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UV-SLAM: Unconstrained Line-based SLAM Using Vanishing Points for Structural Mapping
Hyunjun Lim, Jinwoo Jeon, Hyun Myung
TL;DR
Existing line-based SLAM can leave 3D lines ambiguously mapped, while point features have limitations in low-texture and structural mapping settings. UV-SLAM adds vanishing-point measurements without Manhattan-world assumptions; the paper reports improved localization and mapping results against state-of-the-art methods on public datasets.
Problem
Existing line-based SLAM measurement models do not resolve 3D mapping problems such as degeneracy, which can prevent unique determination of 3D features.
Source: §I · p. 1Method
UV-SLAM adds vanishing-point measurements from image lines to optimization-based SLAM for structural mapping without a Manhattan-world assumption.
Source: §I · p. 2, E. Vanishing Point Measurement Model · p. 5Results
Across EuRoC datasets, UV-SLAM outperformed the compared algorithms, with 32.3% smaller average error than VINS-Mono.
Source: §V · p. 6Takeaways & Limitations
Fisher information matrix rank analysis verifies line observability, and comparisons report improved localization accuracy and mapping quality.
Source: §VI · p. 7
Abstract
from arXiv · showhide
In feature-based simultaneous localization and mapping (SLAM), line features complement the sparsity of point features, making it possible to map the surrounding environment structure. Existing approaches utilizing line features have primarily employed a measurement model that uses line re-projection. However, the direction vectors used in the 3D line mapping process cannot be corrected because the line measurement model employs only the lines' normal vectors in the Pl\"{u}cker coordinate. As a result, problems like degeneracy that occur during the 3D line mapping process cannot be solved. To tackle the problem, this paper presents a UV-SLAM, which is an unconstrained line-based SLAM using vanishing points for structural mapping. This paper focuses on using structural regularities without any constraints, such as the Manhattan world assumption. For this, we use the vanishing points that can be obtained from the line features. The difference between the vanishing point observation calculated through line features in the image and the vanishing point estimation calculated through the direction vector is defined as a residual and added to the cost function of optimization-based SLAM. Furthermore, through Fisher information matrix rank analysis, we prove that vanishing point measurements guarantee a unique mapping solution. Finally, we demonstrate that the localization accuracy and mapping quality are improved compared to the state-of-the-art algorithms using public datasets.
I. INTRODUCTION
Point-based SLAM has weaknesses in low-texture, changing-light, and structural mapping settings, motivating line features; existing line mapping still struggles with degeneracy. UV-SLAM adds vanishing-point measurements without Manhattan-world constraints and analyzes their effect on 3D-line observability.
I. INTRODUCTION
- Point features are sparse, vulnerable to low texture and illumination changes, while line features can help in corridors and expose environmental structure.The paper presents lines as a complement to points for visual SLAM.Source: §I · p. 1
- Existing line methods commonly reproject 3D lines, but degeneracy can prevent unique mapping and normal-only Plücker measurements cannot correct line directions.The paper describes a 2D line near the epipole as corresponding to a 3D line on the epipolar plane.Source: §I · pp. 1–2
- Figure 1 contrasts ALVIO and UV-SLAM top-view 3D line maps overlaid on LiDAR clouds in a real corridor, and the paper describes ALVIO’s map as poor despite structural regularities.Source: Figure 1 · p. 1, §I · p. 2
- UV-SLAM uses structural regularities and vanishing points for line-based mapping without imposing restrictions such as the Manhattan-world assumption.The paper characterizes it as the first optimization-based monocular SLAM using vanishing-point measurements for structural mapping without camera-motion or environment restrictions, to the authors’ knowledge.Source: §I · p. 2
- The method defines a vanishing-point measurement residual and Jacobian for Plücker-coordinate and orthonormal 3D-line representations.Source: §I · p. 2
- Fisher information matrix rank analysis is used to prove that the proposed vanishing-point measurements guarantee 3D-line observability.The paper states that this resolves problems arising in 3D line mapping.Source: §I · p. 2
II. RELATED WORKS
Prior line-SLAM work addresses degeneracy or exploits structural regularities, but existing approaches remain limited by information loss, motion or scene assumptions, or a lack of proof for vanishing-point benefits.
