Algorithm 4 WASM (ASM)

while Until convergence do

${\mathbf{y}}^{\left(k\right)}\leftarrow {\tilde{\mathbf{y}}}^{\left(k\right)}$; calculate a candidate shape by examining the neighboring region of each of the landmark points.

${\tilde{\mathbf{y}}}^{(k+1)}\leftarrow \mathbf{y}\left(k\right)$; given y(k), calcuate ${\tilde{\mathbf{y}}}^{(k+1)}$ by minimizing $\Vert {\tilde{\mathbf{y}}}^{(k+1)}-{\mathbf{y}}^{\left(k\right)}\Vert$ using Algorithm 3 (for WASM) or Algorithm 2 (for ASM).

end while