There have been recent efforts to learn more meaningful representations via
fixed length codewords from mesh data, since a mesh serves as a complete model
of underlying 3D shape compared to a point cloud. However, the mesh
connectivity presents new difficulties when constructing a deep learning
pipeline for meshes. Previous mesh unsupervised learning approaches typically
assume category-specific templates, e.g., human face/body templates. It
restricts the learned latent codes to only be meaningful for objects in a
specific category, so the learned latent spaces are unable to be used across
different types of objects. In this work, we present WrappingNet, the first
mesh autoencoder enabling general mesh unsupervised learning over heterogeneous
objects. It introduces a novel base graph in the bottleneck dedicated to
representing mesh connectivity, which is shown to facilitate learning a shared
latent space representing object shape. The superiority of WrappingNet mesh
learning is further demonstrated via improved reconstruction quality and
competitive classification compared to point cloud learning, as well as latent
interpolation between meshes of different categories.

本文提出了 WrappingNet，第一个能够在异质对象上进行通用网格无监督学习的网格自编码器，通过在瓶颈中引入新的基础图来表示网格连接性，展示了它在对象形状表示方面提供了优势，并通过改进的重建质量和竞争性分类证明了与点云学习相比的优越性，以及不同类别网格之间的潜在插值。

WrappingNet: 深度球面变形的网格自编码器

WrappingNet: Mesh Autoencoder via Deep Sphere Deformation

Analyzing embedded simplicial complexes, such as triangular meshes and
graphs, is an important problem in many fields. We propose a new approach for
analyzing embedded simplicial complexes in a subdivision-invariant and
isometry-invariant way using only topological and geometric information. Our
approach is based on creating and analyzing sufficient statistics and uses a
graph neural network. We demonstrate the effectiveness of our approach using a
synthetic mesh data set.

提出了一种新的方法，利用拓扑和几何信息，仅仅使用统计数据和图神经网络就能对嵌入的单纯复合体进行无细分和等距不变分析。利用合成网格数据集证明了该方法的有效性。

嵌入复合体的不变表示

Invariant Representations of Embedded Simplicial Complexes

3D morphable models are widely used for the shape representation of an object
class in computer vision and graphics applications. In this work, we focus on
deep 3D morphable models that directly apply deep learning on 3D mesh data with
a hierarchical structure to capture information at multiple scales. While great
efforts have been made to design the convolution operator, how to best
aggregate vertex features across hierarchical levels deserves further
attention. In contrast to resorting to mesh decimation, we propose an attention
based module to learn mapping matrices for better feature aggregation across
hierarchical levels. Specifically, the mapping matrices are generated by a
compatibility function of the keys and queries. The keys and queries are
trainable variables, learned by optimizing the target objective, and shared by
all data samples of the same object class. Our proposed module can be used as a
train-only drop-in replacement for the feature aggregation in existing
architectures for both downsampling and upsampling. Our experiments show that
through the end-to-end training of the mapping matrices, we achieve
state-of-the-art results on a variety of 3D shape datasets in comparison to
existing morphable models.

本文介绍了基于深度学习的 3D 变形模型，提出了一种基于注意力机制的模块来优化特征汇聚，通过端到端训练映射矩阵来实现在现有架构上对特征汇聚的替代，取得了在多个 3D 模型数据集上的最新成果。