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.
Recognition of unfamiliar faces is susceptible to image differences caused by angular sizes subtended from the face to the camera. Research on perception of cubes suggests that apparent distortions of a shape due to large camera angle are correctable by placing the observer at the centre of projection, especially when visibility of the picture surface is low (Yang and Kubovy, 1999 Perception & Psychophysics 61 456^467). To explore the implication of this finding for face perception, observers performed recognition and matching tasks where face images with reduced visibility of picture surface were shown with observers either at the centre of projec- tion or at other viewpoints. The results show that, unlike perception of cubes, the effect of perspective transformation on face recognition is largely unaffected by the centre of projection. Furthermore, the use of perspective cues is not affected by textured surfaces. The limitation of perspective in restoring 3-D information of faces suggests a stronger role for image-based, rather than model-based, processes in recognition of unfamiliar faces.  The effect of perspective transformation on transfer of face training was investigated in a yes no recognition task using face stimuli with 42°, 10°, or no perspective convergence. A strong dependence of recognition performance on the magnitude of perspective transformation was found, with large perspective changes such as from 42° at learning to orthogonal at test producing the strongest impairment and small perspective changes such as from 10° at learning to orthogonal at test the least. In a second experiment, the internal and external features of a face from different perspective convergence were artificially combined to produce identical local features between this composite image and the original but producing an impossible perspective transformation from either. The results of transfer between the composite and untouched images showed face recognition to be strongly affected by local featural similarities and relatively insensitive to global coherence of perspective transformation. The authors discuss the limitations of photography in producing representations that lead to the accurate perception of shapes. In particular, they consider two situations in which the photographic representation, although an accurate reproduction of the geometry of the twodimensional image in the eye, does not capture the way human vision changes this geometry to produce a three-dimensionally accurate perception. When looking at a photograph, the viewer’s uncertainty of the camera-to-subject distance and the fact that, unnaturally, a photograph presents almost exactly the same view of an object to the two eyes result in substantially distorted perceptions. These most commonly result in a perceived flattening and fattening of the 3D shape of the object being photographed. The basis on which people make social judgments from the image of a face remains an important open problem in fields ranging from psychology to neuroscience and economics. Multiple cues from facial appearance influence the judgments that viewers make. Here we investigate the contribution of a novel cue: the change in appearance due to the perspective distortion that results from viewing distance. We found that photographs of faces taken from within personal space elicit lower investments in an economic trust game, and lower ratings of social traits (such as trustworthiness, competence, and attractiveness), compared to photographs taken from a greater distance. The effect was replicated across multiple studies that controlled for facial image size, facial expression and lighting, and was not explained by face width-to-height ratio, explicit knowledge of the camera distance, or whether the faces are perceived as typical. These results demonstrate a novel facial cue influencing a range of social judgments as a function of interpersonal distance, an effect that may be processed implicitly.