Parallel Computation of Vernier Offsets, Curvature and Chevrons in Humans

A vernier offset is detected at once among straight lines, and reaction times are almost independent of the number of simultaneously presented stimuli (distractors), indicating parallel processing of vernier offsets. Reaction times for identifying a vernier offset to one side among verniers offset to the opposite side increase with the number of distractors, indicating serial processing. Even deviations below a photoreceptor diameter can be detected at once. The visual system thus attains positional accuracy below the photoreceptor diameter simultaneously at different positions. I conclude that deviation from straightness, or change of orientation, is detected in parallel over the visual field. Discontinuities or gradients in orientation may represent an elementary feature of vision.

The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.