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

Chengzhi Hong, Bijun Li

Abstract

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, 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.

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

Abstract

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 , 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.
Paper Structure (19 sections, 35 equations, 1 figure, 4 tables)

This paper contains 19 sections, 35 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. 3D Lane Detection
  4. Manifold Learning
  5. Method
  6. Lane Representation
  7. Riemannian Manifold Neural Network
  8. Method Overview
  9. SPD Manifold Embedding of Gaussians
  10. Gaussian Statistics on Riemannian Manifolds
  11. Network Embedding of Riemannian Gaussians
  12. Gated Visual--Geometric Feature Fusion
  13. 3D Tunnel Lane IoU Loss
  14. Experiment
  15. Datasets and Evaluation Metrics
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Overall architecture of ReManNet. A backbone and transformer generate initial lane predictions. A position-weighted layer encodes spatial context, and a Riemannian manifold embedding layer maps the resulting features to SPD Gaussian descriptors. A gated visual-geometric fusion layer combines these descriptors with visual features to produce refined predictions. The entire network is trained end-to-end using our geometry-consistent 3D-TLIoU loss alongside standard regression and classification objectives.