対応不要で高速かつロバストな球面点パターン位置合わせ
Correspondence-Free Fast and Robust Spherical Point Pattern Registration
球面上の点パターン間の回転推定を、離散点集合の位置合わせ問題（Wahba問題）として再定式化し、線形時間で動作する3つのアルゴリズムを提案した。外れ値がある場合でも従来手法より10倍以上高速かつ高精度であることを示した。
詳しい要約
1. どんなもの？
2. 先行研究と比べてどこがすごい？
3. 技術・手法の肝は？
4. どうやって有効だと検証した？
5. 議論はある？
6. 次に読むべき論文は？
※ AIが要旨から生成した要約です。正確性は原文をご確認ください。
著者: Anik Sarker, Alan T. Asbeck
分類: cs.CV, cs.RO
原文アブストラクト
Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities greater than cubic $O(n^3)$ with respect to rotation space discretization and lack extensive evaluation under significant outlier contamination. To this end, we propose a rotation estimation algorithm between two spherical patterns with linear time complexity $O(n)$. Unlike existing spherical-function-based methods, we explicitly represent spherical patterns as discrete 3D point sets on the unit sphere, reformulating rotation estimation as a spherical point-set alignment (i.e., Wahba problem for 3D unit vectors). Given the geometric nature of our formulation, our spherical pattern alignment algorithm naturally aligns with the Wahba problem framework for 3D unit vectors. Specifically, we introduce three novel algorithms: (1) SPMC (Spherical Pattern Matching by Correlation), (2) FRS (Fast Rotation Search), and (3) a hybrid approach (SPMC+FRS) that combines the advantages of the previous two methods. Our experiments demonstrate that in the $\mathbb{S}^2$ domain and in correspondence-free settings, our algorithms are over 10x faster and over 10x more accurate than current state-of-the-art methods for the Wahba problem with outliers. We validate our approach through extensive simulations on a new dataset of spherical patterns, the ``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.
