The Pursuit of Leonardo's Constraint

Abstract

Leonardo da Vinci (1452–1519) identified two stimulus situations that cannot be painted faithfully on a canvas: (a) when two objects are located in the same direction with respect to the painter's head, and (b) when parts of a surface are visible to one eye, but occluded from the other eye. He analysed these situations in terms of rays being emitted from the two eyes and, aside from the origin of the rays, the projective geometry he used was correct. His analyses showed that what can be seen from two vantage points cannot be represented on a canvas, because a ‘correct’ painting must be created from a single ‘station point’. He was struck by the consequence of this fact that the depth seen on a canvas cannot match that of viewing the scene with two eyes. Subsequent visual scientists focused on Leonardo's observation about the lack of vivid depth in a picture. We argue that a complete understanding of what we see in the two stimulus situations requires consideration of visual direction in addition to visual depth. More specifically, we argue that the visual directions of the two objects, (a) above, and the visual direction of the monocular areas, (b) above, are dependent upon the constraint that two opaque objects cannot be represented in the same direction. Demonstrations that readers can perform, and that support this argument, are provided on the Perception website at http://www.perceptionweb.com/perc0102/ono.html .