L2M-Reg: Robust LiDAR-to-Model Registration

• L2M-Reg is a registration framework that leverages semantic facade correspondences and uncertainty-aware strategies to align outdoor LiDAR with LoD2 city models.
• Its pseudo-plane constrained Gauss–Helmert model and adaptive vertical translation estimation ensure high accuracy and computational efficiency.
• The methodology is applicable to urban digital twinning, digital construction, and change detection while mitigating errors from model generalization uncertainty.

L2M-Reg refers to a building-level, uncertainty-aware registration methodology for aligning outdoor LiDAR point clouds with semantic 3D city models, specifically when the models are at the Level of Detail 2 (LoD2) and subject to inherent generalization uncertainty. This process is fundamental for applications in urban digital twinning, digital construction, change detection, and model refinement. The L2M-Reg framework introduces three principal steps: reliable facade correspondence extraction, pseudo-plane constrained Gauss–Helmert modeling, and adaptive vertical translation estimation, resulting in superior accuracy and computational efficiency compared to prevailing ICP-based and plane-based registration methods (Xu et al., 20 Sep 2025).

1. Principal Components

L2M-Reg comprises three sequential modules:

1. Establishing Reliable Plane Correspondence
   • Semantic information from the LoD2 city model (e.g., facade surface definitions, unique building identifiers) is utilized to restrict the LiDAR point cloud to regions neighboring each modeled facade.
   • An iterative cut-off algorithm localizes the building's plinth, representing the most reliable base for registration due to horizontal offsets between the LoD2 facade and real-world plinth location.
   • RANSAC-based plane segmentation extracts candidate planar segments from the LiDAR subset, while a geometric consistency (GC) check refines these segments by evaluating point-to-plane distances and normal vector angular deviation. A segment is accepted if its points satisfy both a distance threshold ($T_{dis}$) and an angular threshold ($T_\theta = 0.5 T_\alpha$, $T_\alpha \approx 10^\circ$).
2. Pseudo-plane-Constrained Gauss–Helmert Model
   • In the absence of reliable ground planes from DTM or road models, a “pseudo-plane” with normal vector $n = [0, 0, 1]$ and zero offset is introduced in both source (LiDAR) and target (model) frames. These pseudo-observations contribute additional rows to the Jacobian matrix within the Gauss–Helmert framework and stabilize vertical translation estimation while maintaining geometric consistency.
   • The unknown transformation parameters are compactly encoded using unit quaternions for rotation ($q_0, q_1, q_2, q_3$) and three translation components, $X = [q_0, q_1, q_2, q_3, t_x, t_y, t_z]^T$.
3. Adaptive Estimation of Vertical Translation
   • After solving for the 2D transformation using reliable facade correspondences (with vertical parameters stabilized by the pseudo-plane), the transformed LiDAR points are vertically aligned using localized ground checkpoints—where the mean Z-coordinate deviation between LiDAR and model ground measurements yields the final $t_z$ estimate.

2. Mathematical Modeling

Plane Equation and Consistency Evaluation

• A plane $\omega_0$ is parametrized by $(n_0, d_0)$ with implicit equation $n_0 \cdot x + d_0 = 0$.
• For candidate point $p$, the perpendicular distance is $d(p, \omega_0) = |n_0 \cdot p + d_0|$.
• Post-segmentation, angular deviation $\theta = \arccos(n_0 \cdot n_{new})$ is used in the GC check.

Gauss–Helmert Registration Constraints

• For each plane correspondence $(M_i, L_i)$, the constraint is $f = n_i (R x + t) + d_i = 0$, with unit constraint $c = \sqrt{q_0^2+q_1^2+q_2^2+q_3^2} = 1$.
• Jacobian matrices $A$ and $C$ are constructed accordingly. If only facade planes are included, $A$ is singular w.r.t. $t_z$—the pseudo-plane row rectifies this.

Pseudo-plane Formalism

• Pseudo-planes $\omega_{target}$ and $\omega_{source}$ have identical normals and zero offsets. Adding their rows to $A$ ensures vertical translation is constrained throughout estimation, without altering residuals or injecting observation error.

Adaptive Vertical Registration

• After horizontal transforms, ground control points are extracted, and the vertical translation is updated by the mean absolute deviation in Z between aligned LiDAR and DTM/road model measurements.

3. Experimental Evaluation

L2M-Reg is validated on three diverse urban datasets:

Dataset	Horizontal Error (cm)	Vertical Error (cm)	Runtime (s)
TUM0501 Building	~1	—	—
Pinakothek	—	~2	135.9
Street Building	—	~2.3 (note: GICP ~1.9)	—

Key observations:

• Consistently achieves <1–2 cm horizontal and vertical errors (except marginal deviations due to ground truth limitations).
• Computational efficiency arises from processing only plinth-localized neighborhoods rather than dense point clouds.
• Vertical error variance is primarily influenced by the quality of auxiliary ground models.

4. Applications and Domain Implications

Urban Digital Twinning

• Direct refinement of building-level city models through accurate LiDAR alignment, foundational for emergent urban digital twin platforms.

Digital Construction and Model Refinement

• Enhanced as-built vs. as-designed model updating in construction monitoring, enabling improved change detection and continuous city-scale model refinement.

Change Detection

• Precise registration enables temporal change monitoring, facilitating processes such as structural integrity analysis and illegal construction identification.

Robustness to Data Quality Variations

• The decoupled facade vs. ground estimation strategy ensures L2M-Reg remains effective despite uncertainties or poor quality in DTM/road data.

5. Addressing Challenges

Model Uncertainty

• LoD2 models produced from 2D cadastral footprints and extrusion may introduce horizontal offsets. L2M-Reg’s plinth localization and reliable facade-plane extraction circumvent systematic registration errors.

Vertical Registration under Weak Ground Constraints

• Standard approaches relying on low-res DTM can propagate vertical errors. L2M-Reg stabilizes vertical estimation by pseudo-plane constraints, only utilizing ground observations when local measurements permit.

6. Significance within the Registration Landscape

L2M-Reg advances the field by coupling semantic model information and robust geometric extraction. Its pseudo-plane innovation and decoupled vertical estimation directly address weaknesses in prior ICP and plane-based frameworks where model uncertainty or ground constraint quality hinders full-DoF registration. This strategy represents a substantial methodological shift, prioritizing robust offline geometric reasoning and adaptive estimation over brute-force dense cloud processing.

7. Limitations and Outlook

A plausible implication is that L2M-Reg’s accuracy for vertical translation remains bounded by the auxiliary ground data quality (DTM, road model), and further improvements could arise from the integration of higher-precision ground measurements (e.g., GNSS, total station data) when available. Its efficiency depends on accurate plinth localization and RANSAC segmentation, potentially limiting generalizability where facade geometry is highly irregular or occluded.

In summary, L2M-Reg constitutes a novel registration paradigm that accounts for LoD2 model uncertainty by leveraging semantic correspondences, a pseudo-plane-constrained estimation framework, and adaptive ground-level vertical alignment. These contributions enable robust, efficient, and application-ready building-scale LiDAR-to-Model registration for geospatial and urban informatics workflows.