SRE-Conv: Symmetric Rotation Equivariant Convolution for Biomedical Image Classification

TL;DR

This work tackles the challenge of rotational equivariance in CNNs for biomedical image analysis by introducing SRE-Conv, a centrally symmetric, band-based kernel parameterization that enforces rotation and reflection equivariance without increasing computational cost. The kernel is constructed as $K = M_I \Theta$, with $M_I$ encoding $b=\lfloor k/2\rfloor+2$ symmetric bands derived from a distance matrix, enabling gradient-based learning of rotation-invariant features. The authors integrate SRE-Conv into a fully convolutional network (SRE-CNN) and validate it on the MedMNISTv2 dataset (16 tasks), showing superior performance on rotated and reflected tests and substantial parameter reductions compared to standard and other rotation-equivariant baselines. The results indicate that SRE-Conv provides robust, efficient, and plug-and-play rotation-equivariant representations suitable for diverse biomedical imaging applications, with potential for further gains when combined with orientation encoding in orientation-prior datasets.

Abstract

Convolutional neural networks (CNNs) are essential tools for computer vision tasks, but they lack traditionally desired properties of extracted features that could further improve model performance, e.g., rotational equivariance. Such properties are ubiquitous in biomedical images, which often lack explicit orientation. While current work largely relies on data augmentation or explicit modules to capture orientation information, this comes at the expense of increased training costs or ineffective approximations of the desired equivariance. To overcome these challenges, we propose a novel and efficient implementation of the Symmetric Rotation-Equivariant (SRE) Convolution (SRE-Conv) kernel, designed to learn rotation-invariant features while simultaneously compressing the model size. The SRE-Conv kernel can easily be incorporated into any CNN backbone. We validate the ability of a deep SRE-CNN to capture equivariance to rotation using the public MedMNISTv2 dataset (16 total tasks). SRE-Conv-CNN demonstrated improved rotated image classification performance accuracy on all 16 test datasets in both 2D and 3D images, all while increasing efficiency with fewer parameters and reduced memory footprint. The code is available at https://github.com/XYPB/SRE-Conv.

Figures (2)

• Figure 1: Proposed SRE-Conv Kernel. To construct an SRE-Conv kernel of arbitrary size $k\times k$ with $b$ discrete symmetric bands and $C$ channels, we multiply a small trainable weight matrix $\Theta$ with a pre-defined binary index matrix $M^f_I$ (fixed during training). An SRE-Conv layer can be used in place of any standard convolution layer.
• Figure 2: Feature Map Visualization. We visualize feature maps of the conventional R18 (Conv.) and our SRE-Conv R18 models on two 2D MedMNISTv2 datasets. We rotate input images in $60^\circ$ increments, extract the averaged first layer feature map, and unrotate the feature map back to align with the original input. We apply a circle mask for visualization.