Rethinking the compositionality of point clouds through regularization in the hyperbolic space
This addresses the challenge of modeling tree-like compositional structures in 3D object recognition, which is incremental as it builds on existing supervised models.
The paper tackled the problem of capturing the part-whole hierarchy in 3D point clouds by embedding features into hyperbolic space with regularization, resulting in substantial performance improvements in state-of-the-art supervised models for point cloud classification.
Point clouds of 3D objects exhibit an inherent compositional nature where simple parts can be assembled into progressively more complex shapes to form whole objects. Explicitly capturing such part-whole hierarchy is a long-sought objective in order to build effective models, but its tree-like nature has made the task elusive. In this paper, we propose to embed the features of a point cloud classifier into the hyperbolic space and explicitly regularize the space to account for the part-whole hierarchy. The hyperbolic space is the only space that can successfully embed the tree-like nature of the hierarchy. This leads to substantial improvements in the performance of state-of-art supervised models for point cloud classification.