ws
id
ersi
Sta
PsycINFO classification:
2323
cast
ous
the extent to which observers can ‘‘discount” the distorting effects of curved background surfaces. In
al eve
rnheim
. Attac
more ‘‘realistic” (e.g. Caravaggio, Claesz, Rembrandt, and Wyeth).
Unfortunately, cast shadows have not often been the subjects of
psychophysical investigation. In parsing the available literature
that does exist regarding the perception and mathematics of cast
shadows, it will be helpful to consider the various kinds of cast
shadows that occur in natural, everyday scenes and the types and
quantities of useful information that they contain.
actly coincident with an observer’s line of sight, the cast shadow of
an object will have the same shape as its boundary contour (e.g. see
Plate 19 of Gombrich, 1995). In all other circumstances, however
(e.g. when the direction of illumination deviates from an observer’s
line of sight), the shape of an object’s cast shadow will differ from
that of the boundary contour. For an example of this phenomenon,
see Fig. 2.
In an influential Psychological Review article, Attneave (1954)
hypothesized that the most perceptually informative parts of an
object’s boundary contour were its convexities and concavities
* Corresponding author. Tel.: +1 (270) 745 2094; fax: +1 (270) 745 6934.
Acta Psychologica xxx (2009) xxx–xxx
Contents lists availab
ch
.e ls
ARTICLE IN PRESSE-mail address: Farley.Norman@wku.edu (J.F. Norman).an object when one part of its surface blocks light from reaching
other parts. Cast shadows occur when one object blocks light from
background surfaces (i.e. the shadow of the object is ‘‘cast” onto the
background surface). The presence of cast shadows in visual images
does not impair the recognizability of natural objects (Braje, Legge,
& Kersten, 2000). Indeed, cast shadows have been shown to facili-
tate the perception of an object’s depth, 3-dimensional (3-D) shape,
and its movement in space (Kersten, Knill, Mamassian, & Bülthoff,
1996; Norman, Dawson, & Raines, 2000; Norman & Raines, 2002;
Norman & Todd, 1994; Wallach & O’Connell, 1953). In addition,
painters frequently use shadows to make their paintings appear
on object surfaces that separate visible from invisible regions is a
space curve called the rim (Koendrink, 1984a; Koenderink & van
Doorn, 1982), the occluding bound (Kennedy, 1974), or the contour
generator (Marr, 1982). The projected image of the rim is called
the contour (Koenderink, 1990, pp. 418–420): the contour is thus
a 2-D entity. The outermost portion of the contour (the portion that
bounds the projection of the object) is called a ‘‘silhouette” or ‘‘out-
line” – these distinctions are illustrated in Fig. 1. Other researchers
have referred to these 2-D bounding contours using terms such as
occluding contours, apparent contours, boundary contours, and
profiles. When the direction to an environmental light source is ex-Keywords:
Form and shape perception
Cast shadows
Boundary contours
Shadows are ubiquitous in natur
may be cast or attached (e.g. see A
Knill, Mamassian, & Kersten, 1997)0001-6918/$ - see front matter  2009 Elsevier B.V. A
doi:10.1016/j.actpsy.2009.01.007
Please cite this article in press as: Norman
logica (2009), doi:10.1016/j.actpsy.2009.01our experiments, observers viewed deforming or static shadows of naturally shaped objects, which were
cast upon flat and curved background surfaces. The results showed that the discrimination of 3-D object
shape from cast shadows was generally invariant over the distortions produced by hemispherical back-
ground surfaces. The observers often had difficulty, however, in identifying the shadows cast onto saddle-
shaped background surfaces. The variations in curvature which occur in different directions on saddle-
shaped background surfaces cause shadow distortions that lead to difficulties in object recognition and
discrimination.
 2009 Elsevier B.V. All rights reserved.
ryday scenes. Shadows
, 1974; Gibson, 1966;
hed shadows occur on
When human observers view solid opaque objects, it is neces-
sarily the case that some parts of these objects occlude, or hide,
the surface regions belonging to other parts. The 3-D locus of pointsReceived in revised form 29 January 2009
Accepted 30 January 2009
Available online xxxx
ined the informativeness of shadows cast upon flat background surfaces. In outdoor environments, how-
ever, background surfaces often possess significant curvature (large rocks, trees, hills, etc.), and this
background curvature distorts the shape of cast shadows. The purpose of this study was to determineThe perception of 3-D shape from shado
J. Farley Norman a,*, Young-lim Lee b, Flip Phillips c, H
L. RaShae Jennings a, T. Ryan McBride a
aDepartment of Psychology, 1906 College Heights Blvd. #21030, Western Kentucky Univ
bDepartment of Psychology, Indiana University, Bloomington, IN 47405, United States
cDepartment of Psychology, Skidmore College, Saratoga Springs, NY 12866-1632, United
a r t i c l e i n f o
Article history:
Received 27 June 2008
a b s t r a c t
In a natural environment,
background surfaces. Previ
Acta Psy
journal homepage: wwwll rights reserved.
