Fig.5.5 Data of Experiment 1 of Rosinski
et al. Angle to which palm board was adjusted to match apparent slant
of surface in photograph for the two points of view. Values of independent
variable are determined by assumption that center of projection coincides
with 90° point of view..
.
Let us look at the results of the first experiment, shown
in Figure 5.5. Look first at the line labeled "go." It presents the
data for the adjustments made when the observers looked at the picture from
the center of projection. Had the observers been able to correctly match the
angle of the palm board to the slant of the surface in the photograph, the data
points would fall on the dotted line. Because the data points deviate systematically
from the line, we conclude either that subjects underestimated the extremity
of the deviation of surface slants from the frontal plane or that they overestimated
the extremity of the settings of the palm boards. The data do not allow us to
decide which of these two interpretations is correct. Furthermore, the palm-board
settings were invariably higher when the photographs were viewed from the oblique
vantage point (labeled "135") than when they were viewed from the
center of projection. This means that the photographs looked different when
the observers viewed them from the two different vantage points, but not necessarily
that the observers failed altogether to compensate for the change in vantage
point. As we saw in Chapter 2, we can use geometry
to calculate what an observer who assumes that his or her eye is at the center
of projection can legitimately infer about the represented scene. If we do that
for the data shown in the curve for the eccentric point of view, the shape of
that curve changes somewhat; on the whole, it shifts to the right and, as may
be seen in Figure 5.6 , appears to coincide with the curve for the data obtained
for the view from the center of projection. In other words, the difference between
the data obtained for the two vantage points is eliminated if one assumes that
observers who viewed the picture through a peephole were unable to compensate
for the change in vantage point, and that they perceived the photographs as
if they assumed that the center of projection coincided with their vantage point.
Fig.5.6 Modified data for Experiment 1 of Rosinski
et al. Angle to which palm board was adjusted to match apparent slant
of surface in photograph for the two points of view. Values of independent
variable are determined by assumption that center of projection coincides
with observer's point of view.
Fig.5.7 Data for Experiment 2 of Rosinski
et al. Angle to which palm board was adjusted to match apparent slant
of surface in photograph for the two points of view. Values of independent
variable are determined by assumption that center eat projection coincides
with 90° point of view.
Now we should turn to the results of the second experiment (shown in Figure 5.7). Here Rosinski et al. had made no attempt to reduce the perceptibility of the picture plane. The settings of the palm board appear to be no more accurate than in the first experiment; but the evidence regarding the robustness of perspective is unequivocal: There is no difference between the settings of the palm board for the two vantage points, thus demonstrating that the perceived slant of the plane represented in the photograph was independent of vantage point. So, the Rosinski et al. experiment confirms Pirenne's hypothesis: If the subjects can see the picture plane, perspective is robust; if they cannot, perspective is not robust. In other words, the availability of information regarding the location and the orientation of the picture plane is necessary and sufficient for the robustness of perspective.4
4 In Chapter 7, we will see that this conclusion is a bit too general. Information about the orientation of the picture plane is sufficient only if the picture is on one plane.
