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SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration
Zhi Chen, Kun Sun, Fan Yang, Wenbing Tao
TL;DR
Point cloud registration must remain accurate when feature ambiguity and partial overlap create outlier correspondences. SC^2-PCR uses global second-order compatibility, spectral seed selection, two-stage consensus sampling, and weighted transformation estimation. The method reports state-of-the-art performance and high efficiency, while SC^2 also improves PointDSC when combined with it.
Problem
Partial overlap and feature ambiguity make correspondence-based rigid model estimation vulnerable to outliers and inaccurate alignment.
Method
SC^2-PCR globally measures shared compatibility among correspondences, selects seeds spectrally, expands them into two-stage consensus sets, and estimates candidate transformations with weighted SVD.
Results
SC^2-PCR achieves state-of-the-art performance and high efficiency, and combining SC^2 with PointDSC produces better results.
Takeaways & Limitations
SC^2 provides more distinctive early clustering of inliers and outliers and can be plugged into deep-learning registration frameworks.
Takeaways & Limitations
The theoretical inlier-distance analysis assumes the inlier distance difference is uniformly distributed below a threshold.
Abstract
from arXiv · showhide
In this paper, we present a second order spatial compatibility (SC^2) measure based method for efficient and robust point cloud registration (PCR), called SC^2-PCR. Firstly, we propose a second order spatial compatibility (SC^2) measure to compute the similarity between correspondences. It considers the global compatibility instead of local consistency, allowing for more distinctive clustering between inliers and outliers at early stage. Based on this measure, our registration pipeline employs a global spectral technique to find some reliable seeds from the initial correspondences. Then we design a two-stage strategy to expand each seed to a consensus set based on the SC^2 measure matrix. Finally, we feed each consensus set to a weighted SVD algorithm to generate a candidate rigid transformation and select the best model as the final result. Our method can guarantee to find a certain number of outlier-free consensus sets using fewer samplings, making the model estimation more efficient and robust. In addition, the proposed SC^2 measure is general and can be easily plugged into deep learning based frameworks. Extensive experiments are carried out to investigate the performance of our method. Code will be available at \url{https://github.com/ZhiChen902/SC2-PCR}.
1. Introduction
Point cloud registration must estimate rigid alignment despite correspondence outliers caused by partial overlap and feature ambiguity. SC^2-PCR addresses this by using a global second-order compatibility measure to distinguish inliers, construct reliable consensus sets, and estimate transformations efficiently.
- Point cloud registration aligns two 3D scans and supports applications including SLAM, augmented reality, and robotics.
- Partial overlap and feature ambiguity introduce correspondence outliers that can produce inaccurate or wrong alignments.
- First-order spatial compatibility can assign high scores to outliers that happen to match some inliers, causing performance deterioration.
- SC^2 measures the number of correspondences simultaneously compatible with two compatible correspondences, capturing global rather than local compatibility.
- When there are m inliers among n correspondences, SC^2 enables m reliable model estimations by traversing n rows instead of relying on extensive random sampling.
- SC^2-PCR selects reliable seeds spectrally, expands them through two-stage consensus-set sampling, estimates transformations with weighted SVD, and selects the best model.
2. Related Work
Related work develops robust correspondence establishment and model fitting through geometric compatibility, RANSAC variants, and learning-based methods. These approaches improve registration but generally do not establish entirely outlier-free correspondence sets.
- 3D feature matching uses coordinate-space nearest neighbors or local descriptors, including handcrafted and learned descriptors, to establish correspondences.
- Feature-matching methods achieve substantial performance improvements but can hardly establish a totally outlier-free correspondence set.
- RANSAC and its variants estimate geometric models through generation, verification, improved sampling, or local optimization.
- Learning-based model fitting combines correspondence classification with model estimation, while recent 3D methods use deep networks for correspondence pruning.
3. Method
The method models correspondence similarity with first- and second-order spatial compatibility, then uses ambiguity analysis and staged sampling to build consensus sets for rigid registration. SC^2 emphasizes global common compatibility to improve inlier selection and seed-based estimation.
- The method forms putative correspondences from nearest neighbors in feature space and estimates rotation R and translation t between two point clouds.