, J. F., et al. The perception o
.007cast onto curved surfaces
eko F. Norman a,
ty, Bowling Green, KY 42101-1030, United States
tes
shadows abound. Objects cast shadows both upon themselves and upon
research on the perception of 3-D shape from cast shadows has only exam-
le at ScienceDirect
ologica
evier .com/ locate/actpsyf 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

cho
ARTICLE IN PRESS2 J.F. Norman et al. / Acta Psy(i.e. the areas of maximal curvature). Recent results have tended to
support Attneave’s hypothesis (e.g. De Winter & Wagemans, 2008;
Norman, Phillips, & Ross, 2001). In addition, Norman et al. (2000)
found that static shadows that contained prominent convexities
or concavities were much more recognizable than those that did
not. The probable reason that human observers are sensitive to
the maximally curved parts of boundary contours and shadows is
that these areas contain information about surface shape. For
example, Koenderink (1984a) and Richards, Koenderink, and
Fig. 1. Starting from upper-left and proceeding clockwise are depicted (1) a smoothly
outline, and (4) silhouette. This object is similar to those used by Todd and Norman (19
Fig. 2. A diagram that illustrates both the similarities (left panel) and the differences
projection of the rim onto the retina) and its cast shadow. In these examples, the shado
indicates a situation in which the directions to the light source and the observer are coi
directions are different. Note in the left panel that the shapes of the cast shadow and th
contour is circular, cast shadow is elliptical) in the right panel. The rim and shadow gen
right panel.
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007logica xxx (2009) xxx–xxxHoffman (1987) have demonstrated that the convexities and con-
cavities within a 2-D boundary contour correspond to the projec-
tions of differently curved regions on the surfaces of 3-D objects.
In particular, convex parts of a boundary contour result from the
projection of elliptic or ‘‘bump-like” areas on the surface of an ob-
ject, while concave parts result from the projection of hyperbolic,
or ‘‘saddle-like” surface regions. However, it is important to keep
in mind that individual static boundary contours can often be
ambiguous or misleading. If a particular projection of an object
curved solid object depicted with Lambertian shading, (2) the object’s contour, (3)
95) and Norman, Todd, and Phillips (1995).
(right panel) between an object’s boundary contour (i.e. the outer portion of the
w is cast onto a ‘‘wall” that is perpendicular to the textured ‘‘floor”. The left panel
ncident, whereas the right panel indicates the more general situation in which the
e boundary contour are identical (both circular), while they are different (boundary
erator are identical space curves in the left panel, whereas they are different in the
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

Under these circumstances, there is a second special curve on ob-
ject surfaces which is analogous to, but different from, the rim –
we call it the shadow generator. The shadow generator is the locus
of points on the surface of an object (a 3-D space curve) that pro-
jects to the shadow on a background surface. The shadow genera-
tor is different from the rim, because while the rim is defined
e orientation of the starfruit depicted on the left produces a shadow with a qualitatively
he right.
chologica xxx (2009) xxx–xxx 3
ARTICLE IN PRESSdoes not contain significant boundary convexities or concavities,
key aspects of the object’s ‘‘true” 3-D shape will not be revealed
(see for example, the right panel of Fig. 3).
A number of psychophysical studies have evaluated how well
human observers can identify or recognize objects from static sil-
houettes and/or cast shadows. The depicted objects range from
simple volumetric primitives, such as wedges, cones, and cylinders
(Tjan, Braje, Legge, & Kersten, 1995), to assemblages of simple geo-
metric components (Hayward, Tarr, & Corderoy, 1999; Hayward,
Wong, & Spehar, 2005), to aircraft (Federico, 1991), to objects
encountered in everyday life (animals, manmade objects, body
parts, see Wagemans et al. (2008)), to naturally shaped objects
(bell peppers, see Norman et al., 2000). This past research has
shown that objects can be successfully identified from their silhou-
ettes or cast shadows even when their contours change because of
object rotation in depth (e.g. see Experiment 3 of Hayward et al.,
1999; also Norman, Bartholomew, & Burton, 2008) or because of
the movement of environmental light sources (Norman et al.,
2000).
The addition of motion, either motion of an object or motion of
an observer relative to an object, can add information and disam-
biguate an otherwise ambiguous boundary contour or cast shadow.
