Eq.\ref{Bi} is a projection of the attribute vector $I_i$ in the eigenspace spanned by the first $k_c$ eigenbackgrounds, being $\textbf{b}$ the coefficient vector of the combination. In the standard EIG method the number of eigenbackgrounds retained $k_c$ is chosen by fixing a threshold for the last eigenvalue $\lambda_{k_c}$ retained. The background obtained $B_i$ are then subtracted to the original image and a moving object is identified as the regions of the images in which $I_i-B_i$ is larger than a given threshold.
\\In this work the technique was customized for the detection of the moving membrane. At the scope, the backgrounds are constructed considering only the time varying part, $B_i=\Phi_{k_c} \, \textbf{b}$, having rank $k_c$ computed from the distribution of energy …show more content…
the percentage of rank retained. The criteria to select the cut-off rank $k_{c}$ is based on the observation that $\delta(\hat{k})$ tends to be linear as the contributes of each eigenbackgrounds tend to be equal, i.e. for a fairly uncorrelated noise. Fig.\ref{Sigma_FIG}.b shows the cut-off rank obtained by imposing a tolerance on the second derivative $d^2 \delta/ d \hat{k}^2<10^-3$. For the examples in Fig.\ref{Snap}, this criteria gives $k=23$ for the $PIV$ sequence, $k=35$ for the $IPT$ sequence, showing that the former is more easily compressed than the latter. Fig.\ref{Sigma_FIG}.b shows the background images $B_i$ corresponding to these examples. Remarkably, the decomposition proposed is able to detect the membrane motion in the PIV images using only the two matrix multiplications in eq.\ref{Bi}. On the other hand, the method is not equally effective with the FV video, as a large portion of the flow also shows a high spatial and temporal coherence. Refining the decomposition to remove these portions is the purpose of the HIGL routine that
\\In this work the technique was customized for the detection of the moving membrane. At the scope, the backgrounds are constructed considering only the time varying part, $B_i=\Phi_{k_c} \, \textbf{b}$, having rank $k_c$ computed from the distribution of energy …show more content…
the percentage of rank retained. The criteria to select the cut-off rank $k_{c}$ is based on the observation that $\delta(\hat{k})$ tends to be linear as the contributes of each eigenbackgrounds tend to be equal, i.e. for a fairly uncorrelated noise. Fig.\ref{Sigma_FIG}.b shows the cut-off rank obtained by imposing a tolerance on the second derivative $d^2 \delta/ d \hat{k}^2<10^-3$. For the examples in Fig.\ref{Snap}, this criteria gives $k=23$ for the $PIV$ sequence, $k=35$ for the $IPT$ sequence, showing that the former is more easily compressed than the latter. Fig.\ref{Sigma_FIG}.b shows the background images $B_i$ corresponding to these examples. Remarkably, the decomposition proposed is able to detect the membrane motion in the PIV images using only the two matrix multiplications in eq.\ref{Bi}. On the other hand, the method is not equally effective with the FV video, as a large portion of the flow also shows a high spatial and temporal coherence. Refining the decomposition to remove these portions is the purpose of the HIGL routine that