Learning-based image-to-point-cloud (I2P) registration has garnered increasing attention in recent years. Nevertheless, existing methods still struggle with severe outliers under challenging scenarios with unseen, low-inlier, or distorted cases. A fast and robust 2D-3D correspondence pruning method is therefore highly desirable. Recently, a promising scheme lifts 2D-3D correspondences to 3D-3D correspondences using depth priors, casting correspondence pruning as a Sim(3) registration problem. However, depth priors estimated from monocular images are inherently noisy, which undermines the reliability of this scheme. In this paper, to explicitly model non-negligible depth noise, we reformulate correspondence pruning as an extended Sim(3) registration problem and propose a simple yet effective pruning algorithm termed Ex-Sim(3)-Reg. We further provide a theoretical analysis to justify the effectiveness of our method. Extensive experiments on the 7-Scenes, RGBD-V2, ScanNet, and TUM datasets demonstrate that Ex-Sim(3)-Reg achieves up to \textbf{24.7\% improvement} in registration recall over state-of-the-art baseline methods. Code is released at github.com/anpei96/ex-sim3-demo

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