The motion of an object (e.g. rotation of an object in depth) can
serve to ‘‘bring” an object’s differently curved surface regions to
its boundary contour, where they can be detected as individual
convexities and concavities. In this way, human observers could
potentially create a qualitative representation of an object’s entire
shape as an ‘‘aspect graph” (see Koenderink, 1984b; Koenderink &
van Doorn, 1978). It is possible to go even further than this: for
example, Giblin and Weiss (1987), Cipolla and Giblin (2000),
Mendonça, Wong, and Cipolla (2001), Wong and Cipolla (2004),
Fig. 3. Silhouettes or cast shadows of a starfruit (Averrhoa carambola). Notice that th
different shape than that of a different orientation of the same object depicted on t
J.F. Norman et al. / Acta Psyand Hernández, Schmitt, and Cipolla (2007) have all demonstrated
mathematically that the profiles of moving objects contain a
wealth of information about local 3-D surface shape. The work of
Cipolla and colleagues is especially noteworthy, because they have
shown that it is possible to take a series of actual images, as re-
corded by a video camera, and reconstruct 3-D models solely from
deforming profiles (these methods, however, cannot lead to a com-
pletely accurate reconstruction of an object’s shape, because sur-
face concavities do not affect the shape of an object’s boundary
contour). Cortese and Andersen (1991) and Norman et al. (2000)
have shown that the presence of motion (i.e. deforming boundary
contours or cast shadows) does indeed facilitate human observers’
judgments of object shape.
The situations and mathematics for many real-world scenes are
more complicated than those previously described. In the real
world, an observer views solid 3-D objects that are illuminated
by one or more environmental light sources. The objects block
some of the light emanating from the light sources; as a result cast
shadows of the objects are projected onto background surfaces.
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007relative to the observer’s eye, the shadow generator is defined rel-
ative to environmental light sources. There will be as many shadow
generators as the number of environmental light sources. In the
everyday case of an observer looking at a solid object illuminated
outdoors on a sunny day, the observer will typically see both the
boundary contour (i.e. the projection of the rim) and the shadow
cast onto the background surface (i.e. the projection of the shadow
generator). The mathematical analyses described earlier (e.g. Cipo-
lla & Giblin, 2000; Giblin & Weiss, 1987; Hernández et al., 2007;
Mendonça et al., 2001; Wong & Cipolla, 2004) were only designed
to recover aspects of 3-D shape from profiles. They were not in-
tended to function in the more general case of cast shadows that
are cast onto arbitrarily curved background surfaces.
In a similar vein, nearly all the limited number of psychophys-
ical studies on this topic have investigated the perception and rec-
ognition of objects defined by static and moving boundary
contours. The main purpose of the current study was to investigate
the perception of 3-D object shape from shadows that are cast onto
curved background surfaces. In 1992, Knill (see his Fig. 8) created aFig. 4. The shadows of a circle (114 cm diameter) cast onto an outdoor staircase at
Western Kentucky University. Notice that the shapes of the cast shadows (the
shadows of the circle and the body and arms of the person holding the circle) have
been significantly distorted by the complex 3-D shape of the background surface
(the staircase).
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

ers)
4 J.F. Norman et al. / Acta Psycho
ARTICLE IN PRESSclass of stimuli whose contours are frequently perceived by human
observers to be shadows cast onto curved background surfaces. It
is important to follow up on Knill’s observations and carefully
examine the effects of curved background surfaces, because natu-
ral environmental background surfaces are rarely flat and are often
significantly curved. Indeed, Leonardo da Vinci (1519/1970, see
Plate VI, No. 1) pointed out almost 500 years ago that the shapes
of cast shadows were as much affected by the shapes of back-
ground surfaces as by the shapes of the objects themselves (see
Fig. 4 for an illustration of this phenomenon, also see Jeaurat
(1750, pp. 203, 221)). The primary goal of the current study was
to evaluate the extent to which the human perception of 3-D object
shape from shadows is invariant over the distortions that occur
when cast shadows are projected onto curved background
surfaces.
In the current investigation, Experiment 1 was designed to as-
sess how well human observers can perceive and discriminate 3-
D object shape when the objects were solely defined by deforming
(i.e. moving) cast shadows. The observers were initially trained
with full-cue motion sequences of a set of naturally shaped ob-
jects; they subsequently were required to identify the objects from
deforming shadows that were cast onto flat backgrounds. If
deforming cast shadows contain perceptually useful information
about solid object shape there should be little decrement in perfor-
mance when the full-cue motion sequences are replaced by
deforming shadows. Experiment 2 was designed to extend the re-
sults of Experiment 1 by evaluating the perceptual informativeness
of object shadows cast onto a variety of curved background
surfaces.
1. Experiment 1
1.1. Method
1.1.1. Apparatus
An Apple iMac was used to display the animation sequences.1
The stimulus patterns were presented on a Mitsubishi Diamond Plus
200 22-inch monitor. The observers viewed the experimental stimuli
from a viewing distance of 100 cm.
1.1.2. Stimulus displays
Fig. 5. A photograph of the five naturally shaped solid objects (bell peppThe objects used were replicas of five ordinary bell peppers
(Capsicum annuum, the replicas were made from Smooth-Cast
321 liquid plastic, Smooth-on, Inc.). These five objects, illustrated
in Fig. 5, are a subset of the natural objects used in our previous
investigations (Norman, Clayton, Norman, & Crabtree, 2008;
Norman et al., 2004; Norman et al., 2006). The five peppers were
chosen to have similar sizes in order to prevent discrimination
based on differences in overall size. Eighty different photographs
(full-cue images) or cast shadows (reduced-cue images) of each
1 Samples of the experimental stimuli (rotating full-cue displays and deforming
object shadows cast onto a flat plane) can be found on our laboratory’s website at the
following address: http:// edtech.wku.edu/~fnorman/movies/PepperAnimations.htm.
