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GALoc: Gravity Aligned Wireframes for Depth-Free Monocular Floorplan Localization

Jeahn Han, Minji Kim, Jeongbin Sohn, Jonghyeok Park, Matthias Wuest, Pyojin Kim

arXiv:2609.08385v1cs.CVcs.RO

TL;DR

Floorplan localization avoids appearance-sensitive dense maps, but existing approaches still depend on depth representations that can be brittle in cluttered or unfamiliar scenes. GALoc uses gravity-aligned wireframes instead, matching their BEV layouts to floorplans; where wall coverage exceeds roughly 40%, it matches or surpasses F3Locm at the reported thresholds.

  • Problem

    Floorplan localization offers compact, appearance-invariant maps, but existing methods still rely on depth representations that can mistake furniture for walls or extrapolate poorly in unseen and low-texture scenes.

    Source: §I · p. 1

  • Method

    GALoc uses monocular wireframes and a null-space gravity-alignment search to construct vertical, coplanar 3D structure, then projects it into BEV for metric-free SE(2) floorplan matching.

    Source: §I · p. 1, §III · p. 2, C. Null Space Gravity Alignment · p. 2

  • Results

    Where Structured3D wall coverage exceeds roughly 40%, GALoc matches or surpasses F3Locm at the reported thresholds, while reporting zero confidence on structure-blind frames.

    Source: A. Single Image Localization · p. 6

  • Takeaways & Limitations

    GALoc returns architecturally valid wireframes under input noise, but localization accuracy remains bounded by wireframe-extractor quality.

    Source: E. Ablation: Robustness to Input Noise · p. 7, §V · p. 7

    GALoc assumes Atlanta-world geometry and abstains when wall structure is not visible; the authors also describe their real-world evaluation as limited in scope.

    Source: §V · p. 7

Abstract

from arXiv · show

Floorplans are compact, appearance-invariant maps ideal for indoor localization, yet existing methods rely on depth networks that are brittle in cluttered scenes. We propose GALoc, a geometry-first framework that replaces depth prediction with gravity-aligned wireframes that satisfy verticality and coplanarity by construction. Given monocular RGB, camera intrinsics, relative poses, and IMU orientation, GALoc constructs a linear constraint matrix encoding verticality and coplanarity, and finds the camera gauge minimizing its smallest singular value via global search. The rectified wireframes are projected into bird's-eye-view layouts through a closed-form, FOV-consistent transformation and matched against the floorplan via metric-free SE(2) search. We evaluate end-to-end on Structured3D, with calibrated noise on Gibson, and on real-world author-collected sequences. When sufficient wall geometry is visible, GALoc matches or outperforms depth-based baselines -- achieving 88% sequential localization success at 0.1m over 100-step sequences on Gibson vs the baseline's 68% -- while abstaining in structure-blind scenes.

I. INTRODUCTION

GALoc replaces depth-based floorplan localization with gravity-aligned wireframe geometry and a closed-form bird’s-eye-view pipeline. It builds on prior floorplan methods while extracting and completing wall-panel geometry from monocular images.

I. INTRODUCTION

  • GALoc replaces depth prediction with gravity-aligned wireframes and uses a closed-form, FOV-consistent BEV transformation for floorplan matching.Its null-space yaw search enforces verticality and coplanarity; localization uses metric-free SE(2) search.Source: §I · p. 1

II. RELATED WORKS

  • Prior floorplan methods use depth rays or learned depth representations, while GALoc instead uses wireframe geometry.Existing approaches also include image–floorplan compatibility methods and sequential filters.Source: §II · pp. 1–2

III. FLOORPLAN LOCALIZATION

  • The pipeline extracts wireframes, completes truncated wall cycles, rectifies them into 3D, projects them into BEV, and fuses floorplan observations over time.It takes monocular RGB, intrinsics, relative poses, and IMU gravity directions as inputs.Source: §III · p. 2

A. Wireframe Extraction

  • PolygonHGT extracts wall junctions, their connectivity, and ceiling/floor labels from each RGB image.Wireframe quality is measured by intersection over union against the ground-truth layout mask.Source: A. Wireframe Extraction · p. 2

B. From Truncated Cycles to Full Wall Corners

  • Each visible wall panel is represented as a four-corner cycle, with truncated corners completed when two or three true junctions are available.A panel’s horizontal FOV arc is labeled known only when all four corners are recovered; cases with one or fewer true junctions remain unchanged.Source: B. From Truncated Cycles to Full Wall… · p. 2

C. Null Space Gravity Alignment

GALoc estimates a yaw gauge by searching for a rank-deficient architectural constraint matrix, then recovers a gravity-aligned wireframe whose verticality and coplanarity hold by construction. The resulting structure supports BEV projection and downstream localization.

