Eigenvalue, eigenvector and eigenspace

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…