We conducted an experiment to evaluate the statistical efficiency of h
uman for discrimination between 3-D symmetry, i.e., the 3-D pattern sy
mmetrical about a sagittal plane, and 3-D random which was non-symmetr
ical about a sagittal plane but symmetrical about a vertical axis in t
he fronto-parallel projection plane. We added Gaussian depth noise to
the 3-D symmetry pattern and the 3-D random pattern. The discriminabil
ity (d') of the observers was obtained, and was compared with that of
the ideal cross correlator. In general, the efficiency was lower than
that for 2-D symmetry discrimination, but similar to that for other 3-
D tasks using dot stereograms. Moreover, the efficiency for 3-D symmet
ry discrimination was lower when the pattern was composed of more elem
ents, and it decreased along with increment of the noise variance in l
onger duration condition (1500 ms). From this result, we estimated the
number of elements which observer sampled in performing the task.