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.

使用参数化的微分算子在非结构化网络上，通过替换传统的卷积核为可学习的加权微分算子，训练出性能优异、参数更少的神经网络，并在计算机视觉和气候科学任务上进行了广泛实验验证。