3D morphable models (3DMMs) are generative models for face shape and appearance. Recent works impose face recognition constraints on 3DMM shape parameters so that the face shapes of the same person remain consistent. However, theshape parameters of traditional 3DMMs satisfy the multivariate Gaussian distribution. In contrast, the identity embeddings meet the hypersphere distribution, and this conflict makes it challenging for face reconstruction models to preserve the faithfulness and the shape consistency simultaneously. In other words, recognition loss and reconstruction loss can not decrease jointly due to their conflict distribution. To address this issue, we propose the Sphere Face Model (SFM), a novel 3DMM for monocular face reconstruction, preserving 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. We design a novel loss to resolve the distribution mismatch, enforcing that the shape parameters have the hyperspherical distribution. Our model accepts 2Dand 3D data for constructing the sphere face models. Extensive experiments show that SFM has high representation ability and clustering performance in its shape parameter space. Moreover, it produces high-fidelity face shapes consistently in challenging conditions in monocular face reconstruction. The code will be released at https://github.com/a686432/SIR

There is a steadily growing range of applications that can benefit from facial reconstruction techniques, leading to an increasing demand for reconstruction of high-quality 3D face models. While it is an important expressive part of the human face, the nose has received less attention than other expressive regions in the face reconstruction literature. When applying existing reconstruction methods to facial images, the reconstructed nose models are often inconsistent with the desired shape and expression. In this paper, we propose a coarse-to-fine 3D nose reconstruction and correction pipeline to build a nosemodel from a single image, where 3D and 2D nose curve correspondences are adaptively updated and refined. We first correct the reconstruction result coarsely using constraints of 3D-2D sparse landmark correspondences, and then heuristically update a dense 3D-2D curve correspondence based on the coarsely corrected result. A final refinement step is performed to correct the shape based on the updated 3D-2D dense curve constraints. Experimental results show the advantages of our method for 3D nose reconstruction over existing methods.