# BFSM: 3D Bidirectional Face-Skull Morphable Model

arXiv: https://arxiv.org/abs/2509.24577 · HTML: https://mlsanity.com/paper/2509.24577/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 29 Sep 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [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)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Fake It Till You Make It: Face analysis in the wild using synthetic data alone](https://mlsanity.com/paper/2109.15102/) (2021)
- [FaceScape: a Large-scale High Quality 3D Face Dataset and Detailed Riggable 3D Face Prediction](https://mlsanity.com/paper/2003.13989/) (2020)
- [Face Alignment in Full Pose Range: A 3D Total Solution](https://mlsanity.com/paper/1804.01005/) (2018)
- [Kaolin: A PyTorch Library for Accelerating 3D Deep Learning Research](https://mlsanity.com/paper/1911.05063/) (2019)
- [FaceVerse: a Fine-grained and Detail-controllable 3D Face Morphable Model from a Hybrid Dataset](https://mlsanity.com/paper/2203.14057/) (2022)
- [SMIRK: 3D Facial Expressions through Analysis-by-Neural-Synthesis](https://mlsanity.com/paper/2404.04104/) (2024)
- [Learning Neural Parametric Head Models](https://mlsanity.com/paper/2212.02761/) (2022)
- [3D Face Reconstruction with the Geometric Guidance of Facial Part Segmentation](https://mlsanity.com/paper/2312.00311/) (2023)
- [MonoNPHM: Dynamic Head Reconstruction from Monocular Videos](https://mlsanity.com/paper/2312.06740/) (2023)
- [From Skin to Skeleton: Towards Biomechanically Accurate 3D Digital Humans](https://mlsanity.com/paper/2509.06607/) (2025)
- [OSSO: Obtaining Skeletal Shape from Outside](https://mlsanity.com/paper/2204.10129/) (2022)
- [3D Shape Variational Autoencoder Latent Disentanglement via Mini-Batch Feature Swapping for Bodies and Faces](https://mlsanity.com/paper/2111.12448/) (2021)
- [ShapeFusion: A 3D diffusion model for localized shape editing](https://mlsanity.com/paper/2403.19773/) (2024)
- [Learning a Generalized Physical Face Model From Data](https://mlsanity.com/paper/2402.19477/) (2024)
- [Implicit Neural Representation for Physics-driven Actuated Soft Bodies](https://mlsanity.com/paper/2401.14861/) (2024)
- [S2TD-Face: Reconstruct a Detailed 3D Face with Controllable Texture from a Single Sketch](https://mlsanity.com/paper/2408.01218/) (2024)
- [Anatomically Constrained Implicit Face Models](https://mlsanity.com/paper/2312.07538/) (2023)
- [An Implicit Physical Face Model Driven by Expression and Style](https://mlsanity.com/paper/2401.15414/) (2024)
- [Skull-to-Face: Anatomy-Guided 3D Facial Reconstruction and Editing](https://mlsanity.com/paper/2403.16207/) (2024)
- [SRM-Hair: Single Image Head Mesh Reconstruction via 3D Morphable Hair](https://mlsanity.com/paper/2503.06154/) (2025)

## Built on by (most cited first, 2 of 2)

- [STAvatar: Soft Binding and Temporal Density Control for Monocular 3D Head Avatars Reconstruction](https://mlsanity.com/paper/2511.19854/) (2025)
- [Surface-to-Skeleton 3D Cephalometry: Estimating Hidden Skeletal Landmarks from CT-Derived External Soft-Tissue Surfaces](https://mlsanity.com/paper/2608.12537/) (2026)

## Abstract (arXiv)

Building a joint face-skull morphable model holds great potential for applications such as remote diagnostics, surgical planning, medical education, and physically based facial simulation. However, realizing this vision is constrained by the scarcity of paired face-skull data, insufficient registration accuracy, and limited exploration of reconstruction and clinical applications. Moreover, individuals with craniofacial deformities are often overlooked, resulting in underrepresentation and limited inclusivity. To address these challenges, we first construct a dataset comprising over 200 samples, including both normal cases and rare craniofacial conditions. Each case contains a CT-based skull, a CT-based face, and a high-fidelity textured face scan. Secondly, we propose a novel dense ray matching registration method that ensures topological consistency across face, skull, and their tissue correspondences. Based on this, we introduce the 3D Bidirectional Face-Skull Morphable Model (BFSM), which enables shape inference between the face and skull through a shared coefficient space, while also modeling tissue thickness variation to support one-to-many facial reconstructions from the same skull, reflecting individual changes such as fat over time. Finally, we demonstrate the potential of BFSM in medical applications, including 3D face-skull reconstruction from a single image and surgical planning prediction. Extensive experiments confirm the robustness and accuracy of our method. BFSM is available at https://github.com/wang-zidu/BFSM