Algorithm 2 Inlier Segmentation

1: Divide ${\tilde{X}}^I$ into $\tilde{m}$ sub-regions $\tilde{D}=\left\{{\tilde{d}}^1,{\tilde{d}}^2,\cdots ,{\tilde{d}}^{\tilde{m}}\right\}$ by Euclidean space distance of the points, and initialize

inlier cluster ${\tilde{C}}^O=\cancel{0}$;

2: Conduct random sampling on each sub-region and generate hypotheses $\tilde{H}$;

3: Calculate the permutation preference matrix $P$;

4: Calculate the Spearman footrule distance matrix $F$ for the permutation preferences of points $i$ and $j$

Equation (5);

5: Conduct linkage clustering with distance $F$ and obtain clusters $\tilde{C}=\left\{{\tilde{c}}^1,{\tilde{c}}^2,\cdots ,{\tilde{c}}^{\tilde{n}}\right\}$

6: If $\widehat{C}==\tilde{C}$, return $\tilde{C}$ as the inlier segmentation result; else $\widehat{C}=\tilde{C}$, $\tilde{D}=\tilde{C}$, and return to step 2.