Flattening the Parent Bias: Hierarchical Semantic Segmentation in the Poincare Ball
Authors: Simon Weber, Bar?? Zöngür, Nikita Araslanov, Daniel Cremers

Hierarchy is a natural representation of semantic taxonomies including the ones routinely used in image segmentation. Indeed recent work on semantic segmentation reports improved accuracy from supervised training leveraging hierarchical label structures. Encouraged by these results we revisit the fundamental assumptions behind that work. We postulate and then empirically verify that the reasons for the observed improvement in segmentation accuracy may be entirely unrelated to the use of the semantic hierarchy. To demonstrate this we design a range of cross-domain experiments with a representative hierarchical approach. We find that on the new testing domains a flat (non-hierarchical) segmentation network in which the parents are inferred from the children has superior segmentation accuracy to the hierarchical approach across the board. Complementing these findings and inspired by the intrinsic properties of hyperbolic spaces we study a more principled approach to hierarchical segmentation using the Poincare ball model. The hyperbolic representation largely outperforms the previous (Euclidean) hierarchical approach as well and is on par with our flat Euclidean baseline in terms of segmentation accuracy. However it additionally exhibits surprisingly strong calibration quality of the parent nodes in the semantic hierarchy especially on the more challenging domains. Our combined analysis suggests that the established practice of hierarchical segmentation may be limited to in-domain settings whereas flat classifiers generalize substantially better especially if they are modeled in the hyperbolic space.