Title: PointTruss: K-Truss for Point Cloud Registration
Venue: NeurIPS 2025
Accepted: yes
Keywords: Point cloud registration; compatibility graph; outlier removal; k-truss; correspondence selection
Abstract: Point cloud registration is a fundamental task in 3D computer vision. Recent advances have shown that graph-based methods are effective for outlier rejection in this context. However, existing clique-based methods impose overly strict constraints and are NP-hard, making it difficult to achieve both robustness and efficiency. While the k-core reduces computational complexity, which only considers node degree and ignores higher-order topological structures such as triangles, limiting its effectiveness in complex scenarios. To overcome these limitations, we introduce the $k$-truss from graph theory into point cloud registration, leveraging triangle support as a constraint for inlier selection. We further propose a consensus voting-based low-scale sampling strategy to efficiently extract the structural skeleton of the point cloud prior to $k$-truss decomposition. Additionally, we design a spatial distribution score that balances coverage and uniformity of inliers, preventing selections that concentrate on sparse local clusters. Extensive experiments on KITTI, 3DMatch, and 3DLoMatch demonstrate that our method consistently outperforms both traditional and learning-based approaches in various indoor and outdoor scenarios, achieving state-of-the-art results.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces  PointTruss , a novel graph-based method for point cloud registration. The method leverages the  k-truss  concept from graph theory to enhance the robustness and efficiency of correspondence selection in point cloud registration. Unlike traditional clique-based methods, which are computationally expensive (NP-hard) and overly restrictive, or k-core methods, which lack higher-order topological constraints,  PointTruss  uses triangle support (requiring each edge to participate in at least  k-2  triangles) to identify structurally consistent correspondences. The approach includes a consensus voting-based low-scale sampling strategy to reduce computational complexity and a spatial distribution score (SDS) to evaluate inlier coverage and uniformity, ensuring globally consistent transformations. The pipeline involves constructing a compatibility graph, applying k-truss decomposition, generating transformation hypotheses via weighted SVD, and selecting the optimal transformation using SDS. Extensive experiments on KITTI, 3DMatch, 3DLoMatch, and the Bunny model demonstrate that  PointTruss  outperforms traditional and learning-based methods in registration recall (RR), rotation error (RE), and translation error (TE), particularly in challenging scenarios with high outlier ratios or low overlap.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths：\n\n1.   Quality  : The paper presents a robust and well-validated method. Extensive experiments across diverse datasets (KITTI, 3DMatch, 3DLoMatch, and Bunny) demonstrate superior performance over state-of-the-art methods, both traditional (e.g., RANSAC, FGR, MAC) and learning-based (e.g., PointDSC, VBReg). The use of both FPFH and FCGF descriptors, along with quantitative metrics (RR, RE, TE) and qualitative visualizations (Fig. 5), strengthens the empirical evaluation. The theoretical foundation, including Theorem 1 and its proof in Appendix A.2, provides a rigorous justification for the k-truss approach.\n\n2.   Clarity  : The paper is well-organized, with a clear pipeline (Fig. 2) and detailed explanations of each component (graph construction, sampling, k-truss decomposition, and hypothesis evaluation). Mathematical formulations, such as the SDS function and k-truss definitions, are precise and supported by matrix-based implementations. The experimental setup, including datasets, evaluation criteria, and implementation details, is thoroughly described in Sec. 4.1.\n\n3.   Significance  : The method addresses a critical challenge in point cloud registration—balancing robustness and efficiency in the presence of outliers and low overlap. \n\n4.   Originality  : The introduction of k-truss to point cloud registration is novel, as it leverages higher-order topological structures (triangles) to overcome limitations of clique-based and k-core methods. The consensus voting-based sampling and SDS are innovative additions that enhance both efficiency and global consistency.\n\nWeaknesses\n\n1.  While the experimental results are strong, the paper lacks a detailed ablation study to quantify the individual contributions of the k-truss, consensus voting, and SDS components. This limits the understanding of which elements drive the performance gains. \n\n2.   The paper does not include validation experiments combining PointTruss with state-of-the-art deep learning methods (e.g., GeoTransformer or PareNet) on challenging datasets like 3DLoMatch, which could demonstrate its compatibility with modern learned features and further validate its robustness.\n\nQUESTIONS:\nSee weakness.\n\nLIMITATIONS:\nThe authors adequately address the limitations and potential negative societal impacts of their work in Appendix A.7, as noted in the response to Question 10 (PAGE16). They discuss limitations, likely including challenges in extremely low-overlap scenarios or computational constraints for very large point clouds, and consider societal impacts relevant to applications like autonomous driving or 3D reconstruction. The transparency in addressing these aspects is commendable and aligns with NeurIPS guidelines, rewarding the authors for being upfront about their work’s boundaries.