Spectral Consistency-Guided Multiview Point Cloud Registration for Low-Overlap Scenes

• Existing approaches often handle correspondence reliability, scan-pair selection, and global refinement separately, so expensive transformation estimation may precede pair validation.Source: §1 · p. 2
• GMPCR uses the dominant spectral response of a refined second-order compatibility structure to evaluate correspondence reliability and scan-pair confidence.Source: §1 · p. 2
• Informative scan pairs are selected before relative transformation estimation, and retained pairs produce a sparse pose graph through maximal-clique-based hypothesis generation.Source: §1 · p. 2
• Adaptive history-aware synchronization adjusts residual-history influence as the global rotation residual evolves and lets down-weighted edges regain confidence when consistency improves.Source: §1 · p. 2
• Experiments on 3DMatch, 3DLoMatch, ScanNet, and ETH demonstrate a favorable balance between registration accuracy and computational efficiency.Source: §1 · p. 2

2.1 Correspondence-based Multiview Point Cloud Registration

• Correspondence-based registration uses explicit geometric relations for pairwise estimation and sparse graph construction, followed by global pose recovery.Source: §2.1 · p. 3
• Prior correspondence-based methods improve pairwise or global reliability, but low-overlap scenes still challenge scan-pair assessment from few inliers and many outliers.Source: §2.1 · p. 3
• GMPCR links correspondence filtering, scan-pair selection, and synchronization by using refined spectral geometric consistency before relative transformation estimation.Source: §2.1 · p. 3

2.2 Correspondence-free Multiview Point Cloud Registration

• Correspondence-free approaches use global scene or representation-level objectives, but do not explicitly model pair reliability or make sparse pose-graph construction as direct.Source: §2.2 · p. 3

• Multiview registration estimates a global rigid transformation for each scan, while unknown overlap and contaminated correspondences make exhaustive pairwise registration costly and prone to unreliable edges.Source: §3.1 · p. 4
• The first stage establishes correspondences, scores their compatibility and scan-pair confidence, retains informative pairs, and uses maximal cliques to generate transformation hypotheses.Source: §3.1 · p. 4
• The second stage iteratively refines global poses and edge weights using global consistency, residual history, and recovery of edges whose consistency improves.Source: §3.1 · p. 4

3.2.1 Initial Correspondence Construction

• Feature-space farthest-point sampling retains Ns representative descriptors; mutual-nearest matching keeps No candidates, but feature similarity alone does not ensure geometric correctness.Feature-space sampling promotes descriptor diversity and reduces the dominance of densely distributed, similar descriptors.Source: §3.2.1 · pp. 4–5

3.2.2 Spectral Consistency-Guided Scan Pair Selection

• 0.801 mean pairwise AUC on 3DLoMatch scan pairs; the highest-confidence decile averages approximately 0.485 overlap versus approximately 0.10 across all candidate pairs.The highest-confidence decile's mean overlap is 4.8× the all-pair mean.Source: Figure 2 · p. 6
• GMPCR builds first- and second-order compatibility structures, filters correspondences by dominant-eigenvector response, and recomputes the graph after pruning so discarded matches no longer support neighborhoods.Second-order consistency provides support from multiple neighboring correspondences, making it more robust to false geometric matches than pairwise distance compatibility alone.Source: §3.2.2 · pp. 5–6
• GMPCR scores scan-pair confidence from the refined second-order correspondence graph before transformation estimation, then retains the union of scans' top-K confident neighbors as a sparse graph.An edge is retained if either scan identifies the other as a reliable neighbor.Source: §3.2.2 · pp. 6–7

3.2.3 Clique-Based Transformation Estimation

• For each retained pair, maximal cliques with at least three correspondences generate hypotheses, ranked by mean internal SCG affinity so smaller consistent subsets remain competitive at low overlap.Hypotheses are evaluated on the complete filtered correspondence set, and the transformation with the highest inlier ratio is selected.Source: §3.2.3 · p. 7

