Algorithm 1: Compute FDT

Input: $O=\left(Z^n,{\mu }_O\right)$ Output: an image ($Z^n,\mathsf{\Omega }$) representing FDT of O. 1. For all $pϵ\overline{\mathsf{\Theta }\left(O\right)}$, set $\mathsf{\Omega }\left(p\right)$= 0; 2. For all $pϵ\mathsf{\Theta }\left(O\right)$, set $\mathsf{\Omega }\left(p\right)=\mathrm{MAX}$; 3. For all $pϵ\mathsf{\Theta }\left(O\right)$ such that $N\left(P\right){{\displaystyle \cap }}^{\text{}}\overline{\mathsf{\Theta }\left(O\right)}$ is not empty,   Push $P$ into $Q$; 4. While $Q$ is not empty do 5.    Remove a point $P$ from $Q$; 6.    Find $dis{t}_{min}=mi{n}_{qϵN\left(p\right)}[\mathsf{\Omega }\left(q\right)+w\left(p-q\right)\times \frac{1}{2}({\mu }_o\left(p\right)+\left({\mu }_o\left(q\right)\right]$ 7.    If $dis{t}_{min}<\Omega \left(p\right)$ then 8.        Set $\mathsf{\Omega }\left(p\right)=dis{t}_{min}$ 9.        Push all points $qϵN\left(p\right){{\displaystyle \cap }}^{\text{}}\mathsf{\Theta }\left(O\right)$ into $Q$ 10. Output the FDT image $O$.