When a pair of surfaces is partially covered by a transparent filter, the ratios of cone excitations for the surfaces viewed directly are almost identical to those when the surfaces are viewed through the filter. We have previously shown that in simulations of Mondrian-like patterns partially covered by filters the invariance of the cone-excitation ratios predicts psychophysical performance in discrimination tasks. In this paper we investigate whether the number of surfaces in the display affects the strength of the transparency percept when observers are required to discriminate between displays with almost perfect invariance of cone-excitation ratios and similar displays where the ratios have been perturbed by noise. We find that discrimination performance increases with the increasing number of surfaces in the display. We also find that noise added to the S-cone class alone did not affect discrimination performance.