutional block which aggregates local and regional features as the key construction component to build effective and efficient practical GCN models for 3D object classification and segmentation. We will present experimental results to show that our new technique outperforms state of the art where our models are shown to have the smallest number of parameters and consietently achieve the highest accuracies across a number of benchmark datasets. We will also present ablation studies to demonstrate the soundness of our design principles and the effectiveness of our practical models.
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