  Point clouds and meshes are widely used 3D data structures for many computer
vision applications. While the meshes represent the surfaces of an object,
point cloud represents sampled points from the surface which is also the output
of modern sensors such as LiDAR and RGB-D cameras. Due to the wide application
area of point clouds and the recent advancements in deep neural networks,
studies focusing on robust classification of the 3D point cloud data emerged.
To evaluate the robustness of deep classifier networks, a common method is to
use adversarial attacks where the gradient direction is followed to change the
input slightly. The previous studies on adversarial attacks are generally
evaluated on point clouds of daily objects. However, considering 3D faces,
these adversarial attacks tend to affect the person's facial structure more
than the desired amount and cause malformation. Specifically for facial
expressions, even a small adversarial attack can have a significant effect on
the face structure. In this paper, we suggest an adversarial attack called
$\epsilon$-Mesh Attack, which operates on point cloud data via limiting
perturbations to be on the mesh surface. We also parameterize our attack by
$\epsilon$ to scale the perturbation mesh. Our surface-based attack has tighter
perturbation bounds compared to $L_2$ and $L_\infty$ norm bounded attacks that
operate on unit-ball. Even though our method has additional constraints, our
experiments on CoMA, Bosphorus and FaceWarehouse datasets show that
$\epsilon$-Mesh Attack (Perpendicular) successfully confuses trained DGCNN and
PointNet models $99.72\%$ and $97.06\%$ of the time, with indistinguishable
facial deformations. The code is available at
https://github.com/batuceng/e-mesh-attack.
