The Robustness of Perspective
Although in general perspective is robust, certain pictures are an interesting
exception to robustness. I am referring to an illusion of "following"
that we experience when we move in front of some paintings. Hans Wallach writes:
It is often noticed that the head of the portrait appears to turn
when one walks past the picture. This apparent turning is even more impressive
in the case of landscape that shows strong perspective depth... . I had noticed
it first many years ago when walking past a landscape by Theodore Rousseau in
the Frick Collection [see Figure Village]. It shows a country road
flanked by rows of trees leading straight into the distance. When one walks
past it, the whole scene appears to turn, the foreground moving with the observer.
This rotation is the same as the portrait head's which appears to turn as if
to look after the passing viewer. (1976, p. 65)
Fig.5.8 Pierre-Etienne-Theodore Rousseau, The Village of Becquigny (1857). The Frick Collection, New York. Subjects in Goldstein's (1979) experiment judged apparent orientations road, rut in road, house, and line defined by the two trees in foreground.
Fig.5.9 Schematic maps completed
by two observers in Goldstein's (1979) experiment, A and B,
at two viewing angles, 15° and 165°: To the two Parallel
lines representing road, they were asked to add a short line
to represent rut in road, a rectangle to represent house,
and two dots to represent trees.
This observation has been confirmed experimentally by E. Bruce Goldstein (1979),
who affixed a black-and-white photograph of the painting by Theodore Rousseau
mentioned by Wallach to an upright panel that could be turned right or left
about a vertical axis. Rotating the panel was a convenient substitute for
having the viewer walk around the reproduction. Just below the panel was a
pointer that could turn independently of the panel about the same axis. The
panel was shown to the viewer at several different viewing angles. For each
angle, the observer was asked to adjust the pointer so that it would point
in the same direction as the road. At all angles (ranging from 15°, the
right side of the painting turned toward the observer so that it was seen
almost edge on, to 165°, i.e., the left side of the painting turned toward
the observer so that it was seen almost edge on), each observer set the pointer
to point directly at him or her.5 Because this result appears to
run counter to the robustness of perspective, Goldstein performed a further
experiment: The observers were shown the picture at various orientations and
were given a schematic map with two parallel lines to represent the road.
On this map, they were asked to mark the location of the closest house (on
the left), of the two closest trees, and of a rut cutting across the road
in the foreground. The maps (see Figure 5.9) were unaffected by the rotation
of the picture, lending support to the robustness of perspective. I will explain
the exceptions to the robustness of perspective in the latter part of the
5 When observers were asked to set the pointer to coincide with the orientation of other features of the scene, such as the line connecting the two trees on either side of the road in the foreground, the setting of the pointer varied systematically with the orientation of the picture. Certain aspects of the scener geoemtry wer therefore less robust than others.