SymAD-ECNN: Geometry-Aware Equivariant Learning for Anomaly Detection in Brain MRI

Abstract

Conventional deep learning models for biomedical anomaly detection often exhibit limited geometric awareness, particularly under rotational transformations, resulting in a reliance on computationally expensive data augmentation and large annotated datasets that are often scarce in clinical environments. This paper proposes SymAD-ECNN, a geometry-aware reconstruction-based anomaly detection framework that integrates C4-equivariant convolutions with a group-pooled invariant bottleneck to learn rotation-consistent representations of normal brain anatomy. By explicitly encoding rotational symmetry within the network architecture, the proposed framework reduces reliance on augmentation while preserving anatomically meaningful latent representations. The model is trained exclusively on healthy T1-weighted MRI scans from the IXI dataset and evaluated on pathological BraTS scans under a one-class cross-dataset setting. Anomalies are identified using masked mean reconstruction error with thresholds calibrated solely from healthy validation data. Experimental results demonstrate competitive performance against CNN-based autoencoder baselines, achieving an AUROC of 0.8625 and an AUPRC of 0.9197 while producing high-quality reconstructions (MSE of 0.0043, SSIM of 0.8725) and localized reconstruction error maps for visual interpretation. These findings demonstrate the potential of incorporating geometric priors through equivariant feature learning as an effective and interpretable alternative to augmentation-heavy reconstruction models for unsupervised brain MRI anomaly detection.