In this work, we present a new versatile 3D multilinear statistical face model, based on a tensor factorisation of 3D face scans, that decomposes the shapes into person and expression subspaces. Investigation of the expression subspace reveals an inherent low-dimensional substructure, and further, a star-shaped structure. This is due to two novel findings: (1) increasing the strength of one emotion approximately forms a linear trajectory in the subspace. (2) All these trajectories intersect at a single pointnot at the neutral expression as assumed by almost all prior works -but at an apathetic expression. We utilise these structural findings by reparameterising the expression subspace by the fourth-order moment tensor centred at the point of apathy. We propose a 3D face reconstruction method from single or multiple 2D projections by assuming an uncalibrated projective camera model. The non-linearity caused by the perspective projection can be neatly included into the model. The proposed algorithm separates person and expression subspaces convincingly, and enables flexible, natural modelling of expressions for a wide variety of human faces. Applying the method on independent faces showed that morphing between different persons and expressions can be performed without strong deformations.
In this paper, we use a tensor model based on the Higher-Order Singular Value Decomposition (HOSVD) to discover semantic directions in Generative Adversarial Networks. This is achieved by first embedding a structured facial expression database into the latent space using the e4e encoder. Specifically, we discover directions in latent space corresponding to the six prototypical emotions: anger, disgust, fear, happiness, sadness, and surprise, as well as a direction for yaw rotation. These latent space directions are employed to change the expression or yaw rotation of real face images. We compare our found directions to similar directions found by two other methods. The results show that the visual quality of the resultant edits are on par with State-of-the-Art. It can also be concluded that the tensorbased model is well suited for emotion and yaw editing, i.e., that the emotion or yaw rotation of a novel face image can be robustly changed without a significant effect on identity or other attributes in the images.
We propose a general, prior-free approach for the uncalibrated non-rigid structure-from-motion problem for modelling and analysis of non-rigid objects such as human faces. The word general refers to an approach that recovers the non-rigid affine structure and motion from 2D point correspondences by assuming that (1) the non-rigid shapes are generated by a linear combination of rigid 3D basis shapes, (2) that the non-rigid shapes are affine in nature, i.e., they can be modelled as deviations from the mean, rigid shape, (3) and that the basis shapes are statistically independent. In contrast to the majority of existing works, no prior information is assumed for the structure and motion apart from the assumption the that underlying basis shapes are statistically independent. The independent 3D shape bases are recovered by independent subspace analysis (ISA). Likewise, in contrast to the most previous approaches, no calibration information is assumed for affine cameras; the reconstruction is solved up to a global affine ambiguity that makes our approach simple but efficient. In the experiments, we evaluated the method with several standard data sets including a real face expression data set of 7200 faces with 2D point correspondences and unknown 3D structure and motion for which we obtained promising results.
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