methods ([@rosati98 the ROSAT Deep Cluster survey];[@vikhlinin98_160d the ROSAT 160d survey];[@burenin07_400d the ROSAT 400d survey]; [@fassbender11_XDCP the [*XMM-Newton*]{} Distant Cluster Project]; [@lloyd-davies11_XCS the XMM Cluster Survey]; [@pacaud06 The XMM Large-Scale Structure survey]; [@barkhouse06 the [*Chandra*]{} Multi-wavelength Project]).

Very few alternative lines of research are being developed for exploiting the entire information contained in X-ray images. So far, the only method fully employing the information of the photon counts per pixel and of the counts in neighboring pixels is the background/source separation technique [@guglielmetti09]. This method uses the Bayesian probability theory combined with a two-component mixture model. This way, background and source intensity can be estimated jointly. First results based on this technique and applied to deep [*Chandra*]{} fields are currently under scrutiny (Guglielmetti et al. in preparation). Given this framework, it is well worth putting a significant effort into developing diversified detection algorithms for extended sources.

In this paper, we further develop the VT+FOF algorithm, making a great effort against its major shortcomings. We provide the flexible and efficient [*Extended X-ray Source detection*]{} software ([*EXSdetect*]{}), which can be easily applied to a wide range of X-ray images, and is optimized to detect extended sources. The software, written in [*Python*]{} and 