# Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

arXiv: https://arxiv.org/abs/1905.02876 · HTML: https://mlsanity.com/paper/1905.02876/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2019.

## Built on by (most cited first, 30 of 90)

- [WiLoR: End-to-end 3D Hand Localization and Reconstruction in-the-wild](https://mlsanity.com/paper/2409.12259/) (2024)
- [BRepNet: A topological message passing system for solid models](https://mlsanity.com/paper/2104.00706/) (2021)
- [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)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [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)
- [FaceScape: 3D Facial Dataset and Benchmark for Single-View 3D Face Reconstruction](https://mlsanity.com/paper/2111.01082/) (2021)
- [Neural Face Rigging for Animating and Retargeting Facial Meshes in the Wild](https://mlsanity.com/paper/2305.08296/) (2023)
- [ZoomNAS: Searching for Whole-body Human Pose Estimation in the Wild](https://mlsanity.com/paper/2208.11547/) (2022)
- [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021)
- [RaBit: Parametric Modeling of 3D Biped Cartoon Characters with a Topological-consistent Dataset](https://mlsanity.com/paper/2303.12564/) (2023)
- [Light-weight spatio-temporal graphs for segmentation and ejection fraction prediction in cardiac ultrasound](https://mlsanity.com/paper/2207.02549/) (2022)
- [4D Facial Expression Diffusion Model](https://mlsanity.com/paper/2303.16611/) (2023)
- [Learning Feature Aggregation for Deep 3D Morphable Models](https://mlsanity.com/paper/2105.02173/) (2021)
- [EmoVOCA: Speech-Driven Emotional 3D Talking Heads](https://mlsanity.com/paper/2403.12886/) (2024)
- [Deep Structural Causal Shape Models](https://mlsanity.com/paper/2208.10950/) (2022)
- [3D Shapes Local Geometry Codes Learning with SDF](https://mlsanity.com/paper/2108.08593/) (2021)
- [Learning Landmarks Motion from Speech for Speaker-Agnostic 3D Talking Heads Generation](https://mlsanity.com/paper/2306.01415/) (2023)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representation](https://mlsanity.com/paper/2110.07882/) (2021)
- [FaceTuneGAN: Face Autoencoder for Convolutional Expression Transfer Using Neural Generative Adversarial Networks](https://mlsanity.com/paper/2112.00532/) (2021)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [3inGAN: Learning a 3D Generative Model from Images of a Self-similar Scene](https://mlsanity.com/paper/2211.14902/) (2022)
- [A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts](https://mlsanity.com/paper/2410.14770/) (2024)
- [A Riemannian Framework for Analysis of Human Body Surface](https://mlsanity.com/paper/2108.11449/) (2021)
- [Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes](https://mlsanity.com/paper/2110.09401/) (2021)
- [3D Shape Sequence of Human Comparison and Classification using Current and Varifolds](https://mlsanity.com/paper/2207.12485/) (2022)

## Abstract (arXiv)

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.