Triangle Mesh Reconstruction by Fusion of Residual Graph Convolution and Edge Contraction Pooling

Triangle meshes are a crucial and powerful data type for three-dimensional (3D) shapes, extensively studied in the fields of computer vision and computer graphics. In this paper, we delve into the challenge of analyzing deforming 3D triangle meshes using deep neural networks. While existing methods extend graph-based deep learning to 3D triangle meshes using graph convolution, the lack of effective graph convolutional structures and pooling operations limits the learning capacity of their networks. We propose a variational autoencoder structure that integrates graph convolutional residual blocks with multilayer pooling to explore the latent space of 3D shapes for generation. This framework introduces graph convolutional residual blocks to address the issue of gradient vanishing in deep networks. By employing multilayer pooling and unpooling structures based on triangle mesh simplification, gradually reducing the spatial dimensions of the input, the model can extract more general features. This enables it to handle denser mesh models effectively. Extensive experiments demonstrate that our generalized framework can learn reasonable representations of deformable shape collections with minimal training examples. It produces competitive results across various applications, including shape generation and interpolation, requiring fewer training samples and outperforming state-of-the-art techniques.