For the task of semantic segmentation (SS) under domain shift, active
learning (AL) acquisition strategies based on image regions and pseudo labels
are state-of-the-art (SoA). The presence of diverse pseudo-labels within a
region identifies pixels between different classes, which is a labeling
efficient active learning data acquisition strategy. However, by design,
pseudo-label variations are limited to only select the contours of classes,
limiting the final AL performance. We approach AL for SS in the Poincar\'e
hyperbolic ball model for the first time and leverage the variations of the
radii of pixel embeddings within regions as a novel data acquisition strategy.
This stems from a novel geometric property of a hyperbolic space trained
without enforced hierarchies, which we experimentally prove. Namely, classes
are mapped into compact hyperbolic areas with a comparable intra-class radii
variance, as the model places classes of increasing explainable difficulty at
denser hyperbolic areas, i.e. closer to the Poincar\'e ball edge. The variation
of pixel embedding radii identifies well the class contours, but they also
select a few intra-class peculiar details, which boosts the final performance.
Our proposed HALO (Hyperbolic Active Learning Optimization) surpasses the
supervised learning performance for the first time in AL for SS under domain
shift, by only using a small portion of labels (i.e., 1%). The extensive
experimental analysis is based on two established benchmarks, i.e. GTAV
$\rightarrow$ Cityscapes and SYNTHIA $\rightarrow$ Cityscapes, where we set a
new SoA. The code will be released.

利用 Poincaré 超球模型的变化，提出了一种新的数据获取策略，称为 “HALO”，它可以用极少量的标签（即 1％）首次超越监督学习性能，该方法在解决域漂移下的语义分割中具有潜在的应用。