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

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 full 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 the high cost on non-important pairs. As in feature-based registration methods, the similarity between descriptors of points determines the scaling weight. Given the weights we yield a one step solution. As the runtime is in $\mathcal O (n^2)$, we also propose a variant with keypoints that strongly reduce the cost. The experiments show, that our proposed method gives a one-step solution without an initial guess. Our method exhibits competitive outliers robustness, accuracy compared with various methods. And it is more stable to large rotation. In addition, though feature based algorithms are more sensitive to noise, Our method still provide better result compared with the feature match initialized ICP.