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Ardo Illaste edited res_fitting2.md
almost 10 years ago
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####Shape and location parameters
Each pixel event is characterized by the parameters \(\mathbf{r}\). Four of these (\(A,d,\tau_{d},\tau_{r})\) determine the shape of the event and \(\mu\) the location in time. In order to completely charactarize a pixel event it is also necessary to know the pixel's spatial location. This would require one or two spatial coordinates, respectively for line- or framescans. Hence, a pixel event is wholly defined by two vectors: the shape parameter vector \(\mathbf{p}^s=\left[A,d,\tau_{d},\tau_{r}\right]\) and the position parameter vector
\(\mathbf{p}^p_i=\left[\mu,x,y\right]\). \(\mathbf{p}^p=\left[\mu,x,y\right]\).
The *k*-th event detected in pixel *i* is represented by vectors
\(\mathbf{p}^s_{i,k}\) and \(\mathbf{p}^p_{i,k}\). These vectors can be stacked to create an event matrix (E) for pixel *i*: