Obtaining exact depth from binocular disparities is hard if camera calibration is needed. We will show that qualitative information can be obtained from stereo disparities with little computation, and without prior knowledge (or computation) of camera parameters. First, we derive two expressions that order all matched points in the images by depth in two distinct ways from image coordinates only. Using one for tilt estimation and point separation (in depth) demonstrates some anomalies observed in psychophysical experiments, most notably the "induced size effect". We apply the same approach to detect qualitative changes in the curvature of a contour on the surface of an object, with either x- or y-coordinate fixed. Second, we develop an algorithm to compute axes of zero-curvature from disparities alone. The algorithm is shown to be quite robust against violations of its basic assumptions for synthetic data with relatively large controlled deviations. It performs almost as well on real i...