Algorithm 2 A simple algorithm of calculating suboptimal $\mathcal{T}$ and b by minimizing (5) and incorporating shape contraints.

b ← 0

while Until convergence do

$\mathbf{x}\leftarrow \stackrel{‒}{\mathbf{x}}+\mathbf{Pb}$; generate a shape in the model space using (2).

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.

$\mathbf{b}\leftarrow {\mathbf{P}}^T({\mathbf{x}}^{\prime }-\stackrel{‒}{\mathbf{x}})$; calculate the shape parameters fitting x′ using (3).

Apply shape constraints on b using (6)

end while