Spherical CNNs on Unstructured Grids

TL;DR

This paper introduces a novel spherical CNN method using parameterized differential operators on unstructured grids, achieving high accuracy with fewer parameters across diverse tasks like shape classification and climate pattern segmentation.

Contribution

The paper presents a new CNN approach for spherical signals that employs learnable differential operator kernels, reducing parameters while maintaining or improving performance.

Findings

Achieves comparable or better accuracy than state-of-the-art models.

Uses significantly fewer network parameters.

Effective across computer vision and climate science tasks.

Abstract

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.