Our correspondence algorithm is based on differential geometry and takes explicit advantage of both position and orientation disparities. The basic idea is as follows (Fig.2). A curve in $\mathbb{R}^3$ has a tangent, normal, and binormal frame (Frenet frame) associated with every regular point along it. For simplicity, consider only the tangent in this frame, and imagine it as an (infinitly) short line segment. This space tangent projects into a planar tangent in the left image, and a planar tangent in the right image. Thus, space tangents project to pairs of image tangents. Now, consider the next point along the space curve; it too has a tangent, which projects to another pair of image tangents, one in the left image and one in the right image. The key concept that we utilize in this paper is {\em transport}, or the movement of the frame in $\mathbb{R}^3$ from the second point back to the first, which is essentially contextual information expressed geometrically; note that this transport has a correspondence in the left-right image pairs. Our goal is to use this transport to find corresponding pairs of image tangents such that their image properties match, as closely as the geometry can be approximated, the actual space tangents. Two notions of disparity arise from the above transport model. First, the standard notion of positional disparity corresponds, through the camera model, to depth. Second, an orientation disparity is introduced if the space tangent is not in the epipolar plane. In the computational vision literature, orientation disparity is largely unexplored. The success of our system derives, in part, from the simultaneous use of position and orientation disparities, and the underlying differential geometry that naturally combines them.