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.

翻译：我们提出了一种新颖的基于学习的方法，用于编码和操作三维表面网格。该方法专为可变形形状集合创建可解释的嵌入空间而设计。与以往需要网格一一对应的三维网格自编码器不同，我们的方法以无监督方式对多样化网格进行训练。该方法的核心是一种谱池化技术，该技术建立了一个通用潜空间，摆脱了传统网格连通性和形状类别的限制。整个过程包含两个阶段。第一阶段，我们采用功能映射范式，以无监督方式提取形状集合之间的点对点映射。这些点对点映射随后被用于构建一个通用潜空间，从而确保易于解释且独立于网格连通性和形状类别。通过大量实验，我们证明该方法在重建效果上优于基线方法，且能生成更逼真、更平滑的插值结果。