The finest stereoacuity is known to depend on the disparity of a target relative to other visible points. Here we show that a more important factor in determining sensitivity to displacement can be the disparity of a target relative to an invisible interpolation plane through other neighboring points. We tested the sensitivity of observers to displacements of the central column of a regular grid of dots that was either fronto-parallel or slanted about a vertical axis. We found that subjects' sensitivity to displacement was better predicted by a model based on the disparity of a target with respect to the grid plane than it was by a model based on disparity with respect to other reference points. In control conditions carried out on one subject, we found that this result did not depend on adaptation to the grid slant because it also occurred when the direction of grid slant varied from trial to trial. Nor did it depend on the perception of slant, because the data were similar for trials on which the grid was perceived as approximately fronto-parallel or markedly slanted. Our results indicate that sensitivity to the depth component of the target displacement is based on disparity relative to a local reference plane.