  3D face shape is more expressive and viewpoint-consistent than its 2D
counterpart. However, 3D facial landmark localization in a single image is
challenging due to the ambiguous nature of landmarks under 3D perspective.
Existing approaches typically adopt a suboptimal two-step strategy, performing
2D landmark localization followed by depth estimation. In this paper, we
propose the Joint Voxel and Coordinate Regression (JVCR) method for 3D facial
landmark localization, addressing it more effectively in an end-to-end fashion.
First, a compact volumetric representation is proposed to encode the per-voxel
likelihood of positions being the 3D landmarks. The dimensionality of such a
representation is fixed regardless of the number of target landmarks, so that
the curse of dimensionality could be avoided. Then, a stacked hourglass network
is adopted to estimate the volumetric representation from coarse to fine,
followed by a 3D convolution network that takes the estimated volume as input
and regresses 3D coordinates of the face shape. In this way, the 3D structural
constraints between landmarks could be learned by the neural network in a more
efficient manner. Moreover, the proposed pipeline enables end-to-end training
and improves the robustness and accuracy of 3D facial landmark localization.
The effectiveness of our approach is validated on the 3DFAW and AFLW2000-3D
datasets. Experimental results show that the proposed method achieves
state-of-the-art performance in comparison with existing methods.
