A face image contains geometric cues in the form of configurational information and contours that can be used to estimate 3D face shape. While it is clear that 3D reconstruction from 2D points is highly ambiguous if no further constraints are enforced, one might expect that the face-space constraint solves this problem. We show that this is not the case and that geometric information is an ambiguous cue. There are two sources for this ambiguity. The first is that, within the space of 3D face shapes, there are flexibility modes that remain when some parts of the face are fixed. The second occurs only under perspective projection and is a result of perspective transformation as camera distance varies. Two different faces, when viewed at different distances, can give rise to the same 2D geometry. To demonstrate these ambiguities, we develop new algorithms for fitting a 3D morphable model to 2D landmarks or contours under either orthographic or perspective projection and show how to compute flexibility modes for both cases. We show that both fitting problems can be posed as a separable nonlinear least squares problem and solved efficiently. We demonstrate both quantitatively and qualitatively that the ambiguity is present in reconstructions from geometric information alone but also in reconstructions from a state-of-the-art CNN-based method.
We present a robust method for estimating the facial pose and shape information from a densely annotated facial image. The method relies on Convolutional Point-set Representation (CPR), a carefully designed matrix representation to summarize different layers of information encoded in the set of detected points in the annotated image. The CPR disentangles the dependencies of shape and different pose parameters and enables updating different parameters in a sequential manner via convolutional neural networks and recurrent layers. When updating the pose parameters, we sample reprojection errors along with a predicted direction and update the parameters based on the pattern of reprojection errors. This technique boosts the model's capability in searching a local minimum under challenging scenarios. We also demonstrate that annotation from different sources can be merged under the framework of CPR and contributes to outperforming the current state-of-the-art solutions for 3D face alignment. Experiments indicate the proposed CPRFA (CPR-based Face Alignment) significantly improves 3D alignment accuracy when the densely annotated image contains noise and missing values, which is common under "in-the-wild" acquisition scenarios. We present a minimalistic but effective neural network that computes dense facial correspondences in highly unconstrained RGB images. Our network learns a per-pixel flow and a matchability mask between 2D input photographs of a person and the projection of a textured 3D face model. To train such a network, we generate a massive dataset of synthetic faces with dense labels using renderings of a morphable face model with variations in pose, expressions, lighting, and occlusions. We found that a training refinement using real photographs is required to drastically improve the ability to handle real images. When combined with a facial detection and 3D face fitting step, we show that our approach outperforms the state-of-the-art face alignment methods in terms of accuracy and speed. By directly estimating dense correspondences, we do not rely on the full visibility of sparse facial landmarks and are not limited to the model space of regression-based approaches. We also assess our method on video frames and demonstrate successful per-frame processing under extreme pose variations, occlusions, and lighting conditions. Compared to existing 3D facial tracking techniques, our fitting does not rely on previous frames or frontal facial initialization and is robust to imperfect face detections. It has been recently shown that neural networks can recover the geometric structure of a face from a single given image. A common denominator of most existing face geometry reconstruction methods is the restriction of the solution space to some low-dimensional subspace. While such a model significantly simplifies the reconstruction problem, it is inherently limited in its expressiveness. As an alternative, we propose an Image-to-Image translation network that jointly maps the input image to a depth image and a facial correspondence map. This explicit pixel-based mapping can then be utilized to provide high quality reconstructions of diverse faces under extreme expressions, using a purely geometric refinement process. In the spirit of recent approaches, the network is trained only with synthetic data, and is then evaluated on “in-the-wild” facial images. Both qualitative and quantitative analyses demonstrate the accuracy and the robustness of our approach. In this paper we propose to learn a mapping from image pixels into a dense template grid through a fully convolutional network. We formulate this task as a regression problem and train our network by leveraging upon manually annotated facial landmarks in-the-wild. We use such landmarks to establish a dense correspondence field between a three-dimensional object template and the input image, which then serves as the ground-truth for training our regression system. We show that we can combine ideas from semantic segmentation with regression networks, yielding a highly-accurate quantized regression architecture. Our system, called DenseReg, allows us to estimate dense image-to-template correspondences in a fully convolutional manner. As such our network can provide useful correspondence information as a stand-alone system, while when used as an initialization for Statistical Deformable Models we obtain landmark localization results that largely outperform the current state-of-the-art on the challenging 300W benchmark. We thoroughly evaluate our method on a host of facial analysis tasks, and demonstrate its use for other correspondence estimation tasks, such as the human body and the human ear. DenseReg code is made available at http: alpguler.com DenseReg.html along with supplementary materials.