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

arXiv: https://arxiv.org/abs/2603.19776 · HTML: https://mlsanity.com/paper/2603.19776/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 77 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 30 of 30)

- [MapTRv2: An End-to-End Framework for Online Vectorized HD Map Construction](https://mlsanity.com/paper/2308.05736/) (2023)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [PersFormer: 3D Lane Detection via Perspective Transformer and the OpenLane Benchmark](https://mlsanity.com/paper/2203.11089/) (2022)
- [MonoDTR: Monocular 3D Object Detection with Depth-Aware Transformer](https://mlsanity.com/paper/2203.10981/) (2022)
- [3D-LaneNet: End-to-End 3D Multiple Lane Detection](https://mlsanity.com/paper/1811.10203/) (2018)
- [CLRNet: Cross Layer Refinement Network for Lane Detection](https://mlsanity.com/paper/2203.10350/) (2022)
- [Gen-LaneNet: A Generalized and Scalable Approach for 3D Lane Detection](https://mlsanity.com/paper/2003.10656/) (2020)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Anchor3DLane: Learning to Regress 3D Anchors for Monocular 3D Lane Detection](https://mlsanity.com/paper/2301.02371/) (2023)
- [A neural network based on SPD manifold learning for skeleton-based hand gesture recognition](https://mlsanity.com/paper/1904.12970/) (2019)
- [ONCE-3DLanes: Building Monocular 3D Lane Detection](https://mlsanity.com/paper/2205.00301/) (2022)
- [LATR: 3D Lane Detection from Monocular Images with Transformer](https://mlsanity.com/paper/2308.04583/) (2023)
- [CurveFormer: 3D Lane Detection by Curve Propagation with Curve Queries and Attention](https://mlsanity.com/paper/2209.07989/) (2022)
- [T2SG: Traffic Topology Scene Graph for Topology Reasoning in Autonomous Driving](https://mlsanity.com/paper/2411.18894/) (2024)
- [Learning to Predict 3D Lane Shape and Camera Pose from a Single Image via Geometry Constraints](https://mlsanity.com/paper/2112.15351/) (2021)
- [GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognition](https://mlsanity.com/paper/2111.13089/) (2021)
- [Riemannian Local Mechanism for SPD Neural Networks](https://mlsanity.com/paper/2201.10145/) (2022)
- [LaneCPP: Continuous 3D Lane Detection using Physical Priors](https://mlsanity.com/paper/2406.08381/) (2024)
- [SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space](https://mlsanity.com/paper/2312.08200/) (2023)
- [Adaptive Log-Euclidean Metrics for SPD Matrix Learning](https://mlsanity.com/paper/2303.15477/) (2023)
- [CurveFormer++: 3D Lane Detection by Curve Propagation with Temporal Curve Queries and Attention](https://mlsanity.com/paper/2402.06423/) (2024)
- [WS-3D-Lane: Weakly Supervised 3D Lane Detection With 2D Lane Labels](https://mlsanity.com/paper/2209.11523/) (2022)
- [DV-3DLane: End-to-end Multi-modal 3D Lane Detection with Dual-view Representation](https://mlsanity.com/paper/2406.16072/) (2024)
- [Anchor3DLane++: 3D Lane Detection via Sample-Adaptive Sparse 3D Anchor Regression](https://mlsanity.com/paper/2412.16889/) (2024)
- [M2-3DLaneNet: Exploring Multi-Modal 3D Lane Detection](https://mlsanity.com/paper/2209.05996/) (2022)
- [Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry](https://mlsanity.com/paper/2504.00660/) (2025)
- [Neural Networks on Symmetric Spaces of Noncompact Type](https://mlsanity.com/paper/2601.01097/) (2026)
- [Lane-Keeping Control of Autonomous Vehicles Through a Soft-Constrained Iterative LQR](https://mlsanity.com/paper/2311.16900/) (2023)
- [GLane3D : Detecting Lanes with Graph of 3D Keypoints](https://mlsanity.com/paper/2503.23882/) (2025)

## Abstract (arXiv)

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 ℝ3, lanes are embedded 1D submanifolds, and sampled lane points are dense observations, thereby coupling metric and topology across surfaces, curves, and point sets. Building on this, we propose ReManNet, which 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 through 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 results. On OpenLane, it improves F1 by +8.2% over the baseline and by +1.8% over the previous best, with scenario-level gains of up to +6.6%. The code will be publicly available at https://github.com/changehome717/ReManNet.