Regular SE(3) Group Convolutions for Volumetric Medical Image Analysis

TL;DR

This paper introduces SE(3) group convolutions for volumetric medical images, achieving superior accuracy and generalization over traditional CNNs by leveraging roto-translation equivariance.

Contribution

It proposes a novel SE(3) group convolution kernel separated into rotation and spatial parts, approximating continuous equivariance via uniform SO(3) sampling and RBF interpolation.

Findings

Up to 16.5% accuracy improvement over CNNs.

Consistent outperforming of regular G-CNNs on medical tasks.

Enhanced generalization capabilities in volumetric analysis.

Abstract

Regular group convolutional neural networks (G-CNNs) have been shown to increase model performance and improve equivariance to different geometrical symmetries. This work addresses the problem of SE(3), i.e., roto-translation equivariance, on volumetric data. Volumetric image data is prevalent in many medical settings. Motivated by the recent work on separable group convolutions, we devise a SE(3) group convolution kernel separated into a continuous SO(3) (rotation) kernel and a spatial kernel. We approximate equivariance to the continuous setting by sampling uniform SO(3) grids. Our continuous SO(3) kernel is parameterized via RBF interpolation on similarly uniform grids. We demonstrate the advantages of our approach in volumetric medical image analysis. Our SE(3) equivariant models consistently outperform CNNs and regular discrete G-CNNs on challenging medical classification tasks and show significantly improved generalization capabilities. Our approach achieves up to a 16.5% gain in accuracy over regular CNNs.