Let us consider the $k$‘th ROI $Fk$ which has been wrongly aligned to a phase-specific template at time $t$; in other words, the motion parameter $m^k,t$ has been wrongly estimated so that the $t$’th volume should be rejected as a volume outlier by setting the missingness as $gt=1$. Let $qk,0\u2208Fk$ be a voxel with fixed coordinates inside the $k$‘th ROI of the template (‘0’ denotes a template volume), and let $qk,t$ be the actual location at time $t$ corresponding to the voxel $qk,0$. The volume misalignment leads to the spatial mismatch between $qk,0$ and $qk,t$. For the sake of simplicity, the rotational components of volume misalignment are considered negligible. The geometric distance $nk,t$ between two positions is then equivalent to the measurement error of object motion; that is, $nk,t=qk,t\u2212qk,0=mk,t\u2212m^k,t$. As a result, the actual area of the ROI at time $t$ is updated as $Fk,t\u2261{qk,t|qk,t=qk,0+nk,t,qk,0\u2208Fk}$, and consequently the background at time $t$ would be given as $Bk,t\u2261U\u2212Fk,t$ where $U$ is a set of whole voxels. Finally, the volume misalignment leads to the spatial mismatch between $Fk$ and $Fk,t$ as illustrated in Fig. 4.