# Graphics Capsule: Learning Hierarchical 3D Face Representations from 2D Images

arXiv: https://arxiv.org/abs/2303.10896 · HTML: https://mlsanity.com/paper/2303.10896/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Accurate 3D Face Reconstruction with Weakly-Supervised Learning: From Single Image to Image Set](https://mlsanity.com/paper/1903.08527/) (2019)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [Nonlinear 3D Face Morphable Model](https://mlsanity.com/paper/1804.03786/) (2018)
- [SCOPS: Self-Supervised Co-Part Segmentation](https://mlsanity.com/paper/1905.01298/) (2019)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [Deep Feature Factorization For Concept Discovery](https://mlsanity.com/paper/1806.10206/) (2018)
- [Unsupervised Part Discovery from Contrastive Reconstruction](https://mlsanity.com/paper/2111.06349/) (2021)
- [Explainable Face Recognition](https://mlsanity.com/paper/2008.00916/) (2020)
- [Unsupervised Part Segmentation through Disentangling Appearance and Shape](https://mlsanity.com/paper/2105.12405/) (2021)
- [Unsupervised part representation by Flow Capsules](https://mlsanity.com/paper/2011.13920/) (2020)
- [Dense 3D Face Decoding over 2500FPS: Joint Texture & Shape Convolutional Mesh Decoders](https://mlsanity.com/paper/1904.03525/) (2019)
- [Self-supervised Learning of Detailed 3D Face Reconstruction](https://mlsanity.com/paper/1910.11791/) (2019)
- [Learning to Aggregate and Personalize 3D Face from In-the-Wild Photo Collection](https://mlsanity.com/paper/2106.07852/) (2021)
- [HP-Capsule: Unsupervised Face Part Discovery by Hierarchical Parsing Capsule Network](https://mlsanity.com/paper/2203.10699/) (2022)

## Built on by (most cited first, 3 of 3)

- [BiTT: Bi-directional Texture Reconstruction of Interacting Two Hands from a Single Image](https://mlsanity.com/paper/2403.08262/) (2024)
- [LH2Face: Loss function for Hard High-quality Face](https://mlsanity.com/paper/2506.23555/) (2025)
- [Revisiting Marr in Face: The Building of 2D--2.5D--3D Representations in Deep Neural Networks](https://mlsanity.com/paper/2411.16148/) (2024)

## Abstract (arXiv)

The function of constructing the hierarchy of objects is important to the visual process of the human brain. Previous studies have successfully adopted capsule networks to decompose the digits and faces into parts in an unsupervised manner to investigate the similar perception mechanism of neural networks. However, their descriptions are restricted to the 2D space, limiting their capacities to imitate the intrinsic 3D perception ability of humans. In this paper, we propose an Inverse Graphics Capsule Network (IGC-Net) to learn the hierarchical 3D face representations from large-scale unlabeled images. The core of IGC-Net is a new type of capsule, named graphics capsule, which represents 3D primitives with interpretable parameters in computer graphics (CG), including depth, albedo, and 3D pose. Specifically, IGC-Net first decomposes the objects into a set of semantic-consistent part-level descriptions and then assembles them into object-level descriptions to build the hierarchy. The learned graphics capsules reveal how the neural networks, oriented at visual perception, understand faces as a hierarchy of 3D models. Besides, the discovered parts can be deployed to the unsupervised face segmentation task to evaluate the semantic consistency of our method. Moreover, the part-level descriptions with explicit physical meanings provide insight into the face analysis that originally runs in a black box, such as the importance of shape and texture for face recognition. Experiments on CelebA, BP4D, and Multi-PIE demonstrate the characteristics of our IGC-Net.