We examine whether the rules of cyclopean visual direction, as express
ed by Hering and others, correctly predict the percept of visual direc
tion for structured visual stimuli. Theoretical inspection of the rule
s of cyclopean visual direction shows a paradox for the binocular visu
al directions of stimuli in which objects partly occlude each other. W
e investigate how the rules of cyclopean direction are violated during
viewing of structured random-dot stereograms with different depth pla
nes. The directions of monocular and binocular visual elements are det
ermined in an alignment task. Subjects align a monocular/binocular sli
der with a monocular/binocular test line present in the random-dot ste
reograms. The results show that the available rules of cyclopean direc
tion are not sufficient for human vision in this general situation. Th
e available rules can only be used for alignment of two binocularly vi
sible lines or two monocular lines presented to the same eye. Alignmen
t in these cases is predicted by almost any set of rules that transfor
ms visible lines to a cyclopean eye. Stimulus conditions, in which eit
her one line is presented to one eye and the other line to the other e
ye or one line is presented to one eye and the other line to two eyes,
provide a more critical test for validity of the cyclopean rules. Our
results show that the rules of cyclopean direction fail to predict al
ignment precisely in these conditions. Inspection of the data shows th
at binocular alignment is achieved by alignment of two monocular lines
presented to a single eye.