and choosing the best compromise.

One may argue that a small region (the core circle) is not the best choice for classification, because extended sources are maximally different from unresolved sources at large radii. However, because of the low S/N in the outer regions, it turns out that it is more efficient to focus on the core region where the S/N is maximized. However, this choice may cause the loss of extended sources whenever a bright unresolved source in the center is present.[^8]. This may occur because of a strong (typically unrelated) unresolved source is embedded in the extended emission, or because of the presence of a bright cool core whose size is below the angular resolution. To overcome this problem, we applied a supplementary step to recover most of these sources. We considered all sources that are classified as unresolved but with KS null-hypothesis probability $> 50\%$. For each of these sources, we normalized the local PSF to the total photon inside the core region and calculated the radius where it reaches $1/2$ the [*local*]{} background level. Since the edges resulting from the FOF algorithm are set by the [*overall*]{} background level, the circles defined by this criterion should 