Transformer architecture has shown significant potential in various visual tasks, including point cloud registration. Positional encoding, as an order-aware module, plays a crucial role in Transformer framework. In this paper, we propose OIF-PCR++, a conditional positional encoding (CPE) method for point cloud registration. The core CPE module utilizes length and vector encoding at different stages, conditioned on the relative pose states between the point clouds to be registered. As a result, it progressively alleviates feature ambiguity through the incorporation of geometric cues. Building upon CPE, we introduce an iterative positional encoding optimization pipeline comprising two stages: 1) We find one correspondence via a differentiable optimal transport layer, and use it to encode length information into point cloud features, enhancing spatial consistency across different reference frames. 2) We apply a progressive direction alignment strategy to achieve rough alignment between paired point clouds, and then gradually incorporate direction information with the aid of this alignment, further enhancing feature distinctiveness and reducing feature ambiguity. Through this iterative optimization process, length and direction information are effectively integrated to achieve consistent and distinctive positional encoding, enabling the learning of discriminative point cloud features. Additionally, we present an inlier propagation mechanism that harmoniously integrates consistent geometric information for positional encoding. The proposed method is highly efficient, introducing marginal computational overhead while significantly improving feature distinguishability. Extensive experiments demonstrate superior performance over state-of-the-art methods on indoor, outdoor, object-level, and multi-way benchmarks, as well as strong generalization to complex real-world scenarios.

Outlier removal is a critical part of feature-based point cloud registration. In this paper, we revisit the model generation and selection of the classic RANSAC approach for fast and robust point cloud registration. For the model generation, we propose a second-order spatial compatibility (SC$^{2}$) measure to compute the similarity between correspondences. It takes into account global compatibility instead of local consistency, allowing for more distinctive clustering between inliers and outliers at an early stage. The proposed measure promises to find a certain number of outlier-free consensus sets using fewer samplings, making the model generation more efficient. For the model selection, we propose a new Feature and Spatial consistency constrained Truncated Chamfer Distance (FS-TCD) metric for evaluating the generated models. It considers the alignment quality, the feature matching properness, and the spatial consistency constraint simultaneously, enabling the correct model to be selected even when the inlier rate of the putative correspondence set is extremely low. Extensive experiments are carried out to investigate the performance of our method. In addition, we also experimentally prove that the proposed SC$^{2}$measure and the FS-TCD metric are general and can be easily plugged into deep learning based frameworks. The code will be available athttps://github.com/ZhiChen902/SC2-PCR-plusplus.

Transformer architecture has shown great potential for many visual tasks, including point cloud registration. As an order-aware module, position encoding plays an important role in Transformer architecture applied to point cloud registration task. In this paper, we propose OIF-PCR, a one-inlier based position encoding method for point cloud registration network. Specifically, we first find one correspondence by a differentiable optimal transport layer, and use it to normalize each point for position encoding. It can eliminate the challenges brought by the different reference frames of two point clouds, and mitigate the feature ambiguity by learning the spatial consistency. Then, we propose a joint approach for establishing correspondence and position encoding, presenting an iterative optimization process. Finally, we design a progressive way for point cloud alignment and feature learning to gradually optimize the rigid transformation. The proposed position encoding is very efficient, requiring only a small addition of memory and computing overhead. Extensive experiments demonstrate the proposed method can achieve competitive performance with the state-of-the-art methods in both indoor and outdoor scenes.