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.

翻译：3D 计算机视觉和图形的许多重要应用中产生了3D 几何数据的生成模型。在本文中,我们侧重于3D 的变形形状,这些形状具有共同的地形结构,例如人的脸和身体。可移动模型是首次尝试为这些形状建立缩略图的尝试之一;尽管这些模型是有效和简单的,但由于线性配方,其代表性有限。最近,提出了非线性学习方法,尽管它们大多采用中间表示法,例如3D 的氧化物网格或2D 视图。在本文中,我们引入了以螺旋共振动操作器为基础的直线型Mesh自动编码器和GAN结构,直接在网状上行动并利用其基本几何结构。我们分析了我们的变形操作器,并展示了3D 形状数据集与线性负模型和最近提议的COMA 模型相比的最新艺术结果。