  We present a comparison of three cluster finding algorithms from imaging data
using Monte Carlo simulations of clusters embedded in a 25 deg^2 region of
Sloan Digital Sky Survey (SDSS) imaging data: the Matched Filter (MF; Postman
et al. 1996), the Adaptive Matched Filter (AMF; Kepner et al. 1999) and a
color-magnitude filtered Voronoi Tessellation Technique (VTT). Among the two
matched filters, we find that the MF is more efficient in detecting faint
clusters, whereas the AMF evaluates the redshifts and richnesses more
accurately, therefore suggesting a hybrid method (HMF) that combines the two.
The HMF outperforms the VTT when using a background that is uniform, but it is
more sensitive to the presence of a non-uniform galaxy background than is the
VTT; this is due to the assumption of a uniform background in the HMF model. We
thus find that for the detection thresholds we determine to be appropriate for
the SDSS data, the performance of both algorithms are similar; we present the
selection function for each method evaluated with these thresholds as a
function of redshift and richness. For simulated clusters generated with a
Schechter luminosity function (M_r^* = -21.5 and alpha = -1.1) both algorithms
are complete for Abell richness >= 1 clusters up to z ~ 0.4 for a sample
magnitude limited to r = 21. While the cluster parameter evaluation shows a
mild correlation with the local background density, the detection efficiency is
not significantly affected by the background fluctuations, unlike previous
shallower surveys.
