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

Chengzhi Hong; Bijun Li

cs.CVMar 20, 2026

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

Authors: Chengzhi Hong, Bijun Li

Organizations: State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, China

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.

Figures & tables

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.

Method	F1 (%) $\bm{\uparrow}$	Cate Acc (%) $\bm{\uparrow}$	$\mathbf{Ex/N}$ (m) $\bm{\downarrow}$	$\mathbf{Ex/F}$ (m) $\bm{\downarrow}$	$\mathbf{Ez/N}$ (m) $\bm{\downarrow}$	$\mathbf{Ez/F}$ (m) $\bm{\downarrow}$	Up & Down $\bm{\uparrow}$	Curve $\bm{\uparrow}$	Extreme Weather $\bm{\uparrow}$	Night $\bm{\uparrow}$	Intersection $\bm{\uparrow}$	Merge & Split $\bm{\uparrow}$
	Overall metrics						Scenario F1 (%)
3D-LaneNet [ 17 ] [CVPR2019]	44.1	–	0.479	0.572	0.367	0.443	40.8	46.5	47.5	41.5	32.1	41.7
GenLaneNet [ 18 ] [ECCV2020]	32.3	–	0.591	0.684	0.411	0.521	25.4	33.5	28.1	18.7	21.4	31.0
PersFormer [ 9 ] [ECCV2022]	50.5	92.3	0.485	0.553	0.364	0.431	42.4	55.6	48.6	46.6	40.0	50.7
CurveFormer [ 4 ] [ICRA2023]	50.5	–	0.340	0.772	0.207	0.651	45.2	56.6	49.7	49.1	42.9	45.4
LATR [ 40 ] [ICCV2023]	61.9	92.0	0.219	0.259	0.075	0.104	55.2	68.2	57.1	55.4	52.3	61.5

Table 1: Comparison with SOTA methods on the OpenLane. The left block reports overall metrics: F1, category accuracy (Cate Acc), and mean

x

z

errors for the near (N) and far (F) ranges, denoted as

\mathbf{Ex/N}

\mathbf{Ex/F}

\mathbf{Ez/N}

, and

\mathbf{Ez/F}

. The right block reports scenario-wise F1. R18 and R50 denote ResNet-18 and ResNet-50 backbones; † indicates the baseline. The best results are shown in bold .

Method	Balanced Scenes					Rare Subset					Visual Variations
Method	F1 (%) $\uparrow$	$\mathbf{Ex/N}$ $\downarrow$	$\mathbf{Ex/F}$ $\downarrow$	$\mathbf{Ez/N}$ $\downarrow$	$\mathbf{Ez/F}$ $\downarrow$	F1 (%) $\uparrow$	$\mathbf{Ex/N}$ $\downarrow$	$\mathbf{Ex/F}$ $\downarrow$	$\mathbf{Ez/N}$ $\downarrow$	$\mathbf{Ez/F}$ $\downarrow$	F1 (%) $\uparrow$	$\mathbf{Ex/N}$ $\downarrow$	$\mathbf{Ex/F}$ $\downarrow$	$\mathbf{Ez/N}$ $\downarrow$	$\mathbf{Ez/F}$ $\downarrow$
3DLaneNet [ 17 ] [CVPR2019]	86.4	0.068	0.477	0.015	0.202	72.0	0.166	0.855	0.039	0.521	72.5	0.115	0.601	0.032	0.230
GenLaneNet [ 18 ] [ECCV2020]	88.1	0.061	0.496	0.012	0.214	78.0	0.139	0.903	0.030	0.539	85.3	0.074	0.538	0.015	0.232
CLGo [ 36 ] [AAAI2022]	91.9	0.061	0.361	0.029	0.250	86.1	0.147	0.735	0.071	0.609	87.3	0.084	0.464	0.045	0.312
PersFormer [ 9 ] [ECCV2022]	92.9	0.054	0.356	0.010	0.234	87.5	0.107	0.782	0.024	0.602	89.6	0.074	0.430	0.015	0.266
GP [ 30 ] [CVPR2022]	91.9	0.049	0.387	0.008	0.213	83.7	0.126	0.903	0.023	0.625	89.9	0.060	0.446	0.011	0.235

Table 2: Comparison with SOTA methods on the ApolloSim. Results are reported on the Balanced , Rare , and Visual Variations subsets.

\mathbf{Ex/N}

\mathbf{Ex/F}

\mathbf{Ez/N}

, and

\mathbf{Ez/F}

denote mean

x

z

errors in the near (N) and far (F) ranges. R18 and R50 denote ResNet-18 and ResNet-50 backbones; † indicates the baseline. The best and competitive results are highlighted in bold and underlined , respectively.

Baseline	3D-TLIoU Loss	Riemannian Gaussian	F1 (%) $\uparrow$
✓			57.5
✓	✓		60.5
✓		✓	62.0
✓	✓	✓	65.7

Table 3: Ablation study of ReManNet components.

