The spherical point pattern registration algorithm estimates the rotation that aligns a noisy, rotated source spherical point cloud with the template point cloud.

Overview

We address the problem of rotation estimation between two spherical patterns (S²), a task fundamental to many applications in computer vision and robotics. Traditional correspondence-based or correlation-based methods often fail on the sphere due to unreliable surface correspondences and high computational cost (>O(n³)). We propose a linear-time (O(n)) spherical alignment framework that reformulates rotation estimation as a correspondence-free point-set alignment problem on the unit sphere. Three algorithms — SPMC, FRS, and a hybrid SPMC+FRS — achieve over 10× faster and 10× more accurate performance than current state-of-the-art methods on our new Robust Vector Alignment Dataset.

Furthermore, we adapt our methods to two real-world tasks: (i) Point Cloud Registration (PCR) and (ii) rotation estimation for spherical images. In the PCR task, our approach successfully registers point clouds exhibiting overlap ratios as low as 65%. In spherical image alignment, we show that our method robustly estimates rotations even under challenging conditions involving substantial clutter (over 19%) and large rotational offsets. Our results highlight the effectiveness and robustness of our algorithms in realistic, complex scenarios.

Method 1: Spherical Pattern Matching by Correlation (SPMC)

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