When is a disparity not a disparity? Toward an old theory of three-dimensional vision.

The aims of this paper are twofold: first, to discuss and analyze the concept of binocular disparity and second, to contrast the traditional "air theory" of three-dimensional vision with the much older "ground theory," first suggested by Ibn al-Haytham more than a thousand years ago. The origins of an "air theory" of perception can be traced back to Descartes and subsequently to the philosopher George Berkeley, who claimed that distance "could not be seen" because points lying along the same line of sight (in an empty space) would all project to the same location on the retina. However, Descartes was also aware that the angle of convergence of the two eyes could solve the problem of the "missing" information for the monocular observer and, since then, most visual scientists have assumed that eye vergence plays an important role both in judging absolute distance and for scaling retinal size and binocular disparities. In contrast, al-Haytham's and Gibson's "ground theories," which are based on the geometry of the textured ground plane surface that has surrounded us throughout evolution and during our lifetimes, are not just more ecologically based but they also obviate the need for