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007object were obtained by rotating the objects 360 in depth around
a vertical axis in 4.5 angular increments. For this experiment, the
shadows of the five objects were always cast onto a flat back-
ground surface. To generate the shadows, we placed the objects
20 cm in front of the background surface and illuminated the ob-
jects and background with a 300 watt light source (a Singer Cara-
mate 3200 projector). The distance between the light source and
the objects was 6.5 m. Sample shadows of each of the five objects
are presented in Fig. 6. A Nikon Coolpix 995 digital camera was
used to record the full-cue photographs and the cast shadows at
a resolution of 1024  768 pixels. In capturing the shadows, the
distance from the camera to the objects was 110 cm, while the an-
gle between the camera’s line of sight and the direction of the light
source was 35. Once the 800 digital images were acquired (5
objects  80 frames/object  2 display types, full-cue photographs
vs. cast shadows), they were then transferred to the computer.
1.1.3. Procedure
The procedures used were generally identical to those used by
Norman et al. (2000). All the observers participated in five experi-
mental sessions. Each session consisted of a total of 50 experimen-
tal trials (5 objects  10 trials per object). The order of the object
presentations within a session was randomly determined for each
session and observer. The observers were required to identify the
object (1–5) presented on each trial as depicted by the deforming
cast shadows, where the shadow deformation was caused by the
object rotation in depth. The individual frames of the apparent mo-
tion sequences were updated at a rate of 50 Hz. The observers
made their responses by pressing an appropriate key (1–5) on
the computer’s keyboard. The observers had as much time as they
needed on each trial to view the shadows and identify the object.
The observers never received feedback regarding their perfor-
mance during an experimental session. After completion of all five
sessions, a total of 50 responses had been collected for each of the
five objects (250 total trials per observer).
Prior to the start of an experimental session, all the observers
engaged in a series of practice trials involving full-cue photographs
of the objects. These practice trials were used to familiarize the
observers with the objects, so that they could perform the object
identification task. At the very beginning of the experiment, the
observers were unfamiliar with which object was object 1, which
used to create the shadow stimuli that were used in the current study.
logica xxx (2009) xxx–xxxwas object 2, etc. In order for the observers to be able to perform
the task, we gave them a series of practice sessions of 10 trials each
(2 repetitions  full-cue animations of 5 objects) until their identi-
fication accuracy for a practice session reached a criterion of 90% or
higher correct responses. Feedback, in the form of a short auditory
beep, was given to the observers following each correct response.
Once the 90% criterion was reached, the feedback was turned off
and the experimental session began. It is important to keep in
mind that the observers did not see the deforming cast shadows
until the beginning of an experimental session. Because of this,
the observers never received any feedback for their performance
on trials depicting deforming cast shadows. At the end of the prac-
tice trials, the observers could recognize the full-cue depictions at a
high level of accuracy (because of the feedback). The key question
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

ve s
cho
ARTICLE IN PRESSwas whether this high level of performance would transfer to the
experimental trials (with no feedback) depicting deforming cast
shadows.
1.1.4. Observers
The stimulus displays were presented to five observers, three of
whom were coauthors (JFN, HFN, and LRJ). Two additional observ-
ers (MCW and EM) were naïve with regard to the purposes of the
experiment. All observers were either students or faculty at Wes-
tern Kentucky University. All observers had normal or corrected-
to-normal visual acuity.
Fig. 6. Representative shadows of the fi
J.F. Norman et al. / Acta Psy1.2. Results and discussion
After the very first of the five experimental sessions, the observ-
ers’ identification accuracy was 94%, 100%, 100%, 78%, and 96% cor-
rect for observers EM, JFN, HFN, MCW, and LRJ, respectively. This
level of performance, exhibited for the deforming cast shadows,
did not differ significantly from the criterion performance of 90%
correct that was required for the full-cue animation sequences
(one-sample t-test, t(4) = 0.9, p = .42, 2-tailed). The observers’ total
identification performance across all five experimental sessions
was 98%, 100%, 100%, 95.6%, and 99.2% correct for observers EM,
JFN, HFN, MCW, and LRJ, respectively.
