Disparity curvature and the perception of three-dimensional surfaces

BINOCULAR stereopsis provides information about the relative distance of objects from the differences in the horizontal position of their images on the two retinas1–3. Because the size of the disparity between two points is inversely related to the square of the viewing distance, it is usually assumed that disparities have to be scaled according to distance using the vergence angle of the eyes, or by using the small vertical disparities that also exist between corresponding points of the two images4,5. Here we present evidence that the visual system could extract information about the shapes of surfaces (without the need for scaling) by using the second spatial derivative of disparity–disparity curvature–which remains invariant with viewing distance6. Rather than computing the second derivative, we suggest that an approximation to disparity curvature could be derived from the differences in curvature of corresponding line elements in the two eyes.