Grey-scale images consist of physical measurements of light. Scale-space theories have been developed to unconfound these measurements from the detector grid. In this framework, we look into the problem of binocular stereo. On a sufficiently large scale, a pixel carries information not only of the grey-value, but of the entire grey-value n-jet, i.e., derivatives up to order n. The subject of this paper is to show, in a general context, how the scale-space n-jet can be exploited for binocular matching. The analysis leads (under appropriate assumptions) to a direct determination of the local n-jet of the disparity field. The general result is an analysis which could be incorporated into many existing stereo algorithms to improve their use of the grey value data. In the computational scheme presented here, the estimations are strictly local, but based on image derivatives at a scale where the image structure is significant. This scale is automatically selected by minimising computational uncertainty. Results are shown as direct computations of surface normals on synthetic and real images.