It is clear from the current results that human observers can
accurately recognize complex solid objects from their deforming
cast shadows. All our observers reported compelling perceptions
of solid objects rotating rigidly in depth. The current findings are
thus similar to those of our previous research on deforming bound-
ary contours and cast shadows (Norman & Raines, 2002; Norman
et al., 2000). It is important to keep in mind, however, that objects
with very simple shapes (e.g. single ellipsoids), when depicted so-
lely by their deforming boundary contours or cast shadows, can
easily appear as non-rigid deformations instead of rigid rotations
in depth (e.g. Mach, 1897; Norman & Todd, 1994; Todd, 1985;
Wallach & O’Connell, 1953). Our stimuli are consistently perceived
as solid objects that rigidly rotate in depth – the convexities and
concavities of the cast shadow boundaries are effective ‘‘features”
that permit the perceptual recovery of 3-D structure and rigid mo-
tion (e.g. see Fig. 6). Mach (1897), Wallach and O’Connell (1953),
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007and Todd (1985) have all noted that identifiable features (that
can thus be tracked over time) lead to the elimination of perceptual
ambiguities and permit the perception of rigid motion in depth.
2. Experiment 2
The results of Experiment 1 demonstrate that our deforming
cast shadows (cast onto flat background surfaces) are as informa-
tive for the discrimination of 3-D object shape as animations of
full-cue photographs. The purpose of Experiment 2 was to deter-
mine whether human observers can similarly identify objects
timulus objects cast onto a flat surface.
logica xxx (2009) xxx–xxx 5when their shadows are cast onto curved background surfaces.
2.2. Method
2.2.1. Apparatus
An Apple dual-processor G4 Power Macintosh was used to dis-
play the static and deforming cast shadows of the objects. The
stimulus patterns were presented on a Mitsubishi Diamond Plus
200 22-inch monitor. The stimulus displays were accelerated using
a Radeon 8500 graphics accelerator card (ATI Technologies, Inc).
The observers viewed the cast shadows from a viewing distance
of 100 cm.
2.2.2. Stimulus displays
The methods used to generate the cast shadows were the same
as those used in Experiment 1. Shadows of the same five objects
(Fig. 5) were cast onto either flat or curved opaque surfaces. The
curved surfaces had a radius of curvature of 14 cm, and were either
elliptic (a hemisphere) or hyperbolic (a ‘‘saddle”, or hyperbolic
paraboloid) in shape. Fig. 7 shows shadows of simple 2-D objects
(squares and diamonds) projected onto flat, elliptic, and hyperbolic
background surfaces – note that the straight edges of the objects
typically project to curved edges in the resulting shadows cast onto
the curved background surfaces (i.e. the distortions are not affine).
Sample shadows of object 1 cast onto the flat, elliptic, and hyper-
bolic background surfaces are shown in Figs. 8 and 9. Elliptic and
hyperbolic surface regions were chosen for the curved background
surfaces in this experiment, because they are the only generic
types of regions that exist on the surfaces of arbitrary curved
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

) cas
cho
ARTICLE IN PRESSFig. 7. .Shadows of simple 2-D objects (squares – top row, diamonds – bottom row
6 J.F. Norman et al. / Acta Psyobjects (i.e. arbitrary curved object surfaces can be mathematically
described or decomposed into elliptic and hyperbolic surface
patches – see Guggenheimer (1977, pp. 212–213) and Hilbert
and Cohn-Vossen (1983, pp. 183–185)). Once again, the shadows
were digitally photographed using a Nikon Coolpix 995 digital
camera (1024  768 pixel resolution). Once captured, the resulting
1200 shadow images (5 objects  3 background surfaces  80
shadows/object/background surface) were then transferred to the
computer.
2.2.3. Procedure
The procedures used were similar to those of Experiment 1.
The observers participated in 10 experimental sessions. Each ses-
sion consisted of a total of 300 trials (6 experimental condi-
tions  50 trials per condition). The six conditions were formed
by the orthogonal combination of three background surfaces (flat,
hemisphere, and saddle) and two motion types (deforming shad-
ows vs. static shadows). The order of objects and conditions within
an experimental session was randomly determined for each
Fig. 8. Shadows of object 1 cast onto the flat background surface. The frame number wit
shadow depicts object 1 in the initial frame of the apparent motion sequence (Frame 1)
motion sequence (Frame 80).
column) surfaces.
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007t onto flat (left column), hemispherical (middle column), and saddle-shaped (right
logica xxx (2009) xxx–xxxsession and observer. For a condition depicting a static shadow,
one of the 80 captured shadows for an object was chosen ran-
domly. In conditions depicting deforming shadows, full rotations
of the objects (i.e. all 80 shadows) were presented. The observers’
task was to identify the object (1–5) presented on each trial from
either type of display (deforming or static shadows). The observers
made their responses by pressing an appropriate key (1–5) on the
computer’s keyboard. The observers were given as much time as
they needed on each trial to view the shadow(s) and to identify
the object. The observers never received feedback regarding their
performance during an experimental session. After completion of
all 10 sessions, a total of 500 responses had been collected for each
of the six conditions (3000 total trials per observer).
As in Experiment 1, prior to the start of an experimental session,
the observers engaged in a series of practice trials. Only deforming
shadows cast upon the flat background surface were used.
