Topnet: structural point cloud decoder

3D point cloud generation is of great use for 3D scene modeling and understanding. Real-world 3D object point clouds can be properly described by a collection of low-level and high-level structures such as surfaces, geometric primitives, semantic parts,etc. In fact, there exist many different representations of a 3D object point cloud as a set of point groups. Existing frameworks for point cloud genera-ion either do not consider structure in their proposed solutions, or assume and enforce a specific structure/topology,e.g. a collection of manifolds or surfaces, for the generated point cloud of a 3D object. In this work, we pro-pose a novel decoder that generates a structured point cloud without assuming any specific structure or topology on the underlying point set. Our decoder is softly constrained to generate a point cloud following a hierarchical rooted tree structure. We show that given enough capacity and allowing for redundancies, the proposed decoder is very flexible and able to learn any arbitrary grouping of points including any topology on the point set. We evaluate our decoder on the task of point cloud generation for 3D point cloud shape completion. Combined with encoders from existing frameworks, we show that our proposed decoder significantly outperforms state-of-the-art 3D point cloud completion methods on the Shapenet dataset.