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Many recent works have reconstructed distinctive 3D face shapes by aggregating shape parameters of the same identity and separating those of different people based on parametric models (e.g. 3D morphable models (3DMMs)). However, despite the high accuracy in the face recognition task using these shape parameters, the visual discrimination of face shapes reconstructed from those parameters remains unsatisfactory. Previous works have not answered the following research question: Do discriminative shape parameters guarantee visual discrimination in represented 3D face shapes? This paper analyses the relationship between shape parameters and reconstructed shape geometry, and proposes a novel shape identity-aware regularization (SIR) loss for shape parameters, aiming at increasing discriminability in both the shape parameter and shape geometry domains. Moreover, to cope with the lack of training data containing both landmark and identity annotations, we propose a network structure and an associated training strategy to leverage mixed data containing either identity or landmark labels. In addition, since face recognition accuracy does not mean the recognizability of reconstructed face shapes from the shape parameters, we propose the SIR metric to measure the discriminability of face shapes. We compare our method with existing methods in terms of the reconstruction error, visual discriminability, and face recognition accuracy of the shape parameters and SIR metric. Experimental results show that our method outperforms the state-of-the-art methods. The code will be released at https:// github.com/ a686432/ SIR.

Abstract3D 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, the shape 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 2D and 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

Many recent works have reconstructed distinctive 3D face shapes by aggregating shape parameters of the same identity and separating those of different people based on parametric models (e.g., 3D morphable models (3DMMs)). However, despite the high accuracy in the face recognition task using these shape parameters, the visual discrimination of face shapes reconstructed from those parameters is unsatisfactory. The following research question has not been answered in previous works: Do discriminative shape parameters guarantee visual discrimination in represented 3D face shapes? This paper analyzes the relationship between shape parameters and reconstructed shape geometry and proposes a novel shape identityaware regularization(SIR) loss for shape parameters, aiming at increasing discriminability in both the shape parameter and shape geometry domains. Moreover, to cope with the lack of training data containing both landmark and identity annotations, we propose a network structure and an associated training strategy to leverage mixed data containing either identity or landmark labels. We compare our method with existing methods in terms of the reconstruction error, visual distinguishability, and face recognition accuracy of the shape parameters. Experimental results show that our method outperforms the state-of-the-art methods.