We introduce a hyperbolic neural network approach to pixel-level active learning for semantic segmentation, and propose a novel geometric interpretation of the hyperbolic geometry that arises bottom-up from the statistics of the data. In our formulation the hyperbolic radius emerges as an estimator of the unexplained class complexity, which encompasses the class intrinsic complexity and its scarcity in the dataset. The unexplained class complexity serves as a metric indicating the likelihood that acquiring a particular pixel would contribute to enhancing the data information. We combine this quantity with prediction uncertainty to compute an acquisition score that identifies the most informative pixels for oracle annotation. Our proposed HALO (Hyperbolic Active Learning Optimization) sets a new state-of-the-art in active learning for semantic segmentation under domain shift, and surpasses the supervised domain adaptation performance while only using a small portion of labels (i.e., 1%). We perform extensive experimental analysis based on two established benchmarks, i.e. GTAV $\rightarrow$ Cityscapes and SYNTHIA $\rightarrow$ Cityscapes, and we additionally test on Cityscape $\rightarrow$ ACDC under adverse weather conditions.

翻译：[翻译后的摘要在中国] 我们提出了一种用于像素级语义分割主动学习的双曲神经网络方法，并基于数据统计自下而上地提出了一种新的双曲几何几何解释。在我们的表述中，双曲半径作为未解释类别复杂度的估计量，涵盖了类别内在复杂度及其在数据集中的稀疏性。未解释类别复杂度作为一个度量指标，表示获取特定像素有助于增强数据信息的可能性。我们将该量与预测不确定性相结合，计算出一个获取分数，以识别最需要专家标注的信息量最大的像素。我们提出的HALO（Hyperbolic Active Learning Optimization）方法在域偏移下的语义分割主动学习中达到了新的最优性能，并且在使用仅1%的标签量时，超越了监督域自适应的性能。我们基于两个成熟基准（即GTAV $\rightarrow$ Cityscapes和SYNTHIA $\rightarrow$ Cityscapes）进行了广泛的实验分析，并进一步在恶劣天气条件下的Cityscape $\rightarrow$ ACDC上进行了测试。