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.