2020/03/01 by Yijun Yuan, Dorit Borrmann, Yuan, Yijun +5 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Image and Video Retrieval Techniques #Algorithm #Artificial intelligence #Combinatorics #Computation #Computer science #FOS: Computer and information sciences #Geometry #Image (mathematics) #Kernel (algebra) #Mathematical optimization #Mathematics #Outlier #Robotic Path Planning Algorithms #Robotics (cs.RO) #Robotics and Sensor-Based Localization #Robustness (evolution) #Scaling #Similarity (geometry) #Singular value decomposition #cs.RO
paper · pdf · doi:10.48550/arxiv.2003.00457
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2020/03/01 · openalex created_date 2020/03/06 · arxiv created 2020/07/11 · arxiv updated 2020/07/14 · openalex updated_date 2026/07/28
In this work, we propose to directly find the one-step solution for the point set registration problem without correspondences. Inspired by the Kernel Correlation method, we consider the fully connected objective function between two point sets, thus avoiding the computation of correspondences. By utilizing least square minimization, the transformed objective function is directly solved with existing well-known closed-form solutions, e.g., singular value decomposition, that is usually used for given correspondences. However, using equal weights of costs for each connection will degenerate the solution due to the large influence of distant pairs. Thus, we additionally set a scale on each term to avoid high costs on non-important pairs. As in feature-based registration methods, the similarity between descriptors of points determines the scaling weight. Given the weights, we get a one step solution. As the runtime is in \mathcal O (n2), we also propose a variant with keypoints that strongly reduces the cost. The experiments show that the proposed method gives a one-step solution without an initial guess. Our method exhibits competitive outlier robustness and accuracy, compared to various other methods, and it is more stable in case of large rotations. Additionally, our one-step solution achieves a performance on-par with the state-of-the-art feature based method TEASER.