Feedback was once again given until the observers’ identification
performance reached 90% correct. The purpose of this experiment
was to determine whether this high level of performance would
hin the apparent motion sequence is indicated for each cast shadow. The upper-left
, whereas the lower-right shadow depicts object 1 in the last frame of the apparent
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

of
s plo
d s
cho
ARTICLE IN PRESS(F(1,3) = 256.3, p < .001, g2 = .99) and background surface
(F(2,6) = 18.1, p < .005, g2 = .86). The interaction between motion
and background surface was not significant (F(2,6) = 3.7, p = .09).
The observers were able to identify the objects from their deform-
ing shadows at very high levels of accuracy (except for some object
shadows projected onto the saddle), but their ability was signifi-
cantly reduced for static shadows. The overall identification accu-
racy was 90% correct (d0 = 2.9) for the deforming shadows and
62% correct (d’ = 1.4) for the static shadows. The observers’ perfor-
mance was best when the shadows were cast onto the flat and
hemispherical background surfaces (83.4% and 79.7% correct,
respectively), but deteriorated when the object shadows were cast
onto the saddle-shaped background surfaces (64.8% correct). At
this point, it is important to keep in mind that chance performance
for this task would be 20% correct (d0 = 0). Consequently, the
observers were able to identify the objects correctly in most
Id
en
tif
ic
at
io
n
Ac
cu
ra
cy
( %
c
or
re
ct
)
Gaussian Curvature
-51 0 51
0
20
40
60
80
100
-51
0
20
40
60
80
100
XW
MODEL
Fig. 12. Experimental and model results for object 1. The identification accuracy i
surface curvature. Flat Surfaces have zero Gaussian curvature, while hemispheres an
8 J.F. Norman et al. / Acta Psyinstances.
Fig. 11 plots the observers’ results for each of the individual ob-
jects. The observers’ performance was consistently good when the
shadows were cast onto the flat background surfaces. The perfor-
mances were essentially identical when the object shadows were
cast onto the hemispherical background surfaces. This equivalence
in observer performance is impressive, given the fact that the
hemispherical background surface creates sizeable non-affine dis-
tortions in the shape of the projected object shadows (see Fig. 7).
Fig. 11 also shows that this equivalence in performance did not al-
ways occur when the object shadows were cast onto the saddle-
shaped background surface (a hyperbolic paraboloid). For this
background surface, the equivalence (i.e. performance similar to
the flat plane and hemisphere) only occurred for objects 3–5.
One can see from the figure that there was a reduction in the iden-
tification performance for objects 1 and 2 when their shadows
were cast onto the saddle. This drop in performance was especially
severe for the shadows cast onto the saddle by object 1.
In order to better understand the observers’ responses, we de-
vised a model to examine the effects of affine transformations on
the shadows’ boundary contours. The boundary contours of the
shadows cast onto the curved background surfaces are subjected
to a parameterized affine transformation. When the shape of a
transformed cast shadow matches that of one of the object shad-
ows cast onto the flat plane, the cast shadow is ‘‘recognized” as
being that of the corresponding stimulus object.
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007The model proceeds as follows – the set of planar stimulus pro-
jections are treated as a baseline, ‘target’ set of shadows: one set of
80 views for each of the five objects used in the psychophysical
experiment. Elliptic and hyperbolic projections of the same five ob-
jects (again, 80 views of each) are treated as the ’probe’ shadows.
The goal of the model is to predict which of the five target ob-
jects a given probe stimulus shadow depicts. To do this, a given
probe stimulus is compared to the target stimuli by way of the
associated boundary contours of each shadow. Rather than com-
paring the entire shadow contour, we chose instead to compare a
collection of non-generic points on each shadow’s contour. A given
shadow contour is decomposed into a fixed number of features
based upon the magnitude of local curvature information available
on that contour. Negative extrema serve to break the object into
parts (e.g. see Hoffman & Richards, 1984; Singh, Seyranian, &
Hoffman, 1999), while the positive extrema mark protrusions or
Background Surface (m-2)
Deforming
Static
HFN
MCWRM
-51 0 510 51
tted as functions of shadow type (deforming vs. static shadows) and background
addles have positive and negative Gaussian curvature, respectively.
logica xxx (2009) xxx–xxx‘‘bumps” within parts (these boundary extrema locations agree
well with human observers’ markings of salient ‘‘features”, see
De Winter and Wagemans (2006), De Winter and Wagemans
(2008) and Norman et al. (2001)). Since the shadow boundaries
of these objects are relatively simple, a range of 10–20 features
per shadow are used. The central motivation for this decomposi-
tion lies in the fact that, based on the aforementioned psychophys-
ical evidence, the information conveyed by these non-generic
points is critical in determining a contour’s perceived shape while
the curvature-generic locations are of lesser importance.
The boundary of each probe shadow, P (as defined by the loca-
tions of the boundary extrema), is then subjected to a non-uniform
affine transformation of the form
P0 ¼
a b
c d
 
P þ
tx
ty
 
The transformation optimizes the values of a, b, c, d, tx, and ty
such that the Procrustes distance between the transformed probe
shadow (P’) and a given target shadow (T) is minimized (for a
description of Procrustes methods in the statistical analysis of
shape, see Goodall (1991)). Intuitively speaking, this process aligns
the contours via translating, rotating, and scaling the probe’s
boundary contour to maximize its similarity with the target.
