A Second-Order Attention Mechanism For Prostate Cancer Segmentation and Detection in Bi-Parametric MRI

The detection of clinically significant prostate cancer lesions (csPCa) from biparametric magnetic resonance imaging (bp-MRI) has emerged as a noninvasive imaging technique for improving accurate diagnosis. Nevertheless, the analysis of such images remains highly dependent on the subjective expert interpretation. Deep learning approaches have been proposed for csPCa lesions detection and segmentation, but they remain limited due to their reliance on extensively annotated datasets. Moreover, the high lesion variability across prostate zones poses additional challenges, even for expert radiologists. This work introduces a second-order geometric attention (SOGA) mechanism that guides a dedicated segmentation network, through skip connections, to detect csPCa lesions. The proposed attention is modeled on the Riemannian manifold, learning from symmetric positive definitive (SPD) representations. The proposed mechanism was integrated into standard U-Net and nnU-Net backbones, and was validated on the publicly available PI-CAI dataset, achieving an Average Precision (AP) of 0.37 and an Area Under the ROC Curve (AUC-ROC) of 0.83, outperforming baseline networks and attention-based methods. Furthermore, the approach was evaluated on the Prostate158 dataset as an independent test cohort, achieving an AP of 0.37 and an AUC-ROC of 0.75, confirming robust generalization and suggesting discriminative learned representations.