  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.
