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.
There have been two recent attempts to address the problem of estimating subject-camera distance from monocular, perspective views of a face . The idea is that the configuration of projected 2D face features conveys something about the degree of perspective transformation. @cite_14 approach the problem using exemplar 3D face models. They fit the models to 2D landmarks using perspective-n-point and use the mean of the estimated distances as the estimated subject-camera distance. @cite_3 on the other hand work entirely in 2D. They present a fully automated process for estimating 2D landmark positions to which they apply a linear normalisation. Their idea is to describe 2D landmarks in terms of their offset from mean positions, with the mean calculated either across views at different distances of the same face, or across multiple identities at the same distance. They can then perform regression to relate offsets to distance. They compare performance to humans and show that they are relatively bad at judging distance given only a single image.
@cite_14 @cite_3
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We present a method for estimating the distance between a camera and a human head in 2D images from a calibrated camera. Leading head pose estimation algorithms focus mainly on head orienta- tion (yaw, pitch, and roll) and translations perpendicular to the cam- era principal axis. Our contribution is a system that can estimate head pose under large translations parallel to the camera's principal axis. Our method uses a set of exemplar 3D human heads to estimate the dis- tance between a camera and a previously unseen head. The distance is estimated by solving for the camera pose using Effective Perspective n-Point (EPnP). We present promising experimental results using the Texas 3D Face Recognition Database. We propose the first automated method for estimating distance from frontal pictures of unknown faces. Camera calibration is not necessary, nor is the reconstruction of a 3D representation of the shape of the head. Our method is based on estimating automatically the position of face and head landmarks in the image, and then using a regressor to estimate distance from such measurements. We collected and annotated a dataset of frontal portraits of 53 individuals spanning a number of attributes (sex, age, race, hair), each photographed from seven distances. We find that our proposed method outperforms humans performing the same task. We observe that different physiognomies will bias systematically the estimate of distance, i.e. some people look closer than others. We expire which landmarks are more important for this task.