Second-order geometric representations for YOLO-based lung nodule detection

Lung cancer is one of the most commonly diagnosed cancers and remains the leading cause of cancer-related death worldwide, with approximately 1.8 million deaths reported in 2022. Pulmonary nodule localization in computed tomography (CT) scans is essential for early diagnosis and treatment planning; however, this task is challenging because nodules are often small, morphologically variable, and visually similar to normal anatomical structures. In addition, manual assessment is subjective, with only moderate inter-radiologist agreement reported in the literature. This work presents a geometry-aware YOLO-based framework for lung nodule detection under limited-data conditions. The method integrates a Covariance Feature Enhancement (CFE) module into the detection backbone to model inter-channel second-order relationships and enhance feature discrimination. In addition, a Riemannian false positive reduction module is introduced to classify candidate detections from covariance descriptors represented as symmetric positive definite (SPD) matrices. These descriptors are processed through geometry-preserving operations and then projected onto a Euclidean tangent space for final classification. The proposed strategy combines first-order convolutional features with second-order geometric representations, improving the robustness of the detector when annotated data are scarce. The model was evaluated on the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) dataset for nodule localization. When trained using 5% of the training set, the proposed model achieved a Competition Performance Metric (CPM) of 0.202, compared with 0.075 for YOLOv5s. This corresponds to an absolute improvement of 0.127 and a relative gain of approximately 169%.