Algorithm 6 Base Invariant Wavelet Active Shape Model (BIWASM)

$({\tilde{\mathbf{y}}}^{\left(0\right)},{\mathcal{T}}_b,{\mathbf{w}}_{-1,b})\leftarrow ({\mathbf{y}}_b,{\mathbf{P}}_{-1},{\stackrel{‒}{\mathbf{w}}}_{-1})$; use Algorithm 5 to calculate the initial shape, the transformation, and scaling coefficients at the coarest scale.

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, and the corresponding control landmark points in y(k) are replaced with Sb.

${\mathbf{x}}^{\prime }\leftarrow {\mathcal{T}}_b^{-1}\left({\mathbf{y}}^{\left(k\right)}\right)$; calculate inverse transformatoin of y(k)

${\mathbf{w}}_l\leftarrow \mathcal{W}\left({\mathbf{x}}^{\prime }\right)$; DSWT.

${\mathbf{b}}_l\leftarrow {\mathbf{P}}_l^T({\mathbf{w}}_l-{\stackrel{‒}{\mathbf{w}}}_l),l\ge 0$; calculate the shape parameter fitting wl using (19).

Apply the constraints on bl, l ≥ 0 using (6)

${\mathbf{w}}_l\leftarrow {\stackrel{‒}{\mathbf{w}}}_l+{\mathbf{Pb}}_l,l\ge 0$; generate wavelet coefficients using (17)

$\mathbf{x}\leftarrow {\mathcal{W}}^{-1}({\mathbf{w}}_{-1,b}\cup \{{\mathbf{w}}_l,l\ge 0\left\}\right)$; inverse DSWT.

${\tilde{\mathbf{y}}}^{(k+1)}\leftarrow {\mathcal{T}}_b\left(\mathbf{x}\right)$

end while