Hyperbolic Equivariant Convolutional Neural Networks for Fish-Eye Image Processing

Pierre-Yves Lagrave (1) , Frédéric Barbaresco (2)

1 Thales Research and Technology [Palaiseau]
2 Thales LAS - Thales Land and Air Systems

Fish-Eye image processing with conventional Machine Learning algorithms such as Convolutional Neural Networks is a challenging task because of the distortion effects induced by dewarping the raw hemispherical images into the Euclidean plane. We introduce in this paper an approach based on the emerging field of Geometric Deep Learning in which hyperbolic projection techniques are coupled with equivariance mechanisms in order to preserve native geometrical dependencies and to achieve robustness with respect to natural variations in the perception of the Fish-Eye images. This work in particular motivates the development of efficient SU(1, 1) and SL(2, R) Equivariant Neural Networks.

Mots clés: Fish-Eye image; Hyperbolic Geometry; Equivariant Neural Networks; Geometrical Robustness; Lie Groups

Domaines: Intelligence artificielle [cs.AI]; Mathématiques [math]; Autres [stat.ML]

Pierre-Yves Lagrave, Frédéric Barbaresco. Hyperbolic Equivariant Convolutional Neural Networks for Fish-Eye Image Processing. 2022. ⟨hal-03553274⟩