A model of stereopsis is proposed in which information from each eye's image is organised as a scale-based hierarchy before binocular comparison. The algorithm incorporates coarse-to-fine matching (like Marr and Poggio, 1979) but differs from previous models in that the position, and hence disparity, of features is defined relatively rather than by their retinal co-ordinate. Thus, fine scale disparities are measured and recorded relative to coarse scale disparities. Local surface slant and curvature is represented explicitly at a range of spatial scales. The theory is based on a hierarchical model of encoding position (Watt, 1988). The first experiment investigates the time course of shape discrimination in random dot stereograms. The results are compatible with a model in which the scale of analysis changes from coarse to fine over the first second of viewing. The second experiment measures the magnitude of a new "3-D" Müller-Lyer illusion and compares it to that of the classical (2-D) illusion. Both these and the cyclopean Müller-Lyer illusion are consistent with a model in which hierarchical encoding of position is used by the visual system for 2-D (length comparison) and 3-D (slant) judgements. The third experiment compares the detection of large disparities and large displacements. "D_max" for the motion and stereo tasks is shown to be similar over a wide range of dot densities. The results are interpreted as evidence that similar spatial primitives are used in the correspondence process in both domains. The spacing of MIRAGE centroids (Watt and Morgan, 1985) fit the data well. The proposed hierarchical model is similar to that put forward by Mitchison and McKee (1987), although their scheme was not based on spatial scale. The model bridges the gap between a primal and a 2 1/2-D sketch (Marr, 1982) and has important implications for many issues within stereopsis.