Algorithm 1: Improved FCM

Input: Gray level image Output: Segmented image

➢Set the number of intensity levels and compute a square matrix; I = $\sum \sum \mathbf{G}\left({\mathbf{p}}_{\mathbf{i}},{\mathbf{q}}_{\mathbf{j}}\right)$, and the image matrix G = $\sum \sum \mathbf{G}\left({\mathbf{p}}_{\mathbf{k}},{\mathbf{q}}_{\mathbf{l}}\right)$ ➢Initialize ${\mathit{F}}_{\mathit{x}\mathit{y}}$ = $\mathit{G}\oplus \mathit{I}$ ➢Extract coarse features from ${\mathit{F}}_{\mathit{x}\mathit{y}}$ ➢Segment the brain image ${\mathit{G}}_1$ = $\frac{1}{2}{\sum }_{\mathit{k}=1}^{\mathit{m}}{\sum }_{\mathit{l}=1}^{\mathit{n}}{\mathit{G}}_{\mathit{k}\mathit{l}}{‖{\mathit{p}}_{\mathit{k}}-{\mathit{a}}_{\mathit{l}}‖}^2\ast {\sum }_{\mathit{k}=1+1}^{\mathit{X}}{\sum }_{\mathit{l}=1+1}^{\mathit{Y}}\mathit{T}{‖{\mathit{p}}_{\mathit{k}},{\mathit{q}}_{\mathit{l}}‖}^2$ ➢Repeat until ${\mathit{F}}_{\mathit{x}\mathit{y}}\le {\sum }_{\mathit{i}=1}^{\mathit{H}}{\sum }_{\mathit{j}=1}^{\mathit{z}}[{\mathit{F}}_{\mathit{x}\mathit{y}}\left(\mathit{i}\right)-{\mathit{F}}_{\mathit{x}\mathit{y}}(\mathit{j}\left)\right]$ ➢Update ${\mathit{G}}_1$ ➢Initialize cluster centroid ➢Define membership function ${\mathit{s}}_{\mathit{k}\mathit{l}}^{\left(0\right)}$ of the FCM ➢Update cluster center ${\mathit{T}}_{\mathit{k}}^{\left(\mathit{v}\right)}\iff {\mathit{s}}_{\mathit{k}\mathit{l}}^{\left(\mathit{v}\right)}$, (k = 1,2,… and v = 1,2,3) Update D(${\mathit{p}}_{\mathit{k}}$, ${\mathit{\delta }}_{\mathit{k}}^{\left(\mathit{v}\right)}$) $\iff {\mathit{\delta }}_{\mathit{k}}^{\mathit{v}}$ and ${\mathit{s}}_{\mathit{k}\mathit{l}}$ ➢With c(${\mathit{p}}_{\mathit{k}}$, ${\mathit{\delta }}_{\mathit{k}}^{\left(\mathit{v}\right)}$) until ||${\mathit{s}}_{\mathit{k}\mathit{l}}^{\left(\mathit{v}\right)}-{\mathit{s}}_{\mathit{k}\mathit{l}}^{\left(\mathit{v}+1\right)}$|| $\le \in$, $\in =\left[\mathbf{0},\mathbf{1}\right]$