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Conventional convolution neural networks (CNNs) trained on narrowField-of-View (FoV) images are the state-of-the-art approaches for objectrecognition tasks. Some methods proposed the adaptation of CNNs to ultra-wideFoV images by learning deformable kernels. However, they are limited by theEuclidean geometry and their accuracy degrades under strong distortions causedby fisheye projections. In this work, we demonstrate that learning the shape ofconvolution kernels in non-Euclidean spaces is better than existing deformablekernel methods. In particular, we propose a new approach that learns deformablekernel parameters (positions) in hyperbolic space. FisheyeHDK is a hybrid CNNarchitecture combining hyperbolic and Euclidean convolution layers forpositions and features learning. First, we provide an intuition of hyperbolicspace for wide FoV images. Using synthetic distortion profiles, we demonstratethe effectiveness of our approach. We select two datasets - Cityscapes andBDD100K 2020 - of perspective images which we transform to fisheye equivalentsat different scaling factors (analog to focal lengths). Finally, we provide anexperiment on data collected by a real fisheye camera. Validations andexperiments show that our approach improves existing deformable kernel methodsfor CNN adaptation on fisheye images.

FisheyeHDK: Hyperbolic Deformable Kernel Learning for Ultra-Wide Field-of-View Image Recognition