Fast Rigid 3D Registration Solution: A Simple Method Free of SVD and Eigen-Decomposition

TL;DR

This paper introduces a fast, robust 3D rigid registration method that avoids complex matrix decompositions, enabling efficient implementation on embedded systems with verified high accuracy and significantly reduced computation time.

Contribution

The proposed algorithm simplifies 3D registration by eliminating the need for SVD and eigen-decomposition, providing a faster and easier-to-implement solution.

Findings

Achieves 60-80% reduction in computation time compared to existing methods.

Demonstrates robustness and accuracy on noise-corrupted point clouds.

Successfully applied to real-world robotic navigation tasks.

Abstract

A novel solution is obtained to solve the rigid 3D registration problem, motivated by previous eigen-decomposition approaches. Different from existing solvers, the proposed algorithm does not require sophisticated matrix operations e.g. singular value decomposition or eigenvalue decomposition. Instead, the optimal eigenvector of the point cross-covariance matrix can be computed within several iterations. It is also proven that the optimal rotation matrix can be directly computed for cases without need of quaternion. The simple framework provides very easy approach of integer-implementation on embedded platforms. Simulations on noise-corrupted point clouds have verified the robustness and computation speed of the proposed method. The final results indicate that the proposed algorithm is accurate, robust and owns over $60\% \sim 80\%$ less computation time than representatives. It has also been applied to real-world applications for faster relative robotic navigation.