A Minimal Spanning Tree algorithm for source detection in γ-ray images

We developed a source detection algorithm based on the Minimal Spanning Tree (MST), that is a graph-theoretical method useful for finding clusters in a given set of points. This algorithm is applied to gamma-ray bi-dimensional images where the points correspond to the arrival direction of photons, and the possible sources are associated with the regions where they clusterize. Some filters to select these clusters and to reduce the spurious detections are introduced. An empirical study of the statistical properties of MST on random fields is carried out in order to derive some criteria to estimate the best filter values. We also introduce two parameters useful to verify the goodness of candidate sources. To show how the MST algorithm works in practice, we present an application to an EGRET observation of the Virgo field, at high Galactic latitude and with a low and rather uniform background, in which several sources are detected.