In this paper, the $\u2202\phi /\u2202t$ is approximated by the forward difference, and the $\u2207\phi $ is approximated by the central difference. The approximation of Eq. (20) for the smoothing component $um$ can be simply written as Display Formula
$\phi i,jk+1\u2212\phi i,jk\Delta t=\mu [\Delta (\phi i,jk)\u2212div(\u2207\phi i,jk|\u2207\phi i,jk|)]+\lambda \delta a(\phi i,jk)div(gi,jm\u2207\phi i,jk|\u2207\phi i,jk|)+\nu gi,jm\delta a(\phi i,jk),$(22)
where, $\Delta t$ is the time step, and $gi,jm$ is edge indicator function of the smoothing component $um$. $um$ is calculated by the fixed-point iteration algorithm Display Formula$ui,jm=1\tau m+\u2211p\u2208\Lambda 0\omega m(p)[\u2211p\u2208\Lambda 0\omega m(p)um\u22121(p)+\tau mu0(i,j)].$(23)
For Eq. (23), the smoothing component converges to the mean of the initial image without constraint conditions, which leads to the difference between the features of the object and the surrounding region not being significant. To avoid this phenomenon, we present the confidence level of segmented subregions on two adjacent iterations of the smoothing component, which is defined as following: Display Formula$Pr=card(Am\u2229Am\u22121)max[card(Am),card(Am\u22121)].$(24)
Here the set $Am$ and $Am\u22121$ represent the segmented subregions $[(x,y)|\phi (x,y)\u22640]$ for the smoothing component $um$ and $um\u22121$, respectively. When the confidence level satisfies the following condition, the smooth is terminated: Display Formula$Pr\u2265T,$(25)
where $T$ is the threshold of the regional confidence level.