A Geometric Approach to Steerable Convolutions

TL;DR

This paper introduces a geometric derivation of steerable convolutional neural networks that enhances understanding, proposes a new construction method for convolution layers, and improves robustness to noise.

Contribution

It provides an intuitive geometric derivation of steerable CNNs, introduces a novel layer construction method, and enhances robustness to noisy data.

Findings

Geometric derivation clarifies the structure of steerable CNNs.

New interpolation kernel method improves layer construction.

Enhanced robustness to noisy data in convolution layers.

Abstract

In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on geometric arguments and fundamental principles of pattern matching. We offer an intuitive explanation for the appearance of the Clebsch--Gordan decomposition and spherical harmonic basis functions. Furthermore, we suggest a novel way to construct steerable convolution layers using interpolation kernels that improve upon existing implementation, and offer greater robustness to noisy data.