Abstract

1
Projection Biases Perceived Angles on a
Picture Surface Igor Juricevic, Shazma Rajani,
Sherief Hammad, John M. Kennedy University of
Toronto, Scarborough
Abstract Angles on picture surfaces may be
perceived incorrectly. This illusion may be
caused by projective information. Alternatively,
the angles may only be misperceived if they are
depicting very standard angles such as 90. Two
experiments used parallel perspective to test
these hypotheses. In Experiment 1, subjects
judged angles presented alone (i.e., as V-shapes)
or as parts of a right-angled, scalene triangle
depicted as the top surface of a double-cube
(depicting angles of 26.6, 63.4, and 90). The
largest errors were in the double-cube condition.
They were biased towards each of the depicted
angles of the double-cube. In Experiment 2 the
V-shapes were shown as parts of triangles, to
test whether triangles alone could create the
illusion, perhaps by providing projective 3-D
information for a single triangle being depicted
at different tilts. The errors were indeed biased
towards the depicted angles, but were less than
in the double-cube condition. The results support
a projective theory of the illusion that the
foreshortening depicting a 3-D object such as a
double-cube affects perception of the depicting
features on the picture surface. Introduction In
Figure 1, using parallel projection, the corners
of a cube are depicted by lines that meet at
obtuse or acute angles on the page. What happens
when an observer is asked to judge these
angles-on-the-page? Errors are made in the
direction of the depicted angle of 90 (Hammad et
al., in press). They may be perceived incorrectly
due to the pictures perspective (Arnheim, 1977
Gibson, 1979) and misapplied shape constancy
(Gregory, 1972).
What could cause this perceptual
illusion? Projective Theory the illusion may be
caused by projective information for the angles
of the cube. Good Form Theory the angles may be
misperceived because they are depicting very
standard angles (good forms), such as 90. These
two hypotheses can be tested with pictures that
depict acute angles, for example, pictures of a
double-cube presented at various tilts from 5 to
85 (see Figure 2). Experiment
1 Subjects judged angles presented in two
conditions 1) Double-Cube condition angles
presented as parts of a right-angled, scalene
triangle depicted as the top surface of a
double-cube (with depicted angle X90 and
depicted angles of 26.6 and 63.4 see Figures 1
and 2). 2) V-Shape condition angles presented
alone (i.e., as V-shapes)
Results Subjects responses were converted into
Bias scores. If the response equals the
angle-on-the-page, Bias 0. But if the response
equals the depicted angle, Bias 1. Intermediate
Bias scores reflect the distance of responses
from angle-on-the-page. Errors were biased
towards each of the depicted angles of the
double-cube, not just 90. The largest biases
were in the double-cube condition (see Figure 3).
Bias in the V-shape condition can be explained as
due to restriction of Bias scores to values
between 0 and 1. Experiment 2 The
V-shapes were shown as parts of triangles, to
test whether triangles alone could create the
same magnitude of illusion, perhaps by providing
projective 3-D information for a single triangle
being depicted at different tilts. Subjects
judged angles presented in two conditions 1)
Triangle condition angles presented as part of a
triangle 2) Double-Cube condition same as in
Experiment 1.
Results The largest biases were again in the
double-cube condition (see Figure
4). Conclusion The results from
both experiments support a Projective Theory of
the illusion that the foreshortening depicting a
3-D object such as a double-cube affects
perception of the depicting features on the
picture surface (Arnheim, 1977). Not only were
the errors biased towards good form 90
depicted angles, but also to 26.6 and 63.4
depicted angles that are not good form
angles. DEDICATION We dedicate this poster to
the memory of Rudolf Arnheim (July 15, 1904
June 9, 2007) ACKNOWLEDGEMENTS S.
Bernstein and J. Hockin (TSTOP, Ontario) for
comments, Sandacre Technology for programming,
and I. Abramov, S. Bhasin, S. El Sebae, M. Fazl,
B. Haji-Khamneh, E. Hyatt, G. Ilie, S. Moid, and
D. Press.
Depicted Angles
5
15
25
35
45
55
Depicted Angles
Figure 4. Double-Cube condition Bias scores are
higher than Triangle condition.
65
75
85
Figure 3. Double-Cube condition Bias scores are
higher than V-shape condition.
Figure 2. Double-cubes at various tilts.
X
Figure 1. A double-cube. For angle X,
angle-on-the-page 159 and depicted angle 90