  Reconstructing 3D objects from 2D images is a fundamental task in computer
vision. Accurate structured reconstruction by parsimonious and semantic
primitive representation further broadens its application. When reconstructing
a target shape with multiple primitives, it is preferable that one can
instantly access the union of basic properties of the shape such as collective
volume and surface, treating the primitives as if they are one single shape.
This becomes possible by primitive representation with unified implicit and
explicit representations. However, primitive representations in current
approaches do not satisfy all of the above requirements at the same time. To
solve this problem, we propose a novel primitive representation named neural
star domain (NSD) that learns primitive shapes in the star domain. We show that
NSD is a universal approximator of the star domain and is not only parsimonious
and semantic but also an implicit and explicit shape representation. We
demonstrate that our approach outperforms existing methods in image
reconstruction tasks, semantic capabilities, and speed and quality of sampling
high-resolution meshes.