Baseline	$\mathcal{C}_{i}$	3D LIoU term	F1 (%) $\uparrow$
✓			57.5
✓	✓		58.6
✓		✓	59.9
✓	✓	✓	60.5

Table 4: Ablation study of the 3D-TLIoU loss.

Riemannian Neural Networks

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Jun 30, 2026

HSDF-Lane: Height-Aligned Signed Distance Field with Semantic Lane Prior for 3D Lane Detection

Monocular 3D lane detection plays a critical role in autonomous driving, yet recovering reliable 3D geometry from a single image remains challenging due to inherent depth ambiguity. Prior methods project image features into Bird's-Eye-View (BEV) space under a flat-ground assumption, causing geometric distortion on real-world roads. Recent methods instead predict explicit height maps to capture non-planar surfaces, but still rely on sparse anchor-based regression and exploit the recovered geometry merely for spatial transformation rather than semantic understanding. To overcome these limitations, we propose HSDF-Lane, which implicitly models the road surface as a Height-aligned Signed Distance Field (HSDF) over a densely sampled 3D feature volume. Through differentiable rendering, the HSDF jointly produces an accurate height map and surface-aligned features. We further introduce Lane-aware Semantic Positional Encoding (LSPE), which injects a lane-existence prior derived from the surface-aligned features into the transformer queries, coupling geometric structure with semantic guidance. Extensive experiments on the OpenLane benchmark show that HSDF-Lane achieves state-of-the-art performance in both 3D lane detection and height map estimation.

Jiyong Boo, Byeongin Joung, Hyemin Yang +1

KAIST, Republic of Korea

Signed Distance Functions Autonomous Driving Perception

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Dec 5, 2025

LeAD-M3D: Leveraging Asymmetric Distillation for Real-Time Monocular 3D Detection

Real-time monocular 3D object detection remains challenging due to severe depth ambiguity, viewpoint shifts, and the high computational cost of 3D reasoning. Existing approaches either rely on LiDAR or geometric priors to compensate for missing depth or sacrifice efficiency to achieve competitive accuracy. We introduce LeAD-M3D, a monocular 3D detector that achieves state-of-the-art accuracy and real-time inference without extra modalities. Our method is enabled by three key components. Asymmetric Augmentation Denoising Distillation (A2D2) transfers geometric knowledge from a clean-image teacher to a MixUp-noised student via a quality- and importance-weighted depth-feature loss, enabling stronger depth reasoning without LiDAR. 3D-aware Consistent Matching (CM

_{\text{3D}}

) improves prediction-to-ground truth assignment by integrating 3D MGIoU into the matching score, yielding stable and precise supervision. Finally, Confidence-Gated 3D Inference (CGI

_{\text{3D}}

) accelerates inference by restricting expensive 3D regression to confident regions. Together, these contributions set a new Pareto frontier for monocular 3D detection: LeAD-M3D achieves state-of-the-art accuracy on KITTI and Waymo, and the best reported car AP on Rope3D, while running up to 3.6

\,\times

faster than prior high-accuracy models (e.g., MonoDiff). LeAD-M3D demonstrates that high fidelity and real-time monocular 3D detection is simultaneously attainable, without LiDAR, stereo, or strong geometric assumptions.

Johannes Meier, Jonathan Michel, Oussema Dhaouadi +7

DeepScenario · ETH Zurich · TU Munich +5

Efficient Object Detection Real-Time Object Detection Knowledge Distillation Monocular 3D Object Detection

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Jul 15, 2026

3D Lane Detection with Odometry for High-Speed Vehicle Racing

Lane boundary detection is a critical component in autonomous driving systems and has been rigorously studied in regular driving scenarios. However, it is less explored in vehicle racing, where the car moves at higher speeds across more extreme road geometries. To study this problem, we introduce a new dataset for 3D lane detection in racing, featuring >

250

k images from multiple camera feeds and inertial measurements taken with a Lexus LC 500 driving on a closed circuit. With this dataset, we compare various approaches to 3D lane detection and propose modifications that permit frames to be processed at rates of almost 300Hz while retaining high predictive performance in the racing application. This facilitates a multi-camera ensemble approach that is validated on hardware. We show that sensing modalities such as inertial measurements can be leveraged for pre-integration to regress road geometries over both cameras and time, yielding improvements in key metrics. Compared to methods such as BevLaneDet, adding odometry and ensemble predictions improves the F1 score by 3 points and reduces near-vehicle mean absolute errors (MAEs) by

>30 \%

. We show F1 scores

>

0.9 and lateral MAEs of

<

0.18m in vehicle deployments.

Omoruyi Atekha, John Subosits, Marcus Greiff

Massachusetts Institute of Technology (MIT), Cambridge, MA, USA. · Toyota Research Institute (TRI), 94022 Los Altos, CA, USA.

Autonomous Driving Datasets Autonomous Driving Perception Autonomous Racing Lane Detection

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Abstract

Riemannian Neural Networks

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