3.3 Adaptive History-aware Pose Synchronization

• Each IRLS iteration alternates between estimating global poses under current edge weights and updating edge confidence from relative-rotation consistency.After L iterations, the synchronized transformations are taken as the final global poses.Source: §3.3 · p. 7, §3.3.2 · p. 9

3.3.1 Rotation and Translation Synchronization

• Weighted rotation synchronization minimizes disagreement between measured and globally induced relative rotations; translations are then estimated by weighted linear least squares.The rotation solution uses a weighted connection Laplacian and projects selected eigenvector blocks onto SO(3).Source: §3.3.1 · p. 8

3.3.2 Adaptive History-aware Edge-Weight Update

• Residual history is adjusted using changes in overall rotation error: large changes favor current residuals, while stabilization increases historical smoothing.Relative error variation better captures optimization evolution and is less sensitive to graph size and initial weight scale than absolute error magnitude.Source: §3.3.2 · pp. 8–9
• The recovery term restores confidence only when an edge residual decreases, and updated weights remain capped at their initial pairwise confidence.Edges with non-decreasing residuals receive no recovery; persistent outliers are unlikely to recover substantially because their residual histories remain large.Source: §3.3.2 · p. 9
• Together, pairwise spectral consistency and history-aware reweighting refine transformations using global pose-graph consistency while retaining a sparse, informative graph for low-overlap registration.The process transfers information between local pairwise reliability and global consistency.Source: §3.3.2 · p. 9

4.1.1 Datasets

• Evaluation covers 3DMatch and 3DLoMatch indoor scan pairs, large-scale indoor ScanNet scenes, and four outdoor ETH scenes.The datasets include 1,623 3DMatch pairs, 1,781 low-overlap 3DLoMatch pairs, 960 ScanNet scans, and 713 ETH evaluation pairs.Source: §4.1.1 · p. 9

4.1.2 Metrics

• Registration Recall is the primary metric for 3DMatch, 3DLoMatch, and ETH, while ScanNet is evaluated using rotation and translation errors plus threshold-based recall.Higher recall and lower errors indicate better registration performance.Source: §4.1.2 · p. 10

4.2 Qualitative and Quantitative Results

• 97.2% and 89.6% registration recall on 3DMatch and 3DLoMatch, respectively, outperform all competing methods; GMPCR is 0.1 percentage points below the ETH best.It exceeds SGHR by 1.0 and 8.0 percentage points on 3DMatch and 3DLoMatch, respectively.Source: Table 1 · p. 10, §4.2 · p. 10

4.1.3 Implementation Details

• The implementation uses dataset-specific point, correspondence, spectral-retention, neighborhood, clique, and IRLS settings, with experiments run on a stated CPU, RAM, and GPU configuration.The maximum IRLS iteration counts are 10, 90, 80, and 5 for 3DMatch, 3DLoMatch, ScanNet, and ETH, respectively.Source: §4.1.3 · p. 10

4.2 Qualitative and Quantitative Results

• On ScanNet, GMPCR has a 20.2° mean rotation error and 0.46m mean translation error, matching SMVR on mean translation error and achieving the lowest median translation error at 0.40m.Its mean rotation and translation errors improve on SGHR's 21.7° and 0.56m.Source: §4.2 · p. 10, Table 2 · p. 11
• In Home-MD and Studyroom, GMPCR generally produces more consistent walls and room structures with less visible drift than SGHR and SMVR.The comparison uses three representative 3DMatch scenes; all methods recover coherent structures in Kitchen.Source: §4.2 · p. 11

Ground Truth SGHR SMVR GMPCR

• The qualitative comparison places ground truth in the leftmost column and SGHR, SMVR, and GMPCR results in the remaining columns.The comparison is on 3DMatch.Source: Figure 3 · p. 11
• GMPCR achieves the best performance on 3DMatch and 3DLoMatch while remaining competitive on ETH and ScanNet.The reported overall balance spans registration accuracy, low-overlap robustness, and performance across datasets and scene types.Source: Ground Truth SGHR SMVR GMPCR · pp. 11–12

