  The Density Based Spatial Clustering of Applications with Noise (DBSCAN) is a
topometric algorithm used to cluster spatial data that are affected by
background noise. For the first time, we propose the use of this method for the
detection of sources in gamma-ray astrophysical images obtained from the
Fermi-LAT data, where each point corresponds to the arrival direction of a
photon. We investigate the detection performance of the gamma-ray DBSCAN in
terms of detection efficiency and rejection of spurious clusters, using a
parametric approach, and exploring a large volume of the gamma-ray DBSCAN
parameter space. By means of simulated data we statistically characterize the
gamma-ray DBSCAN, finding signatures that differentiate purely random fields,
from fields with sources. We define a significance level for the detected
clusters, and we successfully test this significance with our simulated data.
We apply the method to real data, and we find an excellent agreement with the
results obtained with simulated data. We find that the gamma-ray DBSCAN can be
successfully used in the detection of clusters in gamma-ray data. The
significance returned by our algorithm is strongly correlated with that
provided by the Maximum Likelihood analysis with standard Fermi-LAT software,
and can be used to safely remove spurious clusters. The positional accuracy of
the reconstructed cluster centroid compares to that returned by standard
Maximum Likelihood analysis, allowing to look for astrophysical counterparts in
narrow regions, minimizing the chance probability in the counterpart
association. We find that gamma-ray DBSCAN is a powerful tool in the detection
of clusters in gamma-ray data, this method can be used both to look for
point-like sources, and extended sources, and can be potentially applied to any
astrophysical field related with detection of clusters in data.
