  3D Shape representation has substantial effects on 3D shape reconstruction.
Primitive-based representations approximate a 3D shape mainly by a set of
simple implicit primitives, but the low geometrical complexity of the
primitives limits the shape resolution. Moreover, setting a sufficient number
of primitives for an arbitrary shape is challenging. To overcome these issues,
we propose a constrained implicit algebraic surface as the primitive with few
learnable coefficients and higher geometrical complexities and a deep neural
network to produce these primitives. Our experiments demonstrate the
superiorities of our method in terms of representation power compared to the
state-of-the-art methods in single RGB image 3D shape reconstruction.
Furthermore, we show that our method can semantically learn segments of 3D
shapes in an unsupervised manner. The code is publicly available from
https://myavartanoo.github.io/3dias/ .
