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In this work, we propose to directly find the one-step solution for the pointset registration problem without correspondences. Inspired by the KernelCorrelation method, we consider the fully connected objective function betweentwo point sets, thus avoiding the computation of correspondences. By utilizingleast square minimization, the transformed objective function is directlysolved with existing well-known closed-form solutions, e.g., singular valuedecomposition, that is usually used for given correspondences. However, usingequal weights of costs for each connection will degenerate the solution due tothe large influence of distant pairs. Thus, we additionally set a scale on eachterm to avoid high costs on non-important pairs. As in feature-basedregistration methods, the similarity between descriptors of points determinesthe scaling weight. Given the weights, we get a one step solution. As theruntime is in $\mathcal O (n^2)$, we also propose a variant with keypoints thatstrongly reduces the cost. The experiments show that the proposed method givesa one-step solution without an initial guess. Our method exhibits competitiveoutlier robustness and accuracy, compared to various other methods, and it ismore stable in case of large rotations. Additionally, our one-step solutionachieves a performance on-par with the state-of-the-art feature based methodTEASER.

Non-iterative One-step Solution for Point Set Registration Problem on Pose Estimation without Correspondence