Summary: This paper states an interesting and novel idea- that learned shape bases could outperform hand-crafted heuristic functions. On the flip side, though, the method and experimental setups make drawing clear conclusions difficult, diminishing the impact. Post-rebuttal: The authors gave convincing responses to questions about the atlasnet comparison and about the number of parameters. So the final review is increased from 6 to 7. Originality: -As stated above, the paper has an interesting and novel high-level key idea. Whether the proposed method is really learning shape bases rather than using heuristic bases is a matter of interpretation, though.

We propose to represent shapes as the deformation and combination of learnt elementary 3D structures. We demonstrate this decomposition in learnt elementary 3D structures is highly interpretable and leads to clear improvements in 3D shape generation and matching. More precisely, we present two complementary approaches to learn elementary structures in a deep learning framework: (i) continuous surface deformation learning and (ii) 3D structure points learning. Both approaches can be extended to abstract structures of higher dimensions for improved results. We evaluate our method on two very different tasks: ShapeNet objects reconstruction and dense correspondences estimation between human scans.

We propose to represent shapes as the deformation and combination of learnt elementary 3D structures. We demonstrate this decomposition in learnt elementary 3D structures is highly interpretable and leads to clear improvements in 3D shape generation and matching. More precisely, we present two complementary approaches to learn elementary structures in a deep learning framework: (i) continuous surface deformation learning and (ii) 3D structure points learning. Both approaches can be extended to abstract structures of higher dimensions for improved results. We evaluate our method on two very different tasks: ShapeNet objects reconstruction and dense correspondences estimation between human scans.