  Hyperbolic geometry, a Riemannian manifold endowed with constant sectional
negative curvature, has been considered an alternative embedding space in many
learning scenarios, \eg, natural language processing, graph learning, \etc, as
a result of its intriguing property of encoding the data's hierarchical
structure (like irregular graph or tree-likeness data). Recent studies prove
that such data hierarchy also exists in the visual dataset, and investigate the
successful practice of hyperbolic geometry in the computer vision (CV) regime,
ranging from the classical image classification to advanced model adaptation
learning. This paper presents the first and most up-to-date literature review
of hyperbolic spaces for CV applications. To this end, we first introduce the
background of hyperbolic geometry, followed by a comprehensive investigation of
algorithms, with geometric prior of hyperbolic space, in the context of visual
applications. We also conclude this manuscript and identify possible future
directions.
