# ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations

arXiv: https://arxiv.org/abs/2312.04028 · HTML: https://mlsanity.com/paper/2312.04028/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 77 of its 108 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Builds on (most cited first, 30 of 77)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [PIFuHD: Multi-Level Pixel-Aligned Implicit Function for High-Resolution 3D Human Digitization](https://mlsanity.com/paper/2004.00452/) (2020)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularization](https://mlsanity.com/paper/2303.07418/) (2023)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [HeadNeRF: A Real-time NeRF-based Parametric Head Model](https://mlsanity.com/paper/2112.05637/) (2021)
- [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)

## Built on by (most cited first, 10 of 10)

- [MonoNPHM: Dynamic Head Reconstruction from Monocular Videos](https://mlsanity.com/paper/2312.06740/) (2023)
- [PanoLAM: Large Avatar Model for Gaussian Full-Head Synthesis from One-shot Unposed Image](https://mlsanity.com/paper/2509.07552/) (2025)
- [Towards Croppable Implicit Neural Representations](https://mlsanity.com/paper/2409.19472/) (2024)
- [Geometric implicit neural representations for signed distance functions](https://mlsanity.com/paper/2511.07206/) (2025)
- [Micro-macro Gaussian Splatting with Enhanced Scalability for Unconstrained Scene Reconstruction](https://mlsanity.com/paper/2506.13516/) (2025)
- [Pix2NPHM: Learning to Regress NPHM Reconstructions From a Single Image](https://mlsanity.com/paper/2512.17773/) (2025)
- [Registration-Free Learnable Multi-View Capture of Faces in Dense Semantic Correspondence](https://mlsanity.com/paper/2605.01450/) (2026)
- [Monocular Avatar Reconstruction via Cascaded Diffusion Priors and UV-Space Differentiable Shading](https://mlsanity.com/paper/2606.28144/) (2026)
- [GLVD: Guided Learned Vertex Descent](https://mlsanity.com/paper/2510.06046/) (2025)
- [CaricatureGS: Exaggerating 3D Gaussian Splatting Faces With Gaussian Curvature](https://mlsanity.com/paper/2601.03319/) (2026)

## Abstract (arXiv)

Accurate representations of 3D faces are of paramount importance in various computer vision and graphics applications. However, the challenges persist due to the limitations imposed by data discretization and model linearity, which hinder the precise capture of identity and expression clues in current studies. This paper presents a novel 3D morphable face model, named ImFace++, to learn a sophisticated and continuous space with implicit neural representations. ImFace++ first constructs two explicitly disentangled deformation fields to model complex shapes associated with identities and expressions, respectively, which simultaneously facilitate automatic learning of point-to-point correspondences across diverse facial shapes. To capture more sophisticated facial details, a refinement displacement field within the template space is further incorporated, enabling fine-grained learning of individual-specific facial details. Furthermore, a Neural Blend-Field is designed to reinforce the representation capabilities through adaptive blending of an array of local fields. In addition to ImFace++, we devise an improved learning strategy to extend expression embeddings, allowing for a broader range of expression variations. Comprehensive qualitative and quantitative evaluation demonstrates that ImFace++ significantly advances the state-of-the-art in terms of both face reconstruction fidelity and correspondence accuracy.