# Nonlinear 3D Face Morphable Model

arXiv: https://arxiv.org/abs/1804.03786 · HTML: https://mlsanity.com/paper/1804.03786/

## Key facts

- Cited by 157 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2018.

## Built on by (most cited first, 30 of 157)

- [I M Avatar: Implicit Morphable Head Avatars from Videos](https://mlsanity.com/paper/2112.07471/) (2021)
- [HeadNeRF: A Real-time NeRF-based Parametric Head Model](https://mlsanity.com/paper/2112.05637/) (2021)
- [MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffolds](https://mlsanity.com/paper/2405.17421/) (2024)
- [Reconstructing Personalized Semantic Facial NeRF Models From Monocular Video](https://mlsanity.com/paper/2210.06108/) (2022)
- [Pixel Codec Avatars](https://mlsanity.com/paper/2104.04638/) (2021)
- [FlashAvatar: High-fidelity Head Avatar with Efficient Gaussian Embedding](https://mlsanity.com/paper/2312.02214/) (2023)
- [FaceVerse: a Fine-grained and Detail-controllable 3D Face Morphable Model from a Hybrid Dataset](https://mlsanity.com/paper/2203.14057/) (2022)
- [MoFaNeRF: Morphable Facial Neural Radiance Field](https://mlsanity.com/paper/2112.02308/) (2021)
- [SMIRK: 3D Facial Expressions through Analysis-by-Neural-Synthesis](https://mlsanity.com/paper/2404.04104/) (2024)
- [H3D-Net: Few-Shot High-Fidelity 3D Head Reconstruction](https://mlsanity.com/paper/2107.12512/) (2021)
- [FantasyTalking: Realistic Talking Portrait Generation via Coherent Motion Synthesis](https://mlsanity.com/paper/2504.04842/) (2025)
- [Learning Neural Parametric Head Models](https://mlsanity.com/paper/2212.02761/) (2022)
- [A Shading-Guided Generative Implicit Model for Shape-Accurate 3D-Aware Image Synthesis](https://mlsanity.com/paper/2110.15678/) (2021)
- [3D face reconstruction with dense landmarks](https://mlsanity.com/paper/2204.02776/) (2022)
- [Let Them Talk: Audio-Driven Multi-Person Conversational Video Generation](https://mlsanity.com/paper/2505.22647/) (2025)
- [ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2203.14510/) (2022)
- [Implicit Identity Representation Conditioned Memory Compensation Network for Talking Head video Generation](https://mlsanity.com/paper/2307.09906/) (2023)
- [3D Gaussian Blendshapes for Head Avatar Animation](https://mlsanity.com/paper/2404.19398/) (2024)
- [Visual Speech-Aware Perceptual 3D Facial Expression Reconstruction from Videos](https://mlsanity.com/paper/2207.11094/) (2022)
- [Towards High Fidelity Monocular Face Reconstruction with Rich Reflectance using Self-supervised Learning and Ray Tracing](https://mlsanity.com/paper/2103.15432/) (2021)
- [RenderMe-360: A Large Digital Asset Library and Benchmarks Towards High-fidelity Head Avatars](https://mlsanity.com/paper/2305.13353/) (2023)
- [Learning Disentangled Avatars with Hybrid 3D Representations](https://mlsanity.com/paper/2309.06441/) (2023)
- [StableAvatar: Infinite-Length Audio-Driven Avatar Video Generation](https://mlsanity.com/paper/2508.08248/) (2025)
- [Face Relighting with Geometrically Consistent Shadows](https://mlsanity.com/paper/2203.16681/) (2022)
- [A Hierarchical Representation Network for Accurate and Detailed Face Reconstruction from In-The-Wild Images](https://mlsanity.com/paper/2302.14434/) (2023)
- [URAvatar: Universal Relightable Gaussian Codec Avatars](https://mlsanity.com/paper/2410.24223/) (2024)
- [Towards High Fidelity Face Relighting with Realistic Shadows](https://mlsanity.com/paper/2104.00825/) (2021)
- [Neural Strands: Learning Hair Geometry and Appearance from Multi-View Images](https://mlsanity.com/paper/2207.14067/) (2022)
- [FFHQ-UV: Normalized Facial UV-Texture Dataset for 3D Face Reconstruction](https://mlsanity.com/paper/2211.13874/) (2022)
- [Media2Face: Co-speech Facial Animation Generation With Multi-Modality Guidance](https://mlsanity.com/paper/2401.15687/) (2024)

## Abstract (arXiv)

As a classic statistical model of 3D facial shape and texture, 3D Morphable Model (3DMM) is widely used in facial analysis, e.g., model fitting, image synthesis. Conventional 3DMM is learned from a set of well-controlled 2D face images with associated 3D face scans, and represented by two sets of PCA basis functions. Due to the type and amount of training data, as well as the linear bases, the representation power of 3DMM can be limited. To address these problems, this paper proposes an innovative framework to learn a nonlinear 3DMM model from a large set of unconstrained face images, without collecting 3D face scans. Specifically, given a face image as input, a network encoder estimates the projection, shape and texture parameters. Two decoders serve as the nonlinear 3DMM to map from the shape and texture parameters to the 3D shape and texture, respectively. With the projection parameter, 3D shape, and texture, a novel analytically-differentiable rendering layer is designed to reconstruct the original input face. The entire network is end-to-end trainable with only weak supervision. We demonstrate the superior representation power of our nonlinear 3DMM over its linear counterpart, and its contribution to face alignment and 3D reconstruction.