Three-component finite element model (3C-FEM)

[5] gives a finite-element model based on three tissue types, labelled rigid, deformable and `fluid'. The deformations are driven by user-supplied landmark displacements and deformations of the deformable regions are constrained by three energy terms:

$$\begin{eqnarray*}E_{\mbox{tension}}(N_i,N_j) & = & \left\vert N_j - N_i - N^0_{i... ... \gamma \\ 2 & \mbox{\hspace{2ex} otherwise} \end{array}\right. \end{eqnarray*}$$

where N⁰_ij is the original distance between the nodes N_i and N_jand the nodes N_i, N_j and N_k are collinear before deformation; nodes N_k, N_l and N_m form a triangle with initial area A₀ and deformed area A and $\gamma$ is a threshold of triangular area reduction. The `fluid' deformations are constrained only by $E_{\mbox{fold}}$ which prevents folding of the image. Rigid regions are obtained by prohibiting the updating of their nodal displacements.