Deep representation learning is a ubiquitous part of modern computer vision. While Euclidean space has been the de facto standard manifold for learning visual representations, hyperbolic space has recently gained rapid traction for learning in computer vision. Specifically, hyperbolic learning has shown a strong potential to embed hierarchical structures, learn from limited samples, quantify uncertainty, add robustness, limit error severity, and more. In this paper, we provide a categorization and in-depth overview of current literature on hyperbolic learning for computer vision. We research both supervised and unsupervised literature and identify three main research themes in each direction. We outline how hyperbolic learning is performed in all themes and discuss the main research problems that benefit from current advances in hyperbolic learning for computer vision. Moreover, we provide a high-level intuition behind hyperbolic geometry and outline open research questions to further advance research in this direction.

翻译：深度表示学习是现代计算机视觉中不可或缺的一部分。尽管欧几里得空间一直是学习视觉表示的事实标准流形，但双曲空间近年来在计算机视觉学习中迅速获得关注。具体而言，双曲学习在嵌入层次结构、从有限样本中学习、量化不确定性、增强鲁棒性、限制错误严重性等方面展现出巨大潜力。本文对当前计算机视觉中双曲学习的文献进行了分类和深入概述。我们研究了有监督和无监督文献，并分别识别出三个主要研究方向。我们概述了所有方向中双曲学习的实现方式，并讨论了当前双曲学习进展所惠及的主要研究问题。此外，我们提供了双曲几何的高层直觉解释，并提出了开放性问题以进一步推动该领域研究。