Fast Symbolic 3D Registration Solution

TL;DR

This paper introduces a fast, symbolic 3D registration method that improves computational speed significantly over traditional SVD/EIG-based approaches without sacrificing accuracy or robustness.

Contribution

A novel symbolic solution for 3D registration that simplifies computation and enhances speed by 50-80% compared to existing numerical algorithms.

Findings

Achieves 50-80% faster computation speed

Maintains accuracy and robustness of registration

Effective on both personal computers and embedded processors

Abstract

3D registration has always been performed invoking singular value decomposition (SVD) or eigenvalue decomposition (EIG) in real engineering practices. However, these numerical algorithms suffer from uncertainty of convergence in many cases. A novel fast symbolic solution is proposed in this paper by following our recent publication in this journal. The equivalence analysis shows that our previous solver can be converted to deal with the 3D registration problem. Rather, the computation procedure is studied for further simplification of computing without complex-number support. Experimental results show that the proposed solver does not loose accuracy and robustness but improves the execution speed to a large extent by almost %50 to %80, on both personal computer and embedded processor.