# A Sparse and Locally Coherent Morphable Face Model for Dense Semantic Correspondence Across Heterogeneous 3D Faces

arXiv: https://arxiv.org/abs/2006.03840 · HTML: https://mlsanity.com/paper/2006.03840/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021)
- [3D-aware Blending with Generative NeRFs](https://mlsanity.com/paper/2302.06608/) (2023)
- [FaceTuneGAN: Face Autoencoder for Convolutional Expression Transfer Using Neural Generative Adversarial Networks](https://mlsanity.com/paper/2112.00532/) (2021)
- [The Florence 4D Facial Expression Dataset](https://mlsanity.com/paper/2210.16807/) (2022)
- [Generating Multiple 4D Expression Transitions by Learning Face Landmark Trajectories](https://mlsanity.com/paper/2208.00050/) (2022)
- [Beyond Fixed Topologies: Unregistered Training and Comprehensive Evaluation Metrics for 3D Talking Heads](https://mlsanity.com/paper/2410.11041/) (2024)
- [Are 3D Face Shapes Expressive Enough for Recognising Continuous Emotions and Action Unit Intensities?](https://mlsanity.com/paper/2207.01113/) (2022)
- [Towards Fine-grained 3D Face Dense Registration: An Optimal Dividing and Diffusing Method](https://mlsanity.com/paper/2109.11204/) (2021)
- [3D Face Reconstruction Error Decomposed: A Modular Benchmark for Fair and Fast Method Evaluation](https://mlsanity.com/paper/2505.18025/) (2025)
- [FreeTalk: Emotional Topology-Free 3D Talking Heads](https://mlsanity.com/paper/2603.15512/) (2026)
- [Polyglot: Multilingual Style Preserving Speech-Driven Facial Animation](https://mlsanity.com/paper/2604.16108/) (2026)

## Abstract (arXiv)

The 3D Morphable Model (3DMM) is a powerful statistical tool for representing 3D face shapes. To build a 3DMM, a training set of face scans in full point-to-point correspondence is required, and its modeling capabilities directly depend on the variability contained in the training data. Thus, to increase the descriptive power of the 3DMM, establishing a dense correspondence across heterogeneous scans with sufficient diversity in terms of identities, ethnicities, or expressions becomes essential. In this manuscript, we present a fully automatic approach that leverages a 3DMM to transfer its dense semantic annotation across raw 3D faces, establishing a dense correspondence between them. We propose a novel formulation to learn a set of sparse deformation components with local support on the face that, together with an original non-rigid deformation algorithm, allow the 3DMM to precisely fit unseen faces and transfer its semantic annotation. We extensively experimented our approach, showing it can effectively generalize to highly diverse samples and accurately establish a dense correspondence even in presence of complex facial expressions. The accuracy of the dense registration is demonstrated by building a heterogeneous, large-scale 3DMM from more than 9,000 fully registered scans obtained by joining three large datasets together.