How is a single visual direction assigned to a binocular feature for w
hich the left and right eyes are signaling different directions? Accor
ding to geometrical principles, binocular visual direction is the aver
age of the visual directions measured from the left and right eyes. Co
ntrary to this prediction, we have found that the relative visual dire
ction between two Gabor targets presented at different stereoscopic de
pths could be manipulated by varying the contrast ratio between the le
ft and right images. This finding is consistent with a new model in wh
ich the relative alignment of depth features is determined from a maxi
mum-likelihood combination of the direction signals from the left and
right eyes. In a second experiment we provide support for this model,
showing that the magnitude of the contrast-dependent bias in visual di
rection is predicted by the uncertainty for spatial localization in th
e left and right images. Lastly we show that visual direction and ster
eopsis have different dependencies on interocular contrast differences
, suggesting that the computation of stereo depth and visual-direction
are mediated via different mechanisms.