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.
@cite_29 investigate ambiguities from a perceptual point of view. They explore whether, after seeing a frontal view, participants accept a 3D reconstruction as the correct profile as often as they do for the original profile. It shows that human observers consider the reconstructed shape equally plausible as ground truth, even if it differs significantly from ground truth and even if choices include the original profile of the face.
@cite_29
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Manipulated versions of three-dimensional faces that have different profiles, but almost the same appearance in frontal views, provide a novel way to investigate if and how humans use class-specific knowledge to infer depth from images of faces. After seeing a frontal view, participants have to select the profile that matches that view. The profiles are original (ground truth), average, random other, and two solutions computed with a linear face model (3D Morphable Model). One solution is based on 2D vertex positions, the other on pixel colors in the frontal view. The human responses demonstrate that humans neither guess nor just choose the average profile. The results also indicate that humans actually use the information from the front view, and not just rely on the plausibility of the profiles per se. All our findings are perfectly consistent with a correlation-based inference in a linear face model. The results also verify that the 3D reconstructions from our computational algorithms (stimuli 4 and 5) are similar to what humans expect, because they are chosen to be the true profile equally often as the ground-truth profiles. Our experiments shed new light on the mechanisms of human face perception and present a new quality measure for 3D reconstruction algorithms. The problem of single-view 3D shape completion or reconstruction is challenging, because among the many possible shapes that explain an observation, most are implausible and do not correspond to natural objects. Recent research in the field has tackled this problem by exploiting the expressiveness of deep convolutional networks. In fact, there is another level of ambiguity that is often overlooked: among plausible shapes, there are still multiple shapes that fit the 2D image equally well; i.e., the ground truth shape is non-deterministic given a single-view input. Existing fully supervised approaches fail to address this issue, and often produce blurry mean shapes with smooth surfaces but no fine details. In this paper, we propose ShapeHD, pushing the limit of single-view shape completion and reconstruction by integrating deep generative models with adversarially learned shape priors. The learned priors serve as a regularizer, penalizing the model only if its output is unrealistic, not if it deviates from the ground truth. Our design thus overcomes both levels of ambiguity aforementioned. Experiments demonstrate that ShapeHD outperforms state of the art by a large margin in both shape completion and shape reconstruction on multiple real datasets. We present a dense reconstruction approach that overcomes the drawbacks of traditional multiview stereo by incorporating semantic information in the form of learned category-level shape priors and object detection. Given training data comprised of 3D scans and images of objects from various viewpoints, we learn a prior comprised of a mean shape and a set of weighted anchor points. The former captures the commonality of shapes across the category, while the latter encodes similarities between instances in the form of appearance and spatial consistency. We propose robust algorithms to match anchor points across instances that enable learning a mean shape for the category, even with large shape variations across instances. We model the shape of an object instance as a warped version of the category mean, along with instance-specific details. Given multiple images of an unseen instance, we collate information from 2D object detectors to align the structure from motion point cloud with the mean shape, which is subsequently warped and refined to approach the actual shape. Extensive experiments demonstrate that our model is general enough to learn semantic priors for different object categories, yet powerful enough to reconstruct individual shapes with large variations. Qualitative and quantitative evaluations show that our framework can produce more accurate reconstructions than alternative state-of-the-art multiview stereo systems. To enable real-time, person-independent 3D registration from 2D video, we developed a 3D cascade regression approach in which facial landmarks remain invariant across pose over a range of approximately 60 degrees. From a single 2D image of a person's face, a dense 3D shape is registered in real time for each frame. The algorithm utilizes a fast cascade regression framework trained on high-resolution 3D face-scans of posed and spontaneous emotion expression. The algorithm first estimates the location of a dense set of markers and their visibility, then reconstructs face shapes by fitting a part-based 3D model. Because no assumptions are required about illumination or surface properties, the method can be applied to a wide range of imaging conditions that include 2D video and uncalibrated multi-view video. The method has been validated in a battery of experiments that evaluate its precision of 3D reconstruction and extension to multi-view reconstruction. Experimental findings strongly support the validity of real-time, 3D registration and reconstruction from 2D video. The software is available online at http: zface.org.