  Humans perceive the 3D world as a set of distinct objects that are
characterized by various low-level (geometry, reflectance) and high-level
(connectivity, adjacency, symmetry) properties. Recent methods based on
convolutional neural networks (CNNs) demonstrated impressive progress in 3D
reconstruction, even when using a single 2D image as input. However, the
majority of these methods focuses on recovering the local 3D geometry of an
object without considering its part-based decomposition or relations between
parts. We address this challenging problem by proposing a novel formulation
that allows to jointly recover the geometry of a 3D object as a set of
primitives as well as their latent hierarchical structure without part-level
supervision. Our model recovers the higher level structural decomposition of
various objects in the form of a binary tree of primitives, where simple parts
are represented with fewer primitives and more complex parts are modeled with
more components. Our experiments on the ShapeNet and D-FAUST datasets
demonstrate that considering the organization of parts indeed facilitates
reasoning about 3D geometry.
