Learned 3D representations of human faces are useful for computer vision problems such as 3D face tracking and reconstruction from images, as well as graphics applications such as character generation and animation. Traditional models learn a latent representation of a face using linear subspaces or higher-order tensor generalizations. Due to this linearity, they can not capture extreme deformations and nonlinear expressions. To address this, we introduce a versatile model that learns a non-linear representation of a face using spectral convolutions on a mesh surface. We introduce mesh sampling operations that enable a hierarchical mesh representation that captures non-linear variations in shape and expression at multiple scales within the model. In a variational setting, our model samples diverse realistic 3D faces from a multivariate Gaussian distribution. Our training data consists of 20,466 meshes of extreme expressions captured over 12 different subjects. Despite limited training data, our trained model outperforms state-of-the-art face models with 50% lower reconstruction error, while using 75% fewer parameters. We show that, replacing the expression space of an existing state-of-theart face model with our model, achieves a lower reconstruction error. Our data, model and code are available at http://coma.is.tue.mpg.de/.

Figure 1: Without 3D supervision, RingNet learns a mapping from the pixels of a single image to the 3D facial parameters of the FLAME model [21]. Top: Images are from the CelebA dataset [22]. Bottom: estimated shape, pose and expression. AbstractThe estimation of 3D face shape from a single image must be robust to variations in lighting, head pose, expression, facial hair, makeup, and occlusions. Robustness requires a large training set of in-the-wild images, which by construction, lack ground truth 3D shape. To train a network without any 2D-to-3D supervision, we present RingNet, which learns to compute 3D face shape from a single image. Our key observation is that an individual's face shape is constant across images, regardless of expression, pose, lighting, etc. RingNet leverages multiple images of a person and automatically detected 2D face features. It uses a novel loss that encourages the face shape to be similar when the identity is the same and different for different people. We achieve invariance to expression by representing the face using the FLAME model. Once trained, our method takes a single image and outputs the parameters of FLAME, which can be readily animated. Additionally we create a new database of faces "not quite in-the-wild" (NoW) with 3D head scans and high-resolution images of the subjects in a wide variety of conditions. We evaluate publicly available methods and find that RingNet is more accurate than methods that use 3D supervision. The dataset, model, and results are available for research purposes at

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