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-16"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel method for improving the accuracy of pairwise registration of 3D scans by extracting reliable information from graphs to filter out outliers. Graph-based methods typically leverage the fact that pairwise distances between points in a scan remain invariant under rigid transformations. However, in practice, deviations arise due to noise, outliers, and incorrect matches.\nTo address this, the paper employs a k-truss decomposition on a correspondences graph to isolate strong inlier correspondences. The proposed pipeline consists of the following steps:\\\n(a) Construction of a compatibility graph, and subsequently a distance-consistency graph, where correspondences are represented as nodes. Edges connect pairs of correspondences whose pairwise distances (within source and target scans) are consistent up to noise. The greater the consistency between two pairs, the higher the edge weight in the distance-consistency graph.\\\n(b) Low-scale sampling: To reduce graph size and computational complexity, the method uses consensus voting to retain correspondences (nodes) with a higher number of consistent neighbours. Non-maximal suppression is then applied to avoid excessive correspondences in dense regions, promoting spatial uniformity among selected inliers.\\\n(c) A k-truss decomposition is applied on the downsampled graph for various values of $k$, yielding subgraphs whose rigid transformations are estimated using weighted SVD.\\\n(d) Among the candidate transformations, the one maximizing a proposed spatial distribution score is selected. This score favors both registration accuracy and a well-distributed set of inliers across the scan.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\\\n1.\tThe paper is well-written and easy to follow. \\\n2.\tThe method avoids the disadvantages of other graph-based techniques in 3d registration, namely the maximal clique selection is computationally expensive for larger 3d scans and the k-core method is not discriminative enough to get an accurate registration. This is because the proposed k-truss method is \\\na.\tGrounded by the theoretical analysis which shows that triangles of consistent correspondences are highly probable to be more accurate.\\\nb.\tIt has an efficient practical implementation in terms of the adjacency matrices. \\\n3.\tAlthough the triangle-based consistency is not entirely novel in computer vision, the way different parts of the pipeline are pieced together is intuitive and novel. \n\nWeaknesses:\n1. The authors appear to have misunderstood the standard definition and computation procedure for k-truss decomposition. Specifically, Algorithm 3 in the supplementary material, which is presented as performing a k-truss extraction, does not implement the correct iterative edge-peeling process, where edges participating in fewer than $k-2$ triangles are repeatedly removed until convergence. Instead, the proposed algorithm functions as a heuristic, and it does not produce true or even approximate k-truss subgraphs in general. Consequently, it is misleading to refer to the method as a k-truss decomposition, including in the paper's title and central claims. This foundational flaw undermines the technical correctness of the paper and renders its core results unreliable. \n2.\tThe Equation-2 is confusing. Is $S_{dist}(c_i, c_j)$ a real number or Boolean? The notation is not consistent from Equation-1 to Equation-2. There is no $q_i$, instead it is written in terms of the source and target scans.\n3.\tThe Theorem-1 seems to give only an intuitive understanding of the strength of triangle-based consistency. It could be made more rigorous and mathematically precise, which can then be interpreted based on different values of the threshold parameters involved. I am not sure if a “$\\gg$” based inequality is rigorous enough to be named a Theorem. \n4.\tIn Section-3.5, the centrality measure used in weighted SVD is undefined.\n5.\tSpatial distribution score function seems to be very complicated (Equation-14). It is not clear if there is any intuitive understanding on how it is derived. \n6.\tSome of the latest literature relevant to non-learning based point cloud registration are not cited or compared against: \"ARCS: Accurate Rotation and Correspondence Search\" by Peng et al., CVPR 2022; \"Adaptive Annealing for Robust Geometric Estimation\" by Sidhartha et al., CVPR 2023.\n\nQUESTIONS:\n1. I believe the paper requires a major revision to address the misinterpretation of the k-truss algorithm. Since this component is central to the proposed methodology and the experimental results, the misunderstanding has significant implications. If the foundation itself is flawed, it becomes extremely difficult to interpret the reported outcomes. Moreover, both intuitively and technically, k-truss-based outlier filtering is generally weaker than clique-based methods such as MAC in capturing highly coherent inliers. However, the ablation results presented in Table 5 of the supplementary material show the opposite — k-truss outperforming MAC even when other settings are kept the same. The discrepancy vindicates the claim that the methodology is likely built upon a flawed interpretation of k-truss decomposition.