We introduce a novel learning-based method for encoding and manipulating 3D
surface meshes. Our method is specifically designed to create an interpretable
embedding space for deformable shape collections. Unlike previous 3D mesh
autoencoders that require meshes to be in a 1-to-1 correspondence, our approach
is trained on diverse meshes in an unsupervised manner. Central to our method
is a spectral pooling technique that establishes a universal latent space,
breaking free from traditional constraints of mesh connectivity and shape
categories. The entire process consists of two stages. In the first stage, we
employ the functional map paradigm to extract point-to-point (p2p) maps between
a collection of shapes in an unsupervised manner. These p2p maps are then
utilized to construct a common latent space, which ensures straightforward
interpretation and independence from mesh connectivity and shape category.
Through extensive experiments, we demonstrate that our method achieves
excellent reconstructions and produces more realistic and smoother
interpolations than baseline approaches.

我们介绍了一种新颖的基于学习的方法，用于编码和操作 3D 表面网格。我们的方法专门设计用于创建可解释的可变形形状集合的嵌入空间。与以前需要网格处于一对一对应关系的 3D 网格自编码器不同，我们的方法是以无监督的方式训练的，可以处理各种各样的网格。我们方法的核心是一种谱池化技术，它建立了一个通用的潜空间，摆脱了网格连通性和形状类别的传统限制。整个过程包括两个阶段。在第一阶段，我们采用函数映射范例以无监督的方式提取一组形状之间的点对点映射。然后利用这些点对点映射构建一个公共的潜空间，以确保直观解释和独立于网格连通性和形状类别。通过大量实验证明，我们的方法实现了优秀的重建，并产生了比基准方法更真实、更平滑的插值。