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$ \phi _{\beta }$ for MRF prior


$\displaystyle \phi_{\beta}\vert.$ $\displaystyle \sim$ $\displaystyle G
\left(
\frac{N_{L}}{2}+\tilde{a}_{\beta},
\right.$  
    $\displaystyle \left.
\frac{1}{4}\sum_{L_{ij}} \sum_{L_{k\ell}\in{\cal
N}_{L_{ij}}}
\left(
(\beta_{ij}-\beta_{k\ell})^2
\right)
+\tilde{b}_{\beta}
\right)$ (39)

where $ N_L$ is the total number of links between voxels.