Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models were among the first attempts to create compact representations for such shapes; despite their effectiveness and simplicity, such models have limited representation power due to their linear formulation. Recently, non-linear learnable methods have been proposed, although most of them resort to intermediate representations, such as 3D grids of voxels or 2D views. In this paper, we introduce a convolutional mesh autoencoder and a GAN architecture based on the spiral convolutional operator, acting directly on the mesh and leveraging its underlying geometric structure. We provide an analysis of our convolution operator and demonstrate state-of-the-art results on 3D shape datasets compared to the linear Morphable Model and the recently proposed COMA model.

本文提出了一种新颖的图卷积算子，通过对网格的本地顺序强制执行连续性，实现对固定底层图形的归纳偏差建模，并将其作为传统深度生成建筑的构件，以多种 3D 形状数据集为例，与线性 Morphable Model 和其他图卷积算子相比，展示出最先进的结果。

神经三维可变模型：螺旋卷积网络用于三维形状表示学习和生成