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

We present a novel algorithm BADF (Bounding Volume Hierarchy Based Adaptive Distance Fields) for accelerating the construction of ADFs (adaptive distance fields) of rigid and deformable models on graphics processing units. Our approach is based on constructing a bounding volume hierarchy (BVH) and we use that hierarchy to generate an octree-based ADF. We exploit the coherence between successive frames and sort the grid points of the octree to accelerate the computation. Our approach is applicable to rigid and deformable models. Our GPU-based (graphics processing unit based) algorithm is about 20x–50x faster than current mainstream central processing unit based algorithms. Our BADF algorithm can construct the distance fields for deformable models with 60k triangles at interactive rates on an NVIDIA GTX GeForce 1060. Moreover, we observe 3x speedup over prior GPU-based ADF algorithms.

We present an efficient and robust method which performs well for both strain limiting and treatment of simultaneous collisions. Our method formulates strain constraints and collision constraints as a serial of linear matrix inequalities (LMIs) and linear polynomial inequalities (LPIs), and solves an optimization problem with standard convex semidefinite programming solvers. When performing strain limiting, our method acts on strain tensors to constrain the singular values of the deformation gradient matrix in a specified interval. Our method can be applied to both triangular surface meshes and tetrahedral volume meshes. Compared with prior strain limiting methods, our method converges much faster and guarantees triangle flipping does not occur when applied to a triangular mesh. When performing treatment of simultaneous collisions, our method eliminates all detected collisions during each iteration, leading to higher efficiency and faster convergence than prior collision treatment methods.