SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration (2203.14453v1)

Abstract: 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}.

• The paper introduces a second order spatial compatibility measure that significantly refines the inlier-outlier separation in point cloud correspondences.
• It employs a two-stage pipeline combining spectral seed selection and a weighted SVD approach for precise rigid transformation estimation.
• Experimental results demonstrate superior registration recall and precision on both indoor and outdoor benchmarks, highlighting its real-time applicability.

Analyzing SC$^2$-PCR: A Novel Approach for Point Cloud Registration

The paper introduces SC$^2$-PCR, a novel method dedicated to enhancing the robustness and efficiency of Point Cloud Registration (PCR) through a second-order spatial compatibility measure. Point Cloud Registration remains a fundamental problem in 3D computer vision applications, requiring precise alignment of two or more sets of 3D points that often suffer from noise, partial overlap, and feature ambiguity. The proposed SC$^2$-PCR leverages the global compatibility of point correspondences over the traditional local consistency approaches, advancing current methodologies chiefly represented by RANSAC and its derivatives.

Methodological Overview

The methodological core of SC$^2$-PCR lies in its two-stage registration pipeline underpinned by the SC$^2$ measure:

1. Second Order Spatial Compatibility Measure:
   • The SC$^2$ introduces a global measure for evaluating correspondences by considering the number of commonly compatible correspondences, thereby refining the inlier-outlier dichotomy significantly better than first-order metrics.
   • Mathematically formalized, the SC$^2$ is derived as a matrix product capturing these global compatibility metrics, which in turn guides the robust sampling strategy.
2. Pipeline Operation:
   • Seed Selection: Utilizes spectral techniques to identify reliable seed correspondences from the initial pool.
   • Consensus Set Expansion: A global spectral strategy followed by a two-stage selection process further refines these seeds into consensus sets that are predominantly inlier-populated.
   • Rigid Transformation Estimation: A weighted SVD approach is employed to derive candidate transformations, and the optimal model is selected against the inlier criterion.
3. Probabilistic Robustness:
   • The paper analytically demonstrates a probabilistic reduction in erroneous sample selection using SC$^2$, explicitly showing a decline in ambiguity during correspondence selection, thus boosting the chance of deriving outlier-free sets.

Experimental Analysis

SC$^2$-PCR's robust performance is validated against leading methods across diverse datasets, demonstrating exceptional registration recall and precision, particularly under conditions of low inlier ratios:

• On indoor benchmarks like 3DMatch, SC$^2$-PCR significantly surpasses competitors such as PointDSC and DHVR, achieving the highest registration recall, demonstrating its efficacy in distinguishing correct point correspondences from outliers.
• Its robustness extends to outdoors, illustrated by superior performance on the KITTI dataset.
• The method preserves efficiency in complex environments, underpinning real-time applications due to reduced computational overhead enabled by its targeted sampling strategy.

Implications and Speculation

SC$^2$-PCR stands out by uniquely addressing sparsity and ambiguity through its global compatibility measure, facilitating more resilient model estimations crucial for applications in augmented reality, SLAM, and autonomous systems. The method's lightweight architecture suggests potential integration paths within deep learning frameworks, providing an avenue for enhanced learning-based point cloud alignment in future research.

In speculating future advancements, the adaptability of SC$^2$ into broader AI frameworks could steer improvements in tasks reliant on structural understanding of 3D environments, for instance, enhancing neural field representations or advancing graph-based neural networks for 3D reconstructions.

Conclusion

The SC$^2$-PCR method represents a substantial stride toward resolving issues inherent in point cloud registration by introducing a comprehensive global compatibility measure. Through its integration into conventional spectral methods and innovative sampling techniques, SC$^2$-PCR will likely shape the foundation for further research and application development within the domain of 3D computer vision.