Algorithm 2 Frontier cell detection

Require:   $gridmap=\left\{cell\left(i,j\right)\left|1\le i\le RowSize,1\le j\le ColSize\right.\right\}$, $window\_size$

Ensure:   $gridmap\_frontier$

1: function Detect-Frontier-Cell($gridmap$, $window\_size$)

2:     set $gridmap\_empty=\left\{empty\left(i,j\right)\left|empty\left(i,j\right)=0,1\le i\le RowSize,1\le j\le ColSize\right.\right\}$

3:     set $gridmap\_frontier=\left\{frontier\left(i,j\right)\left|frontier\left(i,j\right)=0,1\le i\le RowSize,1\le j\le ColSize\right.\right\}$

4:    for all $cell\left(i,j\right)$ do

5:        if $cell\left(i,j\right)<t{h}_{\mathrm{empty}}$ then

6:           $empty\left(i,j\right)\leftarrow 1$

7:        end if

8:    end for

9:    $gridmap\_empty\_close\leftarrow \mathrm{image}\_\mathrm{morph}\_\mathrm{close}\left(gridmap\_empty,wdw\_close\right)$

10:    $gridmap\_empty\_erosion\leftarrow \mathrm{image}\_\mathrm{morph}\_\mathrm{erosion}\left(gridmap\_empty,wdw\_erosion\right)$

11:    $gridmap\_empty\_edge\leftarrow gridmap\_empty\_close-gridmap\_empty\_erosion$

12:    for all $grid\_empty\_edge\left(i,j\right)\in gridmap\_empty\_edge$ do

13:        if $grid\_empty\_edge\left(i,j\right)=1$ then

14:           $frontier\left(i,j\right)$←Inspect-Safe-Frontier-Cell$\left({\left[i,j\right]}^T,window\_size,gridmap\right)$

15:        end if

16:    end for

17:    return $gridmap\_frontier$

18: end function