# Multilinear Wavelets: A Statistical Shape Space for Human Faces

arXiv: https://arxiv.org/abs/1401.2818 · HTML: https://mlsanity.com/paper/1401.2818/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2014.

## Built on by (most cited first, 30 of 32)

- [FaceVerse: a Fine-grained and Detail-controllable 3D Face Morphable Model from a Hybrid Dataset](https://mlsanity.com/paper/2203.14057/) (2022)
- [Learning Neural Parametric Head Models](https://mlsanity.com/paper/2212.02761/) (2022)
- [ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2203.14510/) (2022)
- [HAvatar: High-fidelity Head Avatar via Facial Model Conditioned Neural Radiance Field](https://mlsanity.com/paper/2309.17128/) (2023)
- [FaceScape: 3D Facial Dataset and Benchmark for Single-View 3D Face Reconstruction](https://mlsanity.com/paper/2111.01082/) (2021)
- [HHAvatar: Gaussian Head Avatar with Dynamic Hairs](https://mlsanity.com/paper/2312.03029/) (2023)
- [SunStage: Portrait Reconstruction and Relighting using the Sun as a Light Stage](https://mlsanity.com/paper/2204.03648/) (2022)
- [Neural Face Rigging for Animating and Retargeting Facial Meshes in the Wild](https://mlsanity.com/paper/2305.08296/) (2023)
- [SUPR: A Sparse Unified Part-Based Human Representation](https://mlsanity.com/paper/2210.13861/) (2022)
- [TextToon: Real-Time Text Toonify Head Avatar from Single Video](https://mlsanity.com/paper/2410.07160/) (2024)
- [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021)
- [ScaffoldAvatar: High-Fidelity Gaussian Avatars with Patch Expressions](https://mlsanity.com/paper/2507.10542/) (2025)
- [DPHMs: Diffusion Parametric Head Models for Depth-based Tracking](https://mlsanity.com/paper/2312.01068/) (2023)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [Towards 3D Face Reconstruction in Perspective Projection: Estimating 6DoF Face Pose from Monocular Image](https://mlsanity.com/paper/2205.04126/) (2022)
- [Tensor-based Emotion Editing in the StyleGAN Latent Space](https://mlsanity.com/paper/2205.06102/) (2022)
- [Generating Multiple 4D Expression Transitions by Learning Face Landmark Trajectories](https://mlsanity.com/paper/2208.00050/) (2022)
- [Neuromorphic Facial Analysis with Cross-Modal Supervision](https://mlsanity.com/paper/2409.10213/) (2024)
- [Neural Face Skinning for Mesh-agnostic Facial Expression Cloning](https://mlsanity.com/paper/2505.22416/) (2025)
- [Structure-aware Editable Morphable Model for 3D Facial Detail Animation and Manipulation](https://mlsanity.com/paper/2207.09019/) (2022)
- [InstantAvatar: Efficient 3D Head Reconstruction via Surface Rendering](https://mlsanity.com/paper/2308.04868/) (2023)
- [Tensor-based Subspace Factorization for StyleGAN](https://mlsanity.com/paper/2111.04554/) (2021)
- [SCULPTOR: Skeleton-Consistent Face Creation Using a Learned Parametric Generator](https://mlsanity.com/paper/2209.06423/) (2022)
- [Approximating Intersections and Differences Between Linear Statistical Shape Models Using Markov Chain Monte Carlo](https://mlsanity.com/paper/2211.16314/) (2022)
- [Spatio-temporal Transformers for Action Unit Classification with Event Cameras](https://mlsanity.com/paper/2410.21958/) (2024)
- [High-Fidelity Mobile Avatars with Pruned Local Blendshapes](https://mlsanity.com/paper/2605.01854/) (2026)
- [FaceCom: Towards High-fidelity 3D Facial Shape Completion via Optimization and Inpainting Guidance](https://mlsanity.com/paper/2406.02074/) (2024)
- [OmniFaceRig: Fully Automatic Inner-Mouth-Aware Face Rigging Across Diverse 3D Character Topologies](https://mlsanity.com/paper/2606.08043/) (2026)
- [Probabilistic Registration for Gaussian Process 3D shape modelling in the presence of extensive missing data](https://mlsanity.com/paper/2203.14113/) (2022)
- [Accurate Gaze Estimation using an Active-gaze Morphable Model](https://mlsanity.com/paper/2301.13186/) (2023)

## Abstract (arXiv)

We present a statistical model for 3D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using this model we are able to reconstruct faces from noisy and occluded 3D face scans, and facial motion sequences. Accurate reconstruction of face shape is important for applications such as tele-presence and gaming. The localized and multi-scale nature of our model allows for recovery of fine-scale detail while retaining robustness to severe noise and occlusion, and is computationally efficient and scalable. We validate these properties experimentally on challenging data in the form of static scans and motion sequences. We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject.