With the rising popularity of virtual worlds, the importance of data-driven
parametric models of 3D meshes has grown rapidly. Numerous applications, such
as computer vision, procedural generation, and mesh editing, vastly rely on
these models. However, current approaches do not allow for independent editing
of deformations at different frequency levels. They also do not benefit from
representing deformations at different frequencies with dedicated
representations, which would better expose their properties and improve the
generated meshes' geometric and perceptual quality. In this work, spectral
meshes are introduced as a method to decompose mesh deformations into
low-frequency and high-frequency deformations. These features of low- and
high-frequency deformations are used for representation learning with graph
convolutional networks. A parametric model for 3D facial mesh synthesis is
built upon the proposed framework, exposing user parameters that control
disentangled high- and low-frequency deformations. Independent control of
deformations at different frequencies and generation of plausible synthetic
examples are mutually exclusive objectives. A Conditioning Factor is introduced
to leverage these objectives. Our model takes further advantage of spectral
partitioning by representing different frequency levels with disparate, more
suitable representations. Low frequencies are represented with standardised
Euclidean coordinates, and high frequencies with a normalised deformation
representation (DR). This paper investigates applications of our proposed
approach in mesh reconstruction, mesh interpolation, and multi-frequency
editing. It is demonstrated that our method improves the overall quality of
generated meshes on most datasets when considering both the $L_1$ norm and
perceptual Dihedral Angle Mesh Error (DAME) metrics.

基于频谱网格的表示学习方法应用于虚拟世界中的参数化模型，提供了在不同频率级别上独立编辑变形的能力，并通过不同的表示方式改进了生成网格的几何和感知质量。

深度光谱网格：用图神经网络进行多频面部网格处理

Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph  Neural Networks

Direct mesh editing and deformation are key components in the geometric
modeling and animation pipeline. Direct mesh editing methods are typically
framed as optimization problems combining user-specified vertex constraints
with a regularizer that determines the position of the rest of the vertices.
The choice of the regularizer is key to the realism and authenticity of the
final result. Physics and geometry-based regularizers are not aware of the
global context and semantics of the object, and the more recent deep learning
priors are limited to a specific class of 3D object deformations. In this work,
our main contribution is a local mesh editing method called DragD3D for global
context-aware realistic deformation through direct manipulation of a few
vertices. DragD3D is not restricted to any class of objects. It achieves this
by combining the classic geometric ARAP (as rigid as possible) regularizer with
2D priors obtained from a large-scale diffusion model. Specifically, we render
the objects from multiple viewpoints through a differentiable renderer and use
the recently introduced DDS loss which scores the faithfulness of the rendered
image to one from a diffusion model. DragD3D combines the approximate gradients
of the DDS with gradients from the ARAP loss to modify the mesh vertices via
neural Jacobian field, while also satisfying vertex constraints. We show that
our deformations are realistic and aware of the global context of the objects,
and provide better results than just using geometric regularizers.

通过直接操作少量顶点，结合几何 ARAP 正则化器和基于大规模扩散模型的 2D 先验，我们提出了一种名为 DragD3D 的局部网格编辑方法，实现全局上下文感知的逼真变形。我们的研究表明，我们的变形方法比仅使用几何正则化器获得更好的结果，且能够意识到对象的全局上下文。