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After paramater optimization with the extended fit function the same signal is fitted with a line. For both models the corrected Akaike Information Criterion (AICc \cite{Burnham_2004}) is calculated and the region is accepted only if the AICc for the fit function is less than the AICc for the line. This ensures that the goodness of the fit obtained with the fit function justifies the use of a more complicated model.  In order to reconstruct the entire image with all the pixels it is also necessary to know the location of the pixels. The parameter vector \(\mathbf{p}_i\) is extended with the coordinates of pixel *i*:  \[  \mathbf{r}_i = \left[\mathbf{p}_i,x_i,y_i\right]  =\left[A_i, d_i ,\tau_{d,i},\tau_{r,i},\mu_i,x_i,y_i\right] =  \left[\mathbf{p}^s_{i}, \mathbf{p}^p_{i}\right]  \]  , where \(\mathbf{p}^s=\left[A,d,\tau{d},\tau_{r}\right]\) is the shape paramater vector and \(\mathbf{p}^p=\left[\mu,x,y\right]\) is the position parameter vector.   All *k* events detected in pixel *i* are represented by vectors   \(\mathbf{p}^s_{i,k}\) and \(\mathbf{p}^p_{i,k}\). These vectors can be stacked to creat an event matrix for pixel *i*:  \[  E_i =   \left(  \begin{array}{l l}  \mathbf{p}^s_{i,0}&\mathbf{p}^p_{i,k}\\\\  \mathbf{p}^s_{i,1}&\mathbf{p}^p_{i,k}\\\\  \ldots\\\\  \mathbf{p}^s_{i,k}&\mathbf{p}^p_{i,k}  \end{array}  \right)  =  \left(  \begin{array}{l l}  E_i^s & E_i^p  \end{array}  \right)  \]  The event matrix for the entire image is obtained by stacking all pixel event matrices:  \[  E=\left(  \begin{array}{l}  E_0\\\\  E_1\\\\  \vdots\\\\  E_i  \end{array}  \right)  =\left(  \begin{array}{l l}  E_0^s& E_0^p\\\\  E_1^s& E_1^p\\\\  \vdots&\vdots\\\\  E_i^s& E_i^p  \end{array}  \right)  =\left(  \begin{array}{l l}  E^s & E^p  \end{array}  \right)  \]  , where \(E^s\) and \(E^p\) are shape and position submatrices, respectively, containing event shape and position parameters for all events from all pixels and making up the entire image event matrix \(E\). The separation of shape and position parameters for events is necessary in the next clustering step.