Algorithm 1 Wall Boundary extraction

Input: Lebeled wall point cloud:{$P_0$} Distance threshold to remove the point cloud: $T_{d1}$ Distance threshold to filter the plane: $T_{d2}$ Angle threshold to filter the plane: $T_a$ Distance threshold to reserve the point cloud: $T_{d3}$ Percentage threshold to end the loop: $T_p$

Output: 2D Wall Lines in floor plane: $\mathbb{L}$

1: initialize: remaining point cloud:{$P_r$} = {$P_0$} 2: while $C\left(\left\{P_r\right\}\right)< C\left(\left\{P_0\right\}\ast T_p\right)$ do 3:    Plane candidate: $p_c=F\left(\left\{P_r\right\}\right)$ 4:    if $\mathbb{L}$ is empty then 5:       add $Proj\left(p_c\right)$ to $\mathbb{L}$ 6:       Distance between points and plane: $\mathbb{D}\mathbb{P}= D_1\left(\left\{P_r\right\}\right)$ 7:       Distance between points and line in floor plane: $\mathbb{D}\mathbb{F}=D_2\left(Proj\left(p_c\right), \left\{P_r\right\}\right)$ 8:       for $i=1, i\le C\left(\left\{P_r\right\}\right), i++$do 9:          if $\mathbb{D}{\mathbb{P}}_i$ < $T_{d1}$ and $\mathbb{D}{\mathbb{F}}_i$ < $T_{d3}$ then 10:           add ${\left\{P_r\right\}}_i$ to ready to remove set $\left\{P_m\right\}$ 11:         end if 12:       end for 13:   else 14:       for $j=1, j\le length\left(\mathbb{L}\right), j++$ do 15:         Distance between planes: $d_p=Dis\left(p_c, {\mathbb{L}}_j\right)$ 16:         Angle between planes: $a_p=Ang\left(p_c, {\mathbb{L}}_j\right)$ 17:         if $d_p< T_{d2}$ and $a_p< T_a$ then 18:           Continue 19:         end if 20:       end for 21:       if $j==length\left(\mathbb{L}\right)$ then 22:         add $Proj\left(p_c\right)$ to $\mathbb{L}$ 23:         Distance between points and plane: $\mathbb{D}\mathbb{P}= D_1\left(\left\{P_r\right\}\right)$ 24:         Distance between points and line in floor plane: $\mathbb{D}\mathbb{F}=D_2\left(Proj\left(p_c\right), \left\{P_r\right\}\right)$ 25:         for $i=1, i\le C\left(\left\{P_r\right\}\right), i++$do 26:          if $\mathbb{D}{\mathbb{P}}_i$ < $T_{d1}$ and $\mathbb{D}{\mathbb{F}}_i$ < $T_{d3}$ then 27:             add ${\left\{P_r\right\}}_i$ to ready to remove set $\left\{P_m\right\}$ 28:          end if 29:         end for 30:      end if 31:   end if 32:   remove point from $\left\{P_r\right\}$: $\left\{P_r\right\}= \left\{P_r\right\}-\left\{P_m\right\}$ 33: end while 34: Return: $\mathbb{L}$