Fast Symbolic 3D Registration Solution
This work addresses convergence issues in 3D registration for engineering applications, but it is incremental as it builds on a previous solver.
The paper tackles the problem of 3D registration by proposing a fast symbolic solution to replace traditional numerical methods like SVD or EIG, which suffer from convergence uncertainty, and achieves a 50% to 80% improvement in execution speed without losing accuracy or robustness.
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.