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.

We address the challenge of point cloud registration using color information, where traditional methods relying solely on geometric features often struggle in lowoverlap and incomplete scenarios. To overcome these limitations, we propose GeGS-PCR, a novel two-stage method that combines geometric, color, and Gaussian information for robust registration. Our approach incorporates a dedicated color encoder that enhances color features by extracting multi-level geometric and color data from the original point cloud. We introduce the Geometric-3DGS module, which encodes the local neighborhood information of colored superpoints to ensure a globally invariant geometric-color context. Leveraging LORA optimization, we maintain high performance while preserving the expressiveness of 3DGS. Additionally, fast differentiable rendering is utilized to refine the registration process, leading to improved convergence. To further enhance performance, we propose a joint photometric loss that exploits both geometric and color features. This enables strong performance in challenging conditions with extremely low point cloud overlap.

Multi-instance point cloud registration aims to estimate the pose of all instances of a model point cloud in the whole scene. Existing methods all adopt the strategy of first obtaining the global correspondence and then clustering to obtain the pose of each instance. However, due to the cluttered and occluded objects in the scene, it is difficult to obtain an accurate correspondence between the model point cloud and all instances in the scene. To this end, we propose a simple yet powerful 3D focusing-and-matching network for multi-instance point cloud registration by learning the multiple pair-wise point cloud registration. Specifically, we first present a 3D multi-object focusing module to locate the center of each object and generate object proposals. By using self-attention and cross-attention to associate the model point cloud with structurally similar objects, we can locate potential matching instances by regressing object centers. Then, we propose a 3D dual-masking instance matching module to estimate the pose between the model point cloud and each object proposal. It performs instance mask and overlap mask masks to accurately predict the pair-wise correspondence. Extensive experiments on two public benchmarks, Scan2CAD and ROBI, show that our method achieves a new state-of-the-art performance on the multi-instance point cloud registration task.

Correspondences in point cloud registration are prone to outliers, significantly reducing registration accuracy and highlighting the need for precise inlier identification. In this paper, we propose a robust inlier identification algorithm for point cloud registration by reformulating the conventional registration problem as an alignment error $\ell_0$-minimization problem. The $\ell_0$-minimization problem is formulated for each local set, where those local sets are built on a compatibility graph of input correspondences. To resolve the $\ell_0$-minimization, we develop a novel two-stage decoupling strategy, which first decouples the alignment error into a rotation fitting error and a translation fitting error. Second, null-space matrices are employed to decouple inlier identification from the estimation of rotation and translation respectively, thereby applying Bayesian theory to $\ell_0$-minimization problems and solving for fitting errors. Correspondences with the smallest errors are identified as inliers to generate a transformation hypothesis for each local set. The best hypothesis is selected to perform registration. We demonstrate that the proposed inlier identification algorithm is robust under high outlier ratios and noise through experiments. Extensive results on the KITTI, 3DMatch, and 3DLoMatch datasets demonstrate that our method achieves state-of-the-art performance compared to both traditional and learning-based methods in various indoor and outdoor scenes.

However, point cloud registration methods struggle to achieve precise global pose estimation, whereas previous pose-free NeRFs overlook geometric consistency in global reconstruction.

However, establishing these correspondences has been challenging due to the noisy, irregular, non-uniform, and textureless nature of 3D point clouds. Feature matching has long been the mainstream of data association without pose priors.