# Sphere Face Model:A 3D Morphable Model with Hypersphere Manifold Latent Space

arXiv: https://arxiv.org/abs/2112.02238 · HTML: https://mlsanity.com/paper/2112.02238/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 71 references that are in the map.
- First posted on arXiv 4 Dec 2021.

## Builds on (most cited first, 30 of 37)

- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Accurate 3D Face Reconstruction with Weakly-Supervised Learning: From Single Image to Image Set](https://mlsanity.com/paper/1903.08527/) (2019)
- [Learning an Animatable Detailed 3D Face Model from In-The-Wild Images](https://mlsanity.com/paper/2012.04012/) (2020)
- [CurricularFace: Adaptive Curriculum Learning Loss for Deep Face Recognition](https://mlsanity.com/paper/2004.00288/) (2020)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Additive Margin Softmax for Face Verification](https://mlsanity.com/paper/1801.05599/) (2018)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [Towards Fast, Accurate and Stable 3D Dense Face Alignment](https://mlsanity.com/paper/2009.09960/) (2020)
- [FaceScape: a Large-scale High Quality 3D Face Dataset and Detailed Riggable 3D Face Prediction](https://mlsanity.com/paper/2003.13989/) (2020)
- [Joint 3D Face Reconstruction and Dense Alignment with Position Map Regression Network](https://mlsanity.com/paper/1803.07835/) (2018)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [Learning to Regress 3D Face Shape and Expression from an Image without 3D Supervision](https://mlsanity.com/paper/1905.06817/) (2019)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [Nonlinear 3D Face Morphable Model](https://mlsanity.com/paper/1804.03786/) (2018)
- [GANFIT: Generative Adversarial Network Fitting for High Fidelity 3D Face Reconstruction](https://mlsanity.com/paper/1902.05978/) (2019)
- [Face Alignment in Full Pose Range: A 3D Total Solution](https://mlsanity.com/paper/1804.01005/) (2018)
- [Morphable Face Models - An Open Framework](https://mlsanity.com/paper/1709.08398/) (2017)
- [Regressing Robust and Discriminative 3D Morphable Models with a very Deep Neural Network](https://mlsanity.com/paper/1612.04904/) (2016)
- [Self-supervised Multi-level Face Model Learning for Monocular Reconstruction at over 250 Hz](https://mlsanity.com/paper/1712.02859/) (2017)
- [Towards High-fidelity Nonlinear 3D Face Morphable Model](https://mlsanity.com/paper/1904.04933/) (2019)
- [AvatarMe: Realistically Renderable 3D Facial Reconstruction "in-the-wild"](https://mlsanity.com/paper/2003.13845/) (2020)
- [AdaCos: Adaptively Scaling Cosine Logits for Effectively Learning Deep Face Representations](https://mlsanity.com/paper/1905.00292/) (2019)
- [Self-Supervised Monocular 3D Face Reconstruction by Occlusion-Aware Multi-view Geometry Consistency](https://mlsanity.com/paper/2007.12494/) (2020)
- [A Morphable Face Albedo Model](https://mlsanity.com/paper/2004.02711/) (2020)
- [Towards High-Fidelity 3D Face Reconstruction from In-the-Wild Images Using Graph Convolutional Networks](https://mlsanity.com/paper/2003.05653/) (2020)
- [Disentangled Representation Learning for 3D Face Shape](https://mlsanity.com/paper/1902.09887/) (2019)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Registration for Gaussian Process 3D shape modelling in the presence of extensive missing data](https://mlsanity.com/paper/2203.14113/) (2022)

## Abstract (arXiv)

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.