  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.
