Algorithm 2 Global Scale Recovery for RGB images + Pau Ta Norm and RANSAC

Input: $P_C=\left\{P^i|1\le i\le N\right\}$: 3D points from RGB images; $P_D=\left\{P^{\prime i}|1\le i\le N\right\}$: 3D points from depth images

Output: S

1. $F_s=\varnothing$

2. For i = 1→$\frac{\left[N\times \left(N-1\right)\right]}{2}$ do

3.  Randomly select 2 points from $P_C,P_D$, compute scale value S

4.  $F_s=F_s{{\displaystyle \cup }}^{\text{}}S$

5. End for

6. Compute the mean value $\overline{S}$ and the root-mean-square error $\mathsf{\sigma }$

7. $nInlie{r}_{max}=0,$ S = 0

8. While Iterations <= MaxIterations do

9.   $\mathrm{nInlier}=0$, $F{\prime }_s=\varnothing$

10.  Randomly select 5 scale values from $F_s$, compute the mean value $S_c$

11.  For i = 1→$\frac{\left[N\times \left(N-1\right)\right]}{2}$ do

12.   If $\left|S_c-\overline{S}\right|<3\sigma$ then

13.    nInlier = nInlier + 1

14.    $F{\prime }_s=F{\prime }_s{{\displaystyle \cup }}^{\text{}}{S}_c$

15.   End if

16.  End for

17.  If nInlier > $n3DInlie{r}_{max}$ then

18.   $nInlie{r}_{max}=$nInlier

19.   $S=\frac{{{\displaystyle \sum }}_{n=0}^{{\mathrm{nInlier}}_{max}}F{\prime }_s^n}{nInlie{r}_{max}}$

20.  End if

21. End while

22. Return $S$