  3D Morphable Models (3DMMs) are generative models for face shape and
appearance. However, the shape parameters of traditional 3DMMs satisfy the
multivariate Gaussian distribution while the identity embeddings satisfy the
hypersphere distribution, and this conflict makes it challenging for face
reconstruction models to preserve the faithfulness and the shape consistency
simultaneously. To address this issue, we propose the Sphere Face Model(SFM), a
novel 3DMM for monocular face reconstruction, which can preserve both shape
fidelity and identity consistency. The core of our SFM is the basis matrix
which can be used to reconstruct 3D face shapes, and the basic matrix is
learned by adopting a two-stage training approach where 3D and 2D training data
are used in the first and second stages, respectively. To resolve the
distribution mismatch, we design a novel loss to make the shape parameters have
a hyperspherical latent space. Extensive experiments show that SFM has high
representation ability and shape parameter space's clustering performance.
Moreover, it produces fidelity face shapes, and the shapes are consistent in
challenging conditions in monocular face reconstruction.
