Learning Affinity with Hyperbolic Representation for Spatial Propagation

Abstract

Recent approaches to representation learning have successfully demonstrated the benefits in hyperbolic space, driven by an excellent ability to make hierarchical relationships. In this work, we demonstrate that the properties of hyperbolic geometry serve as a valuable alternative to learning hierarchical affinity for spatial propagation tasks. We propose a Hyperbolic Affinity learning Module (HAM) to learn spatial affinity by considering geodesic distance on the hyperbolic space. By simply incorporating our HAM into conventional spatial propagation tasks, we validate its effectiveness, capturing the pixel hierarchy of affinity maps in hyperbolic space. The proposed methodology can lead to performance improvements in explicit propagation processes such as depth completion and semantic segmentation.