Algorithm 3 A similar algorithm analogous to Algorithm 2 when WDM is used.

bl ← 0

while Until convergence do

${\mathbf{w}}_l\leftarrow {\stackrel{‒}{\mathbf{w}}}_l+{\mathbf{Pb}}_l$; generate wavelet coefficients in the model space using (17).

$\mathbf{x}\leftarrow {\mathcal{W}}^{-1}\left({\mathbf{w}}_l\right)$; Calculate inverse DSWT of wl.

Calculate $\mathcal{T}$ by minimizing ${\Vert \mathbf{y}-\mathcal{T}\left(\mathbf{x}\right)\Vert }^2$ using [35]

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

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

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

Apply shape constraints on bl analogous to (6)

end while