Under some conditions, the perceived depth of a stereogram made of regularly-spaced points depends on the disparity of the edges of the stereogram rather than on discrete stereo matching of the points themselves. These depth percepts are seen only if the viewing time is brief, less than 2-3 sec, and the spacing between the points is small, less than 5-7 min of arc. In this paper, we examine the hypothesis that depth interpolation reflects a failure of the stereo matching apparatus to resolve the fine structure of the stereogram. We show that fine structure can be resolved during brief presentations (160 msec). It seems likely that interpolation represents an intermediate stage in the stereo matching process.