3D shape analysis is an important research topic in computer vision and
graphics. While existing methods have generalized image-based deep learning to
meshes using graph-based convolutions, the lack of an effective pooling
operation restricts the learning capability of their networks. In this paper,
we propose a novel pooling operation for mesh datasets with the same
connectivity but different geometry, by building a mesh hierarchy using mesh
simplification. For this purpose, we develop a modified mesh simplification
method to avoid generating highly irregularly sized triangles. Our pooling
operation effectively encodes the correspondence between coarser and finer
meshes in the hierarchy. We then present a variational auto-encoder structure
with the edge contraction pooling and graph-based convolutions, to explore
probability latent spaces of 3D surfaces. Our network requires far fewer
parameters than the original mesh VAE and thus can handle denser models thanks
to our new pooling operation and convolutional kernels. Our evaluation also
shows that our method has better generalization ability and is more reliable in
various applications, including shape generation, shape interpolation and shape
embedding.

本文提出了一种基于图卷积的网格平均池化方法，使用改进型网格简化避免产生高度不规则的三角形。在此基础上，提出了一种利用边缩减池化和图卷积的自动编码器结构，能够对 3D 表面进行概率潜空间的探索，并展示了在形态生成、形态插值和形态嵌入等各种应用中其更好的泛化能力和更可靠的性能。