C. Null Space Gravity Alignment

  • GALoc estimates yaw by minimizing the constraint matrix’s smallest singular value, then recovers wireframe depths from its null space.The method retains depth variables so one SVD couples gauge estimation and structure recovery.Source: C. Null Space Gravity Alignment · pp. 2–3
  • Verticality, ceiling coplanarity, and floor coplanarity provide linear constraints on ceiling-depth variables.The floor depth is linked to its ceiling depth, leaving a (3N−2) × N constraint matrix for N vertical wall pairs.Source: C. Null Space Gravity Alignment · p. 3, Table I · p. 3
  • Under pixel noise, GALoc selects the yaw minimizing the smallest singular value because no angle makes the constraints exactly satisfiable.A 1° scan brackets four minima, followed by Brent refinement within ±1° brackets.Source: C. Null Space Gravity Alignment · pp. 3–4
  • The singular-value spectrum is exactly π-periodic, making a 180°-rotated room algebraically indistinguishable.The four candidate angles are disambiguated using positive depth and, if needed, chirality checks.Source: C. Null Space Gravity Alignment · p. 4
  • Eckart–Young–Mirsky produces the nearest rank-deficient constraint matrix in Frobenius norm, whose null-space vector supplies the recovered depths.This enforces architectural constraints on the recovered structure, but does not minimize geometric reprojection error in pixel space.Source: C. Null Space Gravity Alignment · p. 4
  • Coordinate assembly shares horizontal coordinates across ceiling–floor pairs and assigns constant heights per plane, enforcing verticality and coplanarity by construction.The resulting gravity-aligned 3D wireframe feeds downstream BEV projection and localization.Source: C. Null Space Gravity Alignment · p. 4

D. Bird’s Eye View (BEV)

Projecting gravity-aligned wireframes onto the X–Z plane produces a scale-free BEV wall chain. An inscribed-angle correction adjusts camera translation to restore the known field of view under noise.

D. Bird’s Eye View (BEV)

  • The gravity-aligned 3D wireframe is projected onto the X–Z plane to form a BEV wall chain, using its outermost known-arc endpoints and their chord length.The known arc subtends the horizontal image angle Θ.Source: D. Bird’s Eye View (BEV) · p. 4
  • Under noise, the raw BEV camera subtends an incorrect angle, so the camera translation is moved to the nearest-origin point on the circle that restores Θ.The adjustment leaves the yaw gauge and recovered structure unchanged and is scale-free because global scale cancels in cosine-similarity scoring.Source: Figure 7 · p. 5
  • Only known arcs contribute observation rays; unknown FOV segments retain their angular positions but are excluded from ray scoring.Source: Figure 7 · p. 5

E. Raycasting and Floorplan Matching

GALoc casts observation rays only in known FOV sectors and compares them with heading-aligned floorplan profiles to score candidate poses. Sequential localization combines confidence-weighted measurements with odometry in a belief over the SE(2) grid.

E. Raycasting and Floorplan Matching

IV. EXPERIMENTS AND RESULTS

GALoc is evaluated end-to-end on Structured3D, with calibrated junction noise on Gibson and real-world custom sequences. The experiments assess single-image and sequential localization while accounting for input and dataset differences.

IV. EXPERIMENTS AND RESULTS

  • Evaluation spans end-to-end PolygonHGT predictions on Structured3D, calibrated-noise experiments on Gibson, and real-world custom sequences.Source: §IV · p. 5
  • Single-image localization uses recall and heatmap rank, while sequential success requires the pose to remain within the threshold for 10 consecutive frames.Rank remains informative under geometric ambiguities where multiple poses are equally plausible.Source: §IV · p. 5
  • GALoc requires a wireframe extractor but no learned depth, semantic annotations, or panoramic input.Source: Table II · p. 6
  • Visible wall geometry supports accurate single-image localization, whereas a featureless close-up produces zero confidence and leaves the filter to fall back on odometry.Source: Figure 8 · p. 6
  • On Gibson, perturbed junctions yield layout-mask IoUs of 96.76%, 94.73%, and 92.78%; the authors adopt σ=5, whose 94.73% matches PolygonHGT’s 94.66% on Structured3D.The comparison is conservative for GALoc on the domain axis and favorable on input quality because the junctions have correct topology, connectivity, and ceiling/floor labels by construction.Source: §IV · p. 6

A. Single Image Localization

GALoc’s single-image results depend on wall coverage: it can match or surpass F3Locm when sufficient geometry is visible, while structure-blind frames contribute no confident estimate. Coverage distributions help explain its differing aggregate results across Structured3D and Gibson.

A. Single Image Localization

  • On Gibson, GALoc achieves 18.1% recall at 0.1 m (3× F3Locm) and 45.3% rank at 0.01%, versus 19.8% aggregate rank at 0.01%.Source: A. Single Image Localization · p. 6
  • F3Locm has higher aggregate recall on Structured3D because it estimates every frame; GALoc reports zero confidence on structure-blind close-ups, but matches or surpasses F3Locm above roughly 40% wall coverage.The authors characterize this as a trade-off rather than a strict advantage.Source: A. Single Image Localization · p. 6
  • Nearly 40% of Structured3D frames have zero wall coverage, while over 80% of Gibson frames exceed 40% coverage, where GALoc leads on recall.Source: Figure 9 · p. 6

B. Sequential Localization

On Gibson, temporal fusion improves GALoc and F3Loc as sequences grow, but GALoc overtakes F3Loc after a slight short-horizon edge for F3Loc. GALoc abstains on unrecovered panels, allowing high-coverage frames to add evidence without zero-coverage frames misleading the belief.

