R-A3D: Frequency-Aware Riemannian Anchor Learning for Monocular 3D Lane Detection

Monocular 3D lane detection faces challenges due to the loss of directional detail in distant markings during feature downsampling and geometric ambiguity between lateral curvature and road elevation under single-view projection. R-A3D addresses both issues through frequency-aware Riemannian anchor learning in an anchor-regression pipeline. A Haar-based feature pyramid retains four frequency subbands before learned channel projection, strengthening thin and low-contrast lane responses. Each evolving 3D anchor is summarized in the lateral-elevation plane by Gaussian mean and covariance statistics, embedded in a symmetric positive-definite matrix, and mapped to a tangent-space feature with the Log-Euclidean metric. This Riemannian anchor feature is residually fused with anchor-aligned visual evidence and recomputed after each cascade stage. On OpenLane, the ResNet-50 model achieves 64.9% F1, 94.1% category accuracy, and far-range lateral and vertical errors of 0.215 m and 0.081 m at 23.5 frames/s; the ResNet-18 model reaches 63.0% F1 at 53.2 frames/s. Across the three ApolloSim subsets, R-A3D improves F1 over the reproducible Anchor3DLane baseline by 1.4–4.3 percentage points and reduces far-range lateral error by 18.7–23.2%. These results indicate complementary benefits from frequency-preserving visual evidence and proposal-dependent Riemannian geometry within the evaluated settings.