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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Tracking across cameras with non-overlapping views is a challenging problem. Firstly, the observations of an object are often widely separated in time and space when viewed from non-overlapping cameras. Secondly, the appearance of an object in one camera view might be very different from its appearance in another camera view due to the differences in illumination, pose and camera properties. To deal with the first problem, we observe that people or vehicles tend to follow the same paths in most cases, i.e., roads, walkways, corridors etc. The proposed algorithm uses this conformity in the traversed paths to establish correspondence. The algorithm learns this conformity and hence the inter-camera relationships in the form of multivariate probability density of space-time variables (entry and exit locations, velocities, and transition times) using kernel density estimation. To handle the appearance change of an object as it moves from one camera to another, we show that all brightness transfer functions from a given camera to another camera lie in a low dimensional subspace. This subspace is learned by using probabilistic principal component analysis and used for appearance matching. The proposed approach does not require explicit inter-camera calibration, rather the system learns the camera topology and subspace of inter-camera brightness transfer functions during a training phase. Once the training is complete, correspondences are assigned using the maximum likelihood (ML) estimation framework using both location and appearance cues. Experiments with real world videos are reported which validate the proposed approach. This paper addresses the problem of obtaining 3d detailed reconstructions of human faces in real-time and with inexpensive hardware. We present an algorithm based on a monocular multi-spectral photometric-stereo setup. This system is known to capture high-detailed deforming 3d surfaces at high frame rates and without having to use any expensive hardware or synchronized light stage. However, the main challenge of such a setup is the calibration stage, which depends on the lights setup and how they interact with the specific material being captured, in this case, human faces. For this purpose we develop a self-calibration technique where the person being captured is asked to perform a rigid motion in front of the camera, maintaining a neutral expression. Rigidity constrains are then used to compute the head's motion with a structure-from-motion algorithm. Once the motion is obtained, a multi-view stereo algorithm reconstructs a coarse 3d model of the face. This coarse model is then used to estimate the lighting parameters with a stratified approach: In the first step we use a RANSAC search to identify purely diffuse points on the face and to simultaneously estimate this diffuse reflectance model. In the second step we apply non-linear optimization to fit a non-Lambertian reflectance model to the outliers of the previous step. The calibration procedure is validated with synthetic and real data. The recovery of 3D human pose with monocular camera is an inherently ill-posed problem due to the large number of possible projections from the same 2D image to 3D space. Aimed at improving the accuracy of 3D motion reconstruction, we introduce the additional built-in knowledge, namely height-map, into the algorithmic scheme of reconstructing the 3D pose motion under a single-view calibrated camera. Our novel proposed framework consists of two major contributions. Firstly, the RGB image and its calculated height-map are combined to detect the landmarks of 2D joints with a dual-stream deep convolution network. Secondly, we formulate a new objective function to estimate 3D motion from the detected 2D joints in the monocular image sequence, which reinforces the temporal coherence constraints on both the camera and 3D poses. Experiments with HumanEva, Human3.6M, and MCAD dataset validate that our method outperforms the state-of-the-art algorithms on both 2D joints localization and 3D motion recovery. Moreover, the evaluation results on HumanEva indicates that the performance of our proposed single-view approach is comparable to that of the multi-view deep learning counterpart. We propose a novel solution to the generalized camera pose problem which includes the internal scale of the generalized camera as an unknown parameter. This further generalization of the well-known absolute camera pose problem has applications in multi-frame loop closure. While a well-calibrated camera rig has a fixed and known scale, camera trajectories produced by monocular motion estimation necessarily lack a scale estimate. Thus, when performing loop closure in monocular visual odometry, or registering separate structure-from-motion reconstructions, we must estimate a seven degree-of-freedom similarity transform from corresponding observations. Existing approaches solve this problem, in specialized configurations, by aligning 3D triangulated points or individual camera pose estimates. Our approach handles general configurations of rays and points and directly estimates the full similarity transformation from the 2D-3D correspondences. Four correspondences are needed in the minimal case, which has eight possible solutions. The minimal solver can be used in a hypothesize-and-test architecture for robust transformation estimation. Our solver also produces a least-squares estimate in the overdetermined case. The approach is evaluated experimentally on synthetic and real datasets, and is shown to produce higher accuracy solutions to multi-frame loop closure than existing approaches.