  We present a novel neural network architecture, termed Decomposer-Composer,
for semantic structure-aware 3D shape modeling. Our method utilizes an
auto-encoder-based pipeline, and produces a novel factorized shape embedding
space, where the semantic structure of the shape collection translates into a
data-dependent sub-space factorization, and where shape composition and
decomposition become simple linear operations on the embedding coordinates. We
further propose to model shape assembly using an explicit learned part
deformation module, which utilizes a 3D spatial transformer network to perform
an in-network volumetric grid deformation, and which allows us to train the
whole system end-to-end. The resulting network allows us to perform part-level
shape manipulation, unattainable by existing approaches. Our extensive ablation
study, comparison to baseline methods and qualitative analysis demonstrate the
improved performance of the proposed method.
