# Effective scaling registration approach by imposing the emphasis on the scale factor

## TL;DR

This paper introduces a novel scaling registration method that emphasizes the scale factor to avoid ill-posed problems, using a new objective function and an iterative algorithm, demonstrating improved efficiency and robustness in practical applications.

## Contribution

It proposes a new objective function for scaling registration that emphasizes the scale factor, along with an iterative algorithm to improve accuracy and robustness.

## Key findings

- Outperforms previous methods in efficiency and robustness
- Effective in aligning partially overlapping point sets
- Successfully applied to merging grid maps of different resolutions

## Abstract

This paper proposes an effective approach for the scaling registration of $m$-D point sets. Different from the rigid transformation, the scaling registration can not be formulated into the common least square function due to the ill-posed problem caused by the scale factor. Therefore, this paper designs a novel objective function for the scaling registration problem. The appearance of this objective function is a rational fraction, where the numerator item is the least square error and the denominator item is the square of the scale factor. By imposing the emphasis on scale factor, the ill-posed problem can be avoided in the scaling registration. Subsequently, the new objective function can be solved by the proposed scaling iterative closest point (ICP) algorithm, which can obtain the optimal scaling transformation. For the practical applications, the scaling ICP algorithm is further extended to align partially overlapping point sets. Finally, the proposed approach is tested on public data sets and applied to merging grid maps of different resolutions. Experimental results demonstrate its superiority over previous approaches on efficiency and robustness.