\n2. It is not clear how much the original distance-consistency graph is reduced after the low-scale sampling step. As a result, it is difficult to assess the actual sizes of the subgraphs on which the rigid transformations are estimated. If the number of nodes (correspondences) in these subgraphs is too small, it raises concerns about the stability and reliability of the estimated rotations and translations obtained via weighted SVD. A more detailed quantitative information of the graph sizes after sampling for various datasets in the experiments would be crucial in assessing the value of this method. \n3. Additionally, an ablation study examining the method’s performance under different levels of graph sampling would be valuable. Such an analysis would help clarify the trade-offs introduced by the consensus-based low-scale sampling, both in terms of accuracy and computational efficiency of the subsequent k-truss decomposition.\n4. Can you comment on the weighting used in weighted SVD? It highly obscures the interpretation of the results, because a rotation error of 1 degree for the proposed method (in Fig.3 top row) also seems to be significant for a synthetic dataset when the noise has a very low $\\sigma=0.01$. A minor question: In Fig.3 in the top row, the rotation and translation errors for the proposed method seem to be constant till an outlier ratio of 80%, where other methods exhibit some variation. Is there any reason for this behaviour?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces the k-truss from graph theory into point cloud registration, leveraging triangle support as a constraint for inlier selection. In addition, a consensus voting-based low-scale sampling strategy is presented to extract the structural skeleton of the point cloud prior to k-truss decomposition. Furthermore, to avoid spatially clustered inliers, a spatial distribution score is introduced to evaluate the coverage and uniformity of inliers. Extensive experiments on KITTI, 3DMatch, and 3DLoMatch demonstrate the effectiveness of the proposed methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengthens:\n- The paper is exceptionally well-structured and accessible, ensuring clarity throughout.\n\n- It compellingly motivates the application of the k-truss (a graph-theoretic concept) to point cloud registration.\n\n- The proposed method achieves state-of-the-art (SOTA) performance across diverse datasets, including outdoor (KITTI) and synthetic benchmarks (3DMatch, 3DLoMatch).\n\n- Comprehensive experiments and ablation studies rigorously validate the efficacy of each component in the framework.\n\nWeaknesses:\n- Figure 2 illustrates examples of subgraphs generated using K-truss decomposition. However, the subgraphs for K=5 and K=6 appear to contain inconsistencies. For instance, in the K=5 subgraph, the edge E(C5, C8) participates in only two triangles: $\\triangle$C3C5C8 and $\\triangle$C4C5C8. This contradicts the requirement that edges within a 5-truss subgraph must belong to at least three triangles (k-2 = 3).\n\n- Table 1 shows that the proposed method achieves the shortest inference time. However, K-truss decomposition is computationally intensive, and its required computation time should be clarified.\n\n- The results reported for VBReg [18] (from the official paper) on KITTI using FPFH features are 0.32 (RE) and 7.17 (TE). These differ from the values of 0.45 (RE) and 8.41 (TE) listed in Table 1. Furthermore, the runtime for PointDSC cited within the VBReg[18] is 0.11 seconds, which is shorter than the 0.45 seconds reported for PointDSC in Table 1.\n\nQUESTIONS:\nPlease refer to the weaknesses.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes PointTruss, a novel graph-based algorithm for point cloud registration that introduces the k-truss concept from graph theory to improve inlier selection.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths：\n\n1）Introducing k-truss to point cloud registration is a novel contribution, as it leverages triangle-based constraints to enhance inlier selection, distinguishing it from clique-based (e.g., TEASER++) and k-core-based (e.g., ROBIN) methods. \n\n2）The evaluation is thorough, covering synthetic  and real-world datasets with FPFH and FCGF descriptors. Quantitative results and qualitative visualizations show strong robustness to outliers and noise.\n\nWeaknesses：\n\n1）While k-truss is novel in this context, the paper does not sufficiently distinguish PointTruss from existing graph-based methods like SC²-PCR or MAC, which also exploit geometric consistency. \n\n2）The lack of ablation studies on key components (e.g., k value, spatial distribution score) weakens the analysis of their contributions.\n\nQUESTIONS:\n1）The paper claims k-truss leverages triangle rigidity for robust inlier selection. Can the authors provide a formal theoretical analysis (e.g., using geometric or graph-theoretic principles) to demonstrate why k-truss is inherently more suitable than k-core or clique-based methods for point cloud registration? This could strengthen the motivation and clarify the method’s design rationale.\n\n2）Why was k-truss chosen over k-core or clique-based methods like SC²-PCR or TEASER++? \n\n3）The method relies on triangles as the “simplest rigid formation” . How does PointTruss handle scenarios where triangle formations are sparse or absent due to extreme noise, occlusions, or low-overlap point clouds? Have the authors analyzed the failure modes of k-truss in such cases, and how do these affect registration accuracy?\n\n4）The k value in k-truss decomposition determines the strength of triangle support. How is the optimal k value chosen, and what is the sensitivity of PointTruss’s performance to variations in k? Could the authors provide an ablation study or theoretical justification for k selection to clarify its impact on robustness and efficiency?\n\nLIMITATIONS:\nNo limitations discussed. See Weaknesses for suggestions.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-04"}