Man-made 3D shapes are naturally organized in parts and hierarchies; such
structures provide important constraints for shape reconstruction and
generation. Modeling shape structures is difficult, because there can be
multiple hierarchies for a given shape, causing ambiguity, and across different
categories the shape structures are correlated with semantics, limiting
generalization. We present StructRe, a structure rewriting system, as a novel
approach to structured shape modeling. Given a 3D object represented by points
and components, StructRe can rewrite it upward into more concise structures, or
downward into more detailed structures; by iterating the rewriting process,
hierarchies are obtained. Such a localized rewriting process enables
probabilistic modeling of ambiguous structures and robust generalization across
object categories. We train StructRe on PartNet data and show its
generalization to cross-category and multiple object hierarchies, and test its
extension to ShapeNet. We also demonstrate the benefits of probabilistic and
generalizable structure modeling for shape reconstruction, generation and
editing tasks.

通过结构重写系统（StructRe）进行局部迭代重写过程，实现不同类别、多个物体层次的形状建模，并在形状重建、生成和编辑任务中展示了概率建模和可推广性对于结构建模的好处。