Algorithm 1 False matches rejection combining depth information + RANSAC

Input: $\mathrm{D}=\{p_j^i|1\le i\le N,1\le j\le M\}$: feature matches set in image space; $\mathrm{C}=\{q_j^i|1\le i\le N,1\le j\le M\}$: 3D points corresponding to feature matches; $d_{XYZ}$: distance threshold in object space for RANSAC iterations; $d_{uv}$: distance threshold in image space

Output: number of inliers: n2DInlier, Inliers: F = $\{p{\prime }_j^i|1\le i\le N,1\le j\le M\}$

1. $\mathrm{F}=\varnothing$

2. For i = 1→n do

3.  Iterations = 0, $n3DInlie{r}_{max}=0$, G = $\varnothing$

4.  While Iterations <= MaxIterations do

5.   n3DInlier = 0

6.   Randomly select 5 feature points in current feature matches from $q^i$, compute the mean value of 3D coordinates $q{\prime }^i$

7.   For $q^i\in \left\{q^i\right\}$ do

8.    If $\parallel q^i-q^{\prime i}\parallel$ < $R.E{.}_{XYZ}$ then

9.      n3DInlier = n3DInlier + 1

10.     $3\mathrm{DInliers}=3\mathrm{DInliers}{{\displaystyle \cup }}^{\text{}}\left\{q^i\right\}$

11.     End if

12.   End for

13.   If n3DInlier > $n3DInlie{r}_{max}$ then

14.    $n3DInlie{r}_{max}=$n3DInlier

15.    $\mathrm{G}=3\mathrm{DInliers}$

16.   End if

17.  End while

18.  $q^{\prime i}=\frac{{{\displaystyle \sum }}_{n=0}^{n3DInlie{r}_{max}}{G}^n}{n3DInlie{r}_{max}}$

19.  n2DInlier = 0, $\mathrm{f}=\varnothing$

20.  For j = 1→m do

21.   Let $q^{\prime i}$ backproject to j-th Frame, obtain the backprojected image point $p{1}_j^i$

22.   If $\parallel p_j^i-p{1}_j^i\parallel$ < $R.E{.}_{uv}$ then

23.    $\mathrm{f}=\mathrm{f}{{\displaystyle \cup }}^{\text{}}{p}_j^i$

24.    $\mathrm{n}2\mathrm{DInlier}=\mathrm{n}2\mathrm{DInlier}+1$

25.   End if

26.  End for

27.  If $\mathrm{n}2\mathrm{DInlier}\ge 3$ then

28.   $\mathrm{F}=\mathrm{F}{{\displaystyle \cup }}^{\text{}}\mathrm{f}$

29.  End if

30. End for

31. Return $\mathrm{n}2\mathrm{DInlier},\mathrm{F}$