This transformation optimization is repeated for all possible tar-
get shadows (80 views encompassing 360 for each of the five ob-
jects – a total of 400 fits per probe shadow). The minimized
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

Procrustes distances are computed for the 400 possible views, and
the best fitting probe shadow is assigned to a given target via the
minimum average distance from the target. Since there were 800
probe shadows (80 orientations of five objects cast onto two
curved background surfaces), a total of 320,000 individual shadow
comparisons (probe vs. target) were performed.
Fig. 12 plots the performance of the model and the four individ-
ual observers for object 1. It is important to keep in mind that the
observers were able to successfully identify object 1 when its shad-
ows were cast onto the hemisphere, but their judgments were sig-
nificantly impaired when its shadows were cast onto the saddle
background surface (see Fig. 11). It is clear from an inspection of
Fig. 12 that the model’s performance strongly resembled that
exhibited by three of the four human observers (HFN, RM, and
XW). It is also clear, however, that observer MCW’s performance
hemispherical background surfaces (d’ = 1.97) and performed
poorly when the object shadows were cast onto the saddle-shaped
backgrounds (d’ = 0.2). This pattern of good performance for the
shadows cast onto the hemispherical backgrounds and poor per-
formance for the shadows cast onto the saddle-shaped back-
grounds was qualitatively similar to that of the human observers.
However, our model cannot explain the totality of the human re-
sults. For example, while the model could not correctly identify
the object shadows when they were cast onto the saddle-shaped
background (d’ = 0.2), the human observers fared much better:
their average d’ value for these static shadows was 1.1. It is clear
that while the human observers’ performance was reduced when
the object shadows were cast onto the saddle-shaped backgrounds
(e.g. see Fig. 10), they performed much better in those conditions
than the model.
bla
ved o
J.F. Norman et al. / Acta Psychologica xxx (2009) xxx–xxx 9
ARTICLE IN PRESSis unusual, because unlike the other human observers and the
model, he was able to identify the shadows of object 1 cast onto
the saddle almost as well as those cast onto the hemisphere. When
the model was presented with the shadows of object 1 cast onto
the saddle, it misidentified the object as being object 4 for 65 of
the 80 possible views/orientations (i.e. the model identified object
1 as being object 4 eighty-one percent of the time). Observer RM’s
detailed performance was the most similar to that of the model –
he mistakenly identified object 1 as being object 4 forty-three per-
cent of the time. Why does this particular mistake occur? To an-
swer this, consider Fig. 13. One can readily see that there is a
strong resemblance in shape between the shadows of object 1 cast
onto the saddle and those of object 4 cast onto the flat plane (left
and middle panels, respectively). Observer RM and the model also
consistently confused objects 3 and 4. In particular, the model mis-
identified the shadows of object 3 cast onto the saddle as being ob-
ject 4 sixty-eight percent of the time, while observer RM exhibited
the same confusion 60% of the time. Fig. 13 also illustrates the
strong resemblance in shape between these shadows (object 3 cast
onto the saddle vs. object 4 cast onto the flat plane). The errors of
observer HFN for object 1 are also understandable, given the shad-
ows depicted in Fig. 13. When presented with the shadows of ob-
ject 1 cast onto the saddle, she correctly identified it as object 1
forty-one percent of the time. However, she also mistakenly iden-
tified the object 1 shadows as being those of object 3 forty-nine
percent of the time. A comparison between the left and right pan-
els of Fig. 13 will illustrate that this confusion is not surprising –
depending upon the particular object orientations, the shadows
of object 1 cast onto the saddle can strongly resemble those of ob-
ject 3.
It is true that our model exhibits some of the important charac-
teristics of the human judgments. Across all objects, the model per-
formed well when the object shadows were cast onto the
Fig. 13. Sample cast shadows. One can see from this figure that there is a strong resem
onto the flat plane. This similarity in projected shadow shape (both are smoothly cur
a persistent confusion between these objects for both the model and observer RM. One
resemble those of object 1 cast onto the saddle – this similarity in projected shape resul
conditions.
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.0073. General discussion
The importance of static shadows and silhouettes for human
perception has apparently been appreciated for many hundreds
of years (Baxandall, 1995; Casati, 2004; Gombrich, 1995), but sci-
entific research on the perceptual informativeness of static shad-
ows and silhouettes is continuing (e.g. De Winter & Wagemans,
2008; Hayward, 1998; Norman & Raines, 2002; Norman et al.,
2000; Norman et al., 2001; Tjan et al., 1995; Tse, 2002; Wagemans
et al., 2008). The importance of motion, however, became clear
only in the 20th century. Early research by Miles (1931) and
Wallach and O’Connell (1953) demonstrated that the deforming
shadows that accompany the rotation of an object in depth lead
to the effective perception of both an object’s motion and 3-D
shape. The early contributions by Miles (1931) and Wallach and
O’Connell (1953) were later extended by Todd (1985), Cortese
and Andersen (1991), Norman and Todd (1994), Norman et al.
