Establishing point correspondence of 3D faces via sparse facial deformable model

Establishing a dense vertex-to-vertex anthropometric correspondence between 3D faces is an important and fundamental problem in 3D face research, which can contribute to most applications of 3D faces. This paper proposes a sparse facial deformable model to automatically achieve this task. For an input 3D face, the basic idea is to generate a new 3D face that has the same mesh topology as a reference face and the highly similar shape to the input face, and whose vertices correspond to those of the reference face in an anthropometric sense. Two constraints: 1) the shape constraint and 2) correspondence constraint are modeled in our method to satisfy the three requirements. The shape constraint is solved by a novel face deformation approach in which a normal-ray scheme is integrated to the closest-vertex scheme to keep high-curvature shapes in deformation. The correspondence constraint is based on an assumption that if the vertices on 3D faces are corresponded, their shape signals lie on a manifold and each face signal can be represented sparsely by a few typical items in a dictionary. The dictionary can be well learnt and contains the distribution information of the corresponded vertices. The correspondence information can be conveyed to the sparse representation of the generated 3D face. Thus, a patch-based sparse representation is proposed as the correspondence constraint. By solving the correspondence constraint iteratively, the vertices of the generated face can be adjusted to correspondence positions gradually. At the early iteration steps, smaller sparsity thresholds are set that yield larger representation errors but better globally corresponded vertices. At the later steps, relatively larger sparsity thresholds are used to encode local shapes. By this method, the vertices in the new face approach the right positions progressively until the final global correspondence is reached. Our method is automatic, and the manual work is needed only in training procedure. The experimental results on a large-scale publicly available 3D face data set, BU-3DFE, demonstrate that our method achieves better performance than existing methods.