4.3 Ablation Study

• Pair selection raises registration recall from 91.6% and 82.5% to 96.0% and 88.7% on 3DMatch and 3DLoMatch, the largest component gains.The full model reaches 97.2% and 89.6% after spectral filtering, adaptive memory, and recovery are added.Source: Table 3 · p. 12, §4.3 · p. 12

4.4 Robustness under increasing Numbers of Views

• The evaluation uses six shared 3DMatch and 3DLoMatch scenes with more than 50 views, sampling subsets of 10, 20, 30, 40, 50, and all views.Fewer views reduce potential geometric connections and effective overlap among selected scans.Source: §4.4 · p. 13
• On 3DLoMatch, GMPCR records recalls of 74.0%, 80.6%, 87.4%, 90.4%, 92.5%, and 93.4% as view counts increase, exceeding all competing methods.It has the highest recall in every tested 3DLoMatch setting and in 3DMatch settings with 20 views or more.Source: §4.4 · p. 13

4.5 Pose Graph Construction Quality

• For pose-graph ranking, top-K neighbors are compared with ground-truth top-K neighbors by overlap; R@K rewards retrieved high-overlap pairs, while lower Regret indicates closer-to-ideal overlap.These measures evaluate whether the selected scan pairs preserve informative connections.Source: §4.5 · p. 14
• GMPCR achieves the best scan-pair retrieval across datasets and K settings, including 3DLoMatch R@K of 73.2%, 74.5%, and 72.7% at K = 4, 8, and 12.On 3DLoMatch, corresponding Regret values are 0.0380, 0.0322, and 0.0287; the passage also reports strong retrieval on ScanNet and ETH.Source: §4.5 · p. 14

4.6 Pose Graph Connectivity Analysis

• Full connectivity is reached at K = 5 on 3DMatch, with LCCmin and Rmin at 100% and 173.0 mean edges, and at K = 8 on 3DLoMatch, with 270.1 mean edges.The connectivity figure reports fully connected scene percentages and worst-scene LCC ratios.Source: Table 6 · p. 14, §4.6 · p. 14, Figure 5 · p. 15
• Increasing K improves connectivity but adds edges; on 3DMatch, raising K from 5 to 10 increases mean edges from 173.0 to 337.2 without changing connectivity.Lower-overlap scenes require more neighboring connections.Source: §4.6 · pp. 14–15

4.7 Time Efficiency Analysis

• GMPCR's main module takes 23.3s and synchronization 0.4s per scene; synchronization is 82.6% and 92.3% faster than SGHR and SMVR.The main module includes graph construction and pairwise relative-pose estimation; synchronization measures global pose optimization.Source: §4.7 · p. 15
• GMPCR takes 23.7s per 3DMatch scene, 15.7s less than SGHR and 19.6s less than SMVR, for speedups of 1.66× and 1.83×.RAP is faster at 10.4s, mainly through feed-forward inference after training; GMPCR does not require training.Source: Table 7 · p. 15, §4.7 · p. 15

5 Conclusion

• GMPCR jointly evaluates correspondence reliability and scan-pair confidence, estimates retained-pair transformations with cliques, and refines the pose graph through adaptive history-aware synchronization.The synchronization adjusts residual-history contributions with global rotation consistency and allows down-weighted edges to recover when consistency improves.Source: §5 · p. 15
• 97.2% and 89.6% registration recall on 3DMatch and 3DLoMatch, respectively; GMPCR remains competitive on ScanNet and ETH.Scan-pair retrieval and runtime analyses also find more accurate connection selection and greater efficiency than existing sparse pose graph methods.Source: §5 · pp. 15–16
• Future work targets reducing candidate-pair evaluation costs and improving robustness in extremely sparse or weakly connected pose graphs.Source: §5 · p. 16