A. Degeneracy of Line Features
- Degenerate-line handling either removes lines, requires intersections with other lines, or is limited to pure translational motion.The cited approaches leave a need for a method independent of camera motion.Source: A. Degeneracy of Line Features · p. 2
B. Line-based SLAM with Manhattan or Atlanta World Assumption
- Manhattan- or Atlanta-world methods exploit dominant structural directions but are practical mainly indoors, where their assumptions are mostly correct.Earlier vanishing-point-based rotation estimation and 2-DoF line representations rely on these assumptions.Source: B. Line-based SLAM with Manhattan or… · p. 2
C. Vanishing Point Measurements
- Unconstrained vanishing-point methods have used parallel-line residuals or an observation model, but reported limitations include sensitivity to initialization and no proof of improved accuracy or mapping.In, inaccurate initialization with degeneracy prevented accurate mapping; did not prove that vanishing-point measurements improve localization or line mapping.Source: C. Vanishing Point Measurements · p. 2
A. Framework of Algorithm
UV-SLAM extends a monocular visual-inertial system with line features and vanishing-point processing. It triangulates 3D lines and optimizes line and vanishing-point residuals alongside localization and mapping.
A. Framework of Algorithm
- The framework builds on VINS-Mono, using Shi-Tomasi points tracked by KLT, IMU pre-integration, and sliding-window optimization with two-way marginalization and Schur complement.Fig. 2 depicts line detection and matching, vanishing-point detection and clustering, 3D-line triangulation, and residual formation before optimization.Source: A. Framework of Algorithm · p. 2, Figure 2 · p. 3
- Lines are detected with LSD and tracked by LBD, represented with Plücker coordinates for triangulation and re-projection, and optimized in a 4-DoF orthonormal representation.Plücker lines have 6 DoF despite 3D lines having 4 DoF, creating over-parameterization in optimization.Source: A. Framework of Algorithm · p. 3
- J-linkage detects vanishing points by sampling line-based hypotheses, merging similar hypotheses, and calculating the resulting points.The method can find more vanishing points than algorithms using the Manhattan-world assumption.Source: A. Framework of Algorithm · p. 3
B. State Definition
The state includes sliding-window body states, inverse depths for point features, and line features represented in orthonormal form.
B. State Definition
- Each sliding-window body state contains position, quaternion, velocity, and accelerometer and gyroscope biases.The notation distinguishes world, camera, and body coordinates, and describes body-to-world transformations.Source: B. State Definition · p. 3
- The entire state includes inverse depths λ_j for point features and orthonormal line representations o for line features.I, J, and K denote the numbers of sliding-window states, point features, and line features, respectively.Source: B. State Definition · p. 3
- The system defines the entire state X from the body states across the sliding window and the point- and line-feature variables.The passage identifies x_i as the body state at the i-th sliding-window position.Source: B. State Definition · p. 3
C. UV-SLAM
UV-SLAM optimizes a cost built from marginalization, IMU, point, line, and vanishing-point residuals. Lines with structural regularity receive a vanishing-point factor in addition to the line factor.
C. UV-SLAM
- The optimization objective combines marginalization, IMU, point, line, and vanishing-point measurement residuals over the defined states.The measurements, sets, covariance matrices, and loss functions are defined for the corresponding residual types.Source: C. UV-SLAM · pp. 3–4
- A line without a vanishing-point measurement uses only a line-feature factor, while a structurally regular line uses both line-feature and vanishing-point factors.The factor-graph example labels these cases o0 and o1, respectively.Source: Figure 3 · p. 4, C. UV-SLAM · p. 4
- The vanishing-point residual uses an inverse-tangent loss, whereas point and line residuals use the Huber norm.The inverse-tangent loss is selected because the vanishing-point measurement model is unbounded.Source: C. UV-SLAM · p. 4
D. Line Measurement Model
The line measurement model re-projects a triangulated 3D line into a new frame and measures its discrepancy from the observed line. In the normalized plane, the re-projected line equals its normal vector.
D. Line Measurement Model
- With identity camera intrinsic matrices on the normalized plane, the re-projected line equals the normal vector in the proposed method.The projection matrix of a line feature and the camera intrinsic parameter are denoted K′ and K, respectively.Source: D. Line Measurement Model · p. 4
- The line residual is the distance from each observed-line endpoint to the re-projected line.The observed line is compared with the re-projection of a 3D line obtained by triangulation.Source: D. Line Measurement Model · p. 4, Figure 4 · p. 4
- The Plücker-coordinate line representation uses a transformation matrix to convert from camera coordinates to body coordinates.Source: D. Line Measurement Model · p. 5
E. Vanishing Point Measurement Model
The model uses vanishing points derived from line features as observations and compares observed points with estimates based on 3D line direction. Lines sharing a vanishing point can be clustered together.
