ReManNet: A Riemannian Manifold Network for Monocular 3D Lane Detection

Monocular 3D lane detection remains challenging due to depth ambiguity and weak geometric constraints. Mainstream methods rely on depth guidance, BEV projection, and anchor- or curve-based heads with simplified physical assumptions, remapping high-dimensional image features while only weakly encoding road geometry. Lacking an invariant geometric–topological coupling between lanes and the underlying road surface, 2D-to-3D lifting is ill-posed and brittle, often degenerating into concavities, bulges, and twists. To address this, we propose the Road-Manifold Assumption: the road is a smooth 2D manifold in $\mathbb{R}^3$, lanes are embedded 1D submanifolds, and sampled lane points are dense observations, coupling metric and topology across surfaces, curves, and samples. Building on this, we propose ReManNet: it first produces initial lane predictions with an image backbone and detection heads, then encodes geometry as Riemannian Gaussian descriptors on the symmetric positive-definite (SPD) manifold, and fuses these descriptors with visual features via a lightweight gate to maintain coherent 3D reasoning. We also propose the 3D Tunnel Lane IoU (3D-TLIoU) loss, a joint point–curve objective that computes slice-wise overlap of tubular neighborhoods along each lane to improve shape-level alignment. Extensive experiments on standard benchmarks demonstrate that ReManNet achieves state-of-the-art (SOTA) or competitive performance, and on OpenLane it improves F1 by +8.2\% over the baseline and by +1.8\% over the previous SOTA, with scenario-level F1 gains of up to +6.6\%.