- Ambiguity analysis: The ambiguity event occurs when an inlier–outlier similarity exceeds an inlier–inlier similarity, indicating that metric-guided sampling may select an outlier neighbor.
- First-order spatial compatibility: First-order SC scores correspondence pairs by the difference between source and target interpoint distances through a decreasing kernel.
- Consensus-set sampling: The pipeline selects seeds spectrally, expands each seed through coarse-to-fine top-K1 and top-K2 neighbor selection, and retains hypotheses for final filtering.
- Ambiguity analysis: On 3DMatch with d_thr = 10cm, SC ambiguity probability is about 0.1, whereas SC^2 has significantly lower ambiguity and approaches zero near a 1% inlier rate.
- Second-order spatial compatibility: SC^2 binarizes compatibility and assigns compatible correspondence pairs the number of correspondences commonly compatible with both, while assigning zero to incompatible pairs.
4. Experiment
Experiments across indoor, low-overlap, outdoor, generalization, and low-inlier settings show that SC^2-PCR is accurate, robust, and efficient across descriptors and datasets. Ablations attribute gains to SC^2-guided sampling, two-stage selection, and local spectral matching.
- Indoor scenes: SC^2-PCR achieves the highest registration recall on 3DMatch with FPFH, improving by about 6% over the closest retested competitors.The closest competitors are PointDSC and CG-SAC.
- Low-overlap scenes: SC^2-PCR achieves the highest registration recall on 3DLoMatch with both FCGF and Predator, including successful alignment under clearly low overlap.The evaluation reports registration recall, rotation error, and translation error.
- Outdoor scenes: On KITTI, SC^2-PCR exceeds RANSAC registration recall by 25.23% with FPFH and 17.84% with FCGF, while also producing lower rotation and translation errors.The comparison includes both learning-based and non-learning methods.
- Robustness: When the inlier rate is below 2%, SC^2-PCR performs significantly better than other methods, demonstrating robustness to noise.The robustness experiment groups 3DMatch pairs into six inlier-ratio ranges.
- Ablation study: SC^2-guided sampling improves recall over RANSAC by 14.79% with FPFH and 1.66% with FCGF, while reducing registration time.SC^2 guidance also outperforms first-order SC because it can eliminate ambiguity.
- Ablation study: Two-stage selection improves recall by 1.96% with FPFH and 0.12% with FCGF, while local spectral matching further improves mean rotation and translation errors.The two-stage procedure reconstructs local SC^2 matrices to prune potential outliers.
5. Conclusion
SC2-PCR uses second-order spatial compatibility to cluster inliers early, generate candidate rigid transformations, and select the best estimate. Experiments report state-of-the-art performance, high efficiency, and compatibility with learning networks.
- SC2-PCR selects reliable seed correspondences through global spectral decomposition with Non-Maximum Suppression.
- A two-stage sampling strategy expands seeds into consensus sets, each producing a rigid transformation before best-model selection.
- Extensive experiments demonstrate state-of-the-art performance and high efficiency, while SC2 can combine with learning networks to boost performance.
7. Supplementary Material
The supplementary material analyzes SC2 mathematically, explains parameter and heat-map behavior, and reports additional registration results. Its analysis links global common compatibility to stronger inlier–outlier separation and evaluates the two-stage selection strategy.
- Derivations: SC2_ij equals C_ij multiplied by M_ij, where M_ij counts correspondences simultaneously compatible with correspondences i and j globally.
- Derivations: The ambiguity probability is expressed through the event that an inlier–outlier SC2 score exceeds an inlier–inlier score, with the compatibility probability p as a factor.
- Derivations: For two inliers, M_in,in follows N·α−2 plus a Bernoulli term, whereas M_in,out is modeled by sums of Bernoulli variables involving p and p^2.
- Ablation Study: The two-stage strategy selects K1 seed neighbors, rebuilds a local SC2 matrix, and retains K2 correspondences; K1=30 and K2=20 give the best recall.
- Ablation Study: On heat maps with inliers ordered before outliers, SC shows high outlier–inlier compatibility, while SC2 leaves those regions clean with low outlier compatibility.