E. Vanishing Point Measurement Model
- Lines with the same vanishing point are clustered and represented in the same color; J-linkage usually extracts three or more vanishing points.Source: E. Vanishing Point Measurement Model · p. 5
- A vanishing point is the projection of a point at infinity on the 3D line, and its estimate uses the line’s direction vector.The estimated vanishing point is found where the projected direction intersects the image plane.Source: E. Vanishing Point Measurement Model · p. 5
- The vanishing-point residual is the difference between the observed point from image lines and the estimate from the 3D line.The model also derives a Jacobian with respect to the vanishing point using body-state and orthonormal-representation changes.Source: Figure 6 · p. 5, E. Vanishing Point Measurement Model · p. 5
IV. FISHER INFORMATION MATRIX RANK ANALYSIS
The rank analysis finds that line measurements alone do not make line features observable, whereas adding vanishing-point measurements yields full observability under the stated exception. The analysis evaluates observability through Fisher information matrix rank.
IV. FISHER INFORMATION MATRIX RANK ANALYSIS
- The Fisher information matrix rank analysis assesses observability, with singularity indicating an unobservable system.The analysis uses the full-column-rank condition for the Jacobian as a criterion for FIM nonsingularity.Source: §IV · p. 5
- Line measurements alone remain insufficient for observability: the line Jacobian rank is at most 2 despite adding a non-endpoint line observation.The orthonormal line representation has four parameters, so the line measurement model alone cannot guarantee observability.Source: §IV · p. 6
- The analysis computes the Fisher information matrix using vanishing-point measurements in the orthonormal representation.The vanishing-point measurement FIM uses the inverse covariance of the vanishing-point observation.Source: §IV · p. 6
- Combining line and vanishing-point measurements gives Jacobian rank 4, making line features fully observable except in the case of (19).The analysis attributes the rank to independent rows for the two measurement types.Source: §IV · p. 6
V. EXPERIMENTAL RESULTS
On EuRoC, UV-SLAM improves localization accuracy and line-mapping quality over the compared methods. Its frontend takes about 3 ms longer because it extracts vanishing points, while backend runtime is similar to other algorithms.
V. EXPERIMENTAL RESULTS
- Experiments compared UV-SLAM with state-of-the-art algorithms on EuRoC MAV datasets spanning different lighting, texture, and speed conditions.The experiments ran on an Intel Core i7-9700K with 32 GB RAM.Source: §V · p. 6
- UV-SLAM has 32.3%, 23.8%, 26.4%, and 17.6% smaller average error than VINS-Mono, PL-VINS, ALVIO, and the authors’ previous work, respectively.The comparison uses translational RMSE across EuRoC datasets; Fig. 7 shows trajectory and distance-indexed RMSE for V2 02 medium.Source: §V · p. 6, Figure 7 · p. 7
- UV-SLAM aligns line direction vectors; ALVIO mapping is degraded by degenerate lines, while the previous method corrected them only during pure translational camera motion.Fig. 8 presents mapping results for MH 05 difficult and V2 01 easy.Source: §V · p. 6, Figure 8 · p. 7
- Frontend runtime averages 53.528 ms and backend runtime 47.086 ms; UV-SLAM’s frontend is only about 3 ms longer than other algorithms.The backend optimization runtime is similar to that of other algorithms.Source: §V · p. 6
VI. CONCLUSION
The conclusion presents UV-SLAM as an unconstrained line-based SLAM method using vanishing-point measurements. The authors report guaranteed line observability through FIM rank analysis and improved localization accuracy and mapping quality in comparisons with state-of-the-art algorithms.
VI. CONCLUSION
- UV-SLAM uses vanishing-point measurements for unconstrained line-based SLAM without assumptions such as the Manhattan world.The authors calculate residual and Jacobian matrices for the measurements.Source: §VI · p. 7
- FIM rank analysis verifies that introducing vanishing-point measurements into the existing method guarantees line observability.Source: §VI · p. 7
- Quantitative and qualitative comparisons with state-of-the-art algorithms show increased localization accuracy and mapping quality.The authors propose sparse-line mapping for future mesh or pixel-wise mapping.Source: §VI · p. 7