  Signed distance field (SDF) is a prominent implicit representation of 3D
meshes. Methods that are based on such representation achieved state-of-the-art
3D shape reconstruction quality. However, these methods struggle to reconstruct
non-convex shapes. One remedy is to incorporate a constructive solid geometry
framework (CSG) that represents a shape as a decomposition into primitives. It
allows to embody a 3D shape of high complexity and non-convexity with a simple
tree representation of Boolean operations. Nevertheless, existing approaches
are supervised and require the entire CSG parse tree that is given upfront
during the training process. On the contrary, we propose a model that extracts
a CSG parse tree without any supervision - UCSG-Net. Our model predicts
parameters of primitives and binarizes their SDF representation through
differentiable indicator function. It is achieved jointly with discovering the
structure of a Boolean operators tree. The model selects dynamically which
operator combination over primitives leads to the reconstruction of high
fidelity. We evaluate our method on 2D and 3D autoencoding tasks. We show that
the predicted parse tree representation is interpretable and can be used in CAD
software.
