Algorithm 2 Random sample consensus robotically actuated delivery sheath localization
Inputs:
$A_c\leftarrow \{{\mathbf{x}}_{c,v|v=1,\dots ,w}\}$   ⊳ Set of detected edge points (${\mathbf{x}}_c$)
$f:H_3\to m_c$   ⊳ Computes the algebraic circle model parameters ($m_c$) from a set ($H_3$) of three randomly selected edge points
$C(m_c,{\mathbf{x}}_c)$   ⊳ Cost function for a single edge point (1 if ${\mathbf{x}}_c$ is an inlier to the algebraic circle parameters ($m_c$), 0 otherwise)
n   ⊳ Number of iterations
Outputs:
$m_c^{*}$   ⊳ Best model parameters
$S_c^{*}$   ⊳ Best consensus set (inliers)
$J_c^{*}$   ⊳ Best cost
Method:
1: for $i\leftarrow 1,n$ do
2: $H_{3,i}\leftarrow \mathrm{random}\_3\mathrm{pnts}(A_c)$   ⊳ (I) Hypothesis
3: $m_c,i\leftarrow f(H_{3,i})$
4: if$\mathrm{suffice}(m_{c,i})$then   ⊳ (II) Preliminary test
5:  $S_c,i\leftarrow \{\forall {\mathbf{x}}_c\in A_c|C(m_{c,i},{\mathbf{x}}_c)=1\}$
6:  $J_c,i\leftarrow \sum _{{\mathbf{x}}_c\in A_c}C(m_{c,i},{\mathbf{x}}_c)$
7:  if$J_c^{*}<J_c,i$then   ⊳ (III) Evaluation
8:   $J_c^{*}\leftarrow J_{c,i}$
9:   $m_c^{*}\leftarrow m_{c,i}$
10:   $S_c^{*}\leftarrow S_{c,i}$
11:  end if
12: end if
13: $i\leftarrow i+1$
14: end for