We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. 
 To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficient neural networks that match or outperform state-of-the-art network architectures in terms of performance but with a significantly lower number of network parameters. We evaluate our algorithm in an extensive series of experiments on a variety of computer vision and climate science tasks, including shape classification, climate pattern segmentation, and omnidirectional image semantic segmentation. Overall, we present (1) a novel CNN approach on unstructured grids using parameterized differential operators for spherical signals, and (2) we show that our unique kernel parameterization allows our model to achieve the same or higher accuracy with significantly fewer network parameters.
We present a new CNN kernel for unstructured grids for spherical signals, and show significant accuracy and parameter efficiency gain on tasks such as 3D classfication and omnidirectional image segmentation. An efficient method enabling deep learning on spherical data that reaches competitive/state-of-the-art numbers with much less parameters than popular approaches. The paper proposes a novel convolutional kernel for CNN on the unstructured grids and formulates the convolution by a linear combination of differential operators.