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

**Authors:** Chang Yu, Xiangyu Zhu, Xiaomei Zhang, Zhaoxiang Zhang, Zhen Lei  
**arXiv:** [2303.10896](https://arxiv.org/abs/2303.10896)  
**Date:** 2023-03-20  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.10896v1/

## Key points

- The human brain's visual process relies on the construction of object hierarchies
- Previous studies have used capsule networks to decompose digits and faces into parts in an unsupervised manner
- However, these descriptions are limited to 2D space, which restricts their ability to imitate humans' intrinsic 3D perception
- This paper proposes an Inverse Graphics Capsule Network (IGC-Net) that learns hierarchical 3D face representations from large-scale unlabeled images using a new type of capsule called graphics capsule
- The IGC-Net first decomposes objects into semantic-consistent part-level descriptions before assembling them into object-level descriptions to build the hierarchy
- Experiments on CelebA, BP4D, and Multi-PIE demonstrate the characteristics of IGC-Net. The proposed method outperforms existing state-of-the-art methods in terms of accuracy and generalization ability.
- The learned graphics capsules reveal how neural networks understand faces as a hierarchy of 3D models.
- The discovered parts can be deployed for unsupervised face segmentation tasks to evaluate the semantic consistency of the method.
- Additionally, the part-level descriptions provide insight into face analysis that originally runs in a black box by highlighting the importance of shape and texture for face recognition.
- The proposed method provides interpretable results that can be used for further analysis or downstream tasks such as facial expression recognition or animation synthesis.

## Summary

, , , , . The human brain's visual process relies on the construction of object hierarchies, and previous studies have successfully used capsule networks to decompose digits and faces into parts in an unsupervised manner. However, these descriptions are limited to 2D space, which restricts their ability to imitate humans' intrinsic 3D perception. To address this limitation, this paper proposes an Inverse Graphics Capsule Network (IGC-Net) that learns hierarchical 3D face representations from large-scale unlabeled images. The IGC-Net uses a new type of capsule called graphics capsule that represents 3D primitives with interpretable parameters in computer graphics (CG), including depth, albedo, and 3D pose. The IGC-Net first decomposes objects into semantic-consistent part-level descriptions before assembling them into object-level descriptions to build the hierarchy. The learned graphics capsules reveal how neural networks understand faces as a hierarchy of 3D models. Furthermore, the discovered parts can be deployed for unsupervised face segmentation tasks to evaluate the semantic consistency of the method. Additionally, the part-level descriptions provide insight into face analysis that originally runs in a black box by highlighting the importance of shape and texture for face recognition. Experiments on CelebA, BP4D, and Multi-PIE demonstrate the characteristics of IGC-Net. The proposed method outperforms existing state-of-the-art methods in terms of accuracy and generalization ability. Moreover, it provides interpretable results that can be used for further analysis or downstream tasks such as facial expression recognition or animation synthesis. In conclusion, this paper presents a novel approach for learning hierarchical 3D face representations using graphics capsules that can help improve our understanding of how neural networks perceive objects in three dimensions.