Algorithm 2 Improved slope-constrained RANSAC algorithm with early termination

Require: Current frame laser stripe point set P, previous slope $m_{\mathrm{prev}}$,

1:            max iterations K, distance threshold $\tau$,

2:            slope tolerance $\delta$, consecutive patience N

Ensure: Optimal line model $(a^{*},b^{*})$, inlier set ${\mathcal{I}}^{*}$

3: Initialize best inliers: ${\mathcal{I}}^{*}\leftarrow ⌀$

4: Initialize optimal model: $(a^{*},b^{*})\leftarrow (0,0)$

5: Iteration counter: $k\leftarrow 0$

6: No improvement counter: $\mathit{no}\_\mathit{improve}\leftarrow 0$

7: while  $k<K$  and  $\mathit{no}\_\mathit{improve}<N$   do

8:     $k\leftarrow k+1$

9:     repeat

10:            Randomly select two distinct points $p_1(x_1,y_1),p_2(x_2,y_2)\in P$

11:            Compute slope: $m_{\mathrm{curr}}\leftarrow {\displaystyle \frac{y_2-y_1}{x_2-x_1+ϵ}}$

12:     until $|m_{\mathrm{curr}}-m_{\mathrm{prev}}|<\delta$

13:     Construct line model: $a\leftarrow m_{\mathrm{curr}},b\leftarrow y_1-a{x}_1$

14:     Temporary inlier set: $\mathcal{I}\leftarrow ⌀$

15:     for each point $p(x,y)\in P$ do

16:            Distance: $d\leftarrow {\displaystyle \frac{|ax-y+b|}{\sqrt{a^2+1}}}$

17:            if $d<\tau$ then

18:                $\mathcal{I}\leftarrow \mathcal{I}\cup \{p\}$

19:            end if

20:     end for

21:     if $|\mathcal{I}|>|{\mathcal{I}}^{*}|$ then

22:           ${\mathcal{I}}^{*}\leftarrow \mathcal{I}$

23:            $(a^{*},b^{*})\leftarrow (a,b)$

24:            $\mathit{no}\_\mathit{improve}\leftarrow 0$

25:     else

26:            $\mathit{no}\_\mathit{improve}\leftarrow \mathit{no}\_\mathit{improve}+1$

27:     end if

28: end while

29: return $(a^{*},b^{*}),{\mathcal{I}}^{*}$