There is substantial psychophysical and physiological evidence that humans solve the binocular correspondence problem by correlating the two eyes' images locally. We have developed an ideal observer of this process. In order to determine perceptual consequences of solving correspondence in this fashion, we have compared the behavior of the ideal observer and humans. We find some striking similarities with respect to the spatial resolution of stereopsis, the disparity gradient limit, the effect of image magnification differing in the two eyes, and stereo transparency effects. Thus, many perceptual effects in stereo vision derive from using local cross correlation to solve the correspondence problem.