  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.
