  Conventional convolution neural networks (CNNs) trained on narrow
Field-of-View (FoV) images are the state-of-the-art approaches for object
recognition tasks. Some methods proposed the adaptation of CNNs to ultra-wide
FoV images by learning deformable kernels. However, they are limited by the
Euclidean geometry and their accuracy degrades under strong distortions caused
by fisheye projections. In this work, we demonstrate that learning the shape of
convolution kernels in non-Euclidean spaces is better than existing deformable
kernel methods. In particular, we propose a new approach that learns deformable
kernel parameters (positions) in hyperbolic space. FisheyeHDK is a hybrid CNN
architecture combining hyperbolic and Euclidean convolution layers for
positions and features learning. First, we provide an intuition of hyperbolic
space for wide FoV images. Using synthetic distortion profiles, we demonstrate
the effectiveness of our approach. We select two datasets - Cityscapes and
BDD100K 2020 - of perspective images which we transform to fisheye equivalents
at different scaling factors (analog to focal lengths). Finally, we provide an
experiment on data collected by a real fisheye camera. Validations and
experiments show that our approach improves existing deformable kernel methods
for CNN adaptation on fisheye images.
