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

TL;DR

This paper introduces a direct, one-step point set registration method that avoids correspondence computation, using a kernel correlation-inspired objective and weighted least squares, achieving competitive accuracy and robustness with reduced runtime.

Contribution

The authors propose a novel one-step registration approach that bypasses correspondence estimation, utilizing a weighted least squares solution inspired by kernel correlation, with a variant for efficiency.

Findings

Achieves accurate registration without initial guesses.

Demonstrates robustness to outliers and large rotations.

Performs comparably to state-of-the-art methods like TEASER.

Abstract

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.