B. Sequential Localization

  • At 15 steps, F3Loc has a slight edge, but GALoc overtakes it as sequence length increases.Both methods improve across sequence lengths of 15, 25, 50, and 100 on Gibson; S3D has no sequential data.Source: B. Sequential Localization · p. 6
  • GALoc abstains when no panel is fully recovered, so zero-coverage frames propagate uncertainty rather than misinforming the belief.High-coverage frames can then accumulate geometric evidence.Source: B. Sequential Localization · p. 6
  • F3Loc’s low-coverage wall-distance estimates inject confident-but-wrong observations that corrupt the filter.At short horizons, few observations also leave geometric ambiguities.Source: B. Sequential Localization · p. 6

C. Real-World Evaluation

On Gibson, GALoc’s sequential performance improves with accumulated evidence, and its single-image recall advantage depends on wall coverage. In real-world sequences, the automatic wireframe detector limits GALoc’s recall, while corridor tests show longer range than the depth-based alternatives discussed.

C. Real-World Evaluation

  • 20% recall at 1 m for GALoc with the automatic detector contrasts with zero recall for F3Loc at all thresholds; hand-labeled junctions raise GALoc to 80% recall at 1 m.The comparison isolates detector domain transfer, rather than localization geometry, as the bottleneck on these five sequences.Source: C. Real-World Evaluation · p. 6
  • 3× the recall of F3Locm at 0.1 m on Gibson accompanies over 80% sufficient-coverage frames, while ∼40% of Structured3D frames have zero wall coverage.GALoc reports zero confidence on structure-blind close-ups, whereas F3Locm estimates every frame.Source: Table III · p. 7
  • 7–10 frames bring GALoc to the ground-truth pose on Gibson, compared with 20–50 frames typically required by F3Loc.GALoc’s convergence is also described as more stable.Source: Figure 10 · p. 7
  • 88% vs. 68% SR at 0.1 m with 100 steps favors GALoc over F3Loc in Gibson sequential localization.At short horizons GALoc trails slightly, then overtakes F3Loc as evidence accumulates.Source: Figure 11 · p. 7
  • Corridor rays reach 34 m, while F3Loc’s estimate collapses on out-of-distribution frames; consumer RGB-D sensors saturate near ∼15 m, matching F3Loc’s maximum range.In offices, F3Loc’s estimate is dominated by furniture.Source: C. Real-World Evaluation · p. 7

D. Runtime Comparison

The runtime comparison reports measurements on an i5-12400F system with 32GB RAM and an RTX3060.

D. Runtime Comparison

  • Runtime is reported for an i5-12400F, 32GB RAM, and an RTX3060.The supplied passage identifies the measurement hardware but gives no runtime values.Source: Table V · p. 7

E. Ablation: Robustness to Input Noise

Independent junction perturbations make the constraint matrix full-rank at every gauge, but the recovered wireframe remains architecturally valid as noise increases. Recall at 1 m falls by 4.2 percentage points from σ=3 to σ=7.

E. Ablation: Robustness to Input Noise

  • 4.2 pp in recall at 1 m are lost as noise rises from σ=3 (96.76%) to σ=7 (92.78%).Noise raises the smallest singular value and shifts the estimated gauge, so the BEV layout degrades rather than collapsing.Source: E. Ablation: Robustness to Input Noise · p. 7

V. LIMITATIONS AND CONCLUSION

GALoc performs best when wall structure is visible, but abstains when it is not; its accuracy is bounded by wireframe extraction, and the real-world evaluation is limited in scope.

V. LIMITATIONS AND CONCLUSION

  • 3× single-image recall at 0.1 m and 88% vs. 68% sequential success on Gibson show GALoc’s complementary regime when wall geometry is visible.GALoc abstains when wall structure is not visible.Source: §V · p. 7
  • GALoc assumes Atlanta-world geometry, and its accuracy and runtime are bounded or dominated by the wireframe extractor.The authors identify zero wall coverage and partial junction detection as failure modes, and describe real-world evaluation as limited in scope.Source: §V · p. 7
  • Real-world sequences had endpoint errors of 0.25–0.6 m in an office and 0.2–0.53 m in a corridor.The office measured 10.8×7.2 m and the corridor 51.6×12.8 m.Source: Figure 12 · p. 8
  • In the corridor comparison, recovered rays reach about 32 m; metric scale is for visualization, while matching is scale-invariant.Source: Figure 13 · p. 8
  • Zero-shot real-world recall was 20% at 1 m, versus 80% with hand-labeled junctions, reflecting the cost of topology and ceiling/floor-label requirements.Source: §V · p. 8
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