  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 $\mathcal O (n^2)$, 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.
