Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph
  Neural Networks
Robert Kosk Richard Southern Lihua You Shaojun Bian Willem Kokke Greg Maguire
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.