(2000), and Norman and Raines (2002). This recent research, con-
ducted over the past 25 years, has added greatly to our under-
standing of how deforming shadows and boundary contours
contribute to the human perception of 3-D shape and 3-D motion.
At the same time, this past research has a number of important
limitations. For example, many of these studies utilized objects
that possess very simple 3-D shapes (e.g. ellipsoids, see Cortese &
Andersen, 1991; Norman & Todd, 1994; Todd, 1985). This is an
important limitation, since most naturally shaped 3-D objects gen-
erate relatively complex cast shadows (see for example, Figs. 5 and
6) whose boundaries contain perceptually important convexities
and concavities (Attneave, 1954; De Winter & Wagemans, 2008;
Norman et al., 2001). The shadows of ellipsoids are unusual in that
their outer contours are always convex and never exhibit any con-
cavities (see Fig. 2). The shadows of naturally shaped objects
nce between the shadows of object 1 cast onto the saddle with those of object 4 cast
n the left side, and possess two prominent ‘‘indentations” on the right side) leads to
can also see in this figure that the shadows of object 3 cast onto the saddle also
ts in a persistent confusion between objects 1 and 3 for observer HFN in the saddle
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

undergoing motion also exhibit informative boundary catastrophes
(see Koenderink & van Doorn, 1976) that do not occur for the cast
shadows of moving ellipsoids. A second limitation that is common
to nearly all of the previous studies on this topic is that they inves-
tigated the perceptual effectiveness of silhouettes or shadows that
were cast onto flat background surfaces. In natural (i.e. non man-
made) environments, background surfaces often possess signifi-
cant curvature.
The results of the present study show that the human ability to
recognize solid objects from their cast shadows is relatively robust
to the distorting effects of curved background surfaces. In fact, for
convex hemispherical backgrounds, the observers’ performance
was essentially identical to that obtained when the shadows were
cast onto flat background surfaces. This is an important result for
several reasons. First, the distorting effects of the curved back-
ground surfaces were large. For example, consider the cast shad-
ows depicted in Fig. 7 – notice that the straight edges of the
object project to curved shadow edges on the hemispherical back-
ground surface. If a curved edge exists in a cast shadow, it therefore
can occur for a variety of reasons: it could derive from a curved ob-
ject casting a shadow onto a flat background or it could result from
an object possessing straight, linear edges (like a polyhedron) cast-
ing a shadow onto a curved background. In the general case, then,
the presence of straight or curved edges in a cast shadow boundary
tells us very little about the shape of the original 3-D object, unless
we also know the shape of the background surface. The current re-
tion in more general environmental contexts than is currently
possible.
The current experimental results also showed that the observ-
ers’ recognition performance decreased significantly, when the ob-
ject shadows were cast onto saddle-shaped background surfaces. It
is important to note, however, that the overall performance for the
saddle conditions was still much higher than chance levels (20%),
especially when motion was present (77.8% correct for deforming
shadows, 51.7% correct for static shadows). The exact reason for
the decline in recognition performance for the shadows that were
cast onto saddle-shaped backgrounds is not obvious. One possibil-
ity is that it is because the shadow deformations themselves are
more complicated when shadows are cast onto saddle-shaped
background surfaces. The additional complexity results from the
simple fact that saddle-shaped surfaces curve in depth oppositely
in perpendicular directions, whereas hemispherical surfaces pos-
sess identical curvatures in all directions. Thus, in the case of sad-
dles, the exact orientation of the principal directions of curvature
relative to object parts and features is a critical factor. Consider
Fig. 14. This figure depicts the shadows of a 2-D object shaped like
a ‘‘dumbbell” cast onto both hemispherical and saddle-shaped
backgrounds. It is readily apparent that the orientation of the ob-
ject casting the shadow has no effect when the shadows are cast
onto the hemispherical surface – the shapes of the resulting shad-
ows are identical. However, this is not true for the saddle-shaped
10 J.F. Norman et al. / Acta Psychologica xxx (2009) xxx–xxx
ARTICLE IN PRESSsults are also important in that they suggest future directions for
computational modeling. Current computational models (e.g.
Cipolla & Giblin, 2000; Giblin & Weiss, 1987; Hernández et al.,
2007; Mendonça et al., 2001; Wong & Cipolla, 2004) have been de-
signed to recover information about an object’s 3-D shape from its
silhouette or occlusion boundary contour. They cannot yet recover
shape from the more general shadows that are cast onto curved
background surfaces. The fact that human observers can recognize
3-D object shape accurately despite the large distortions in the
shape of cast shadows caused by curved background surfaces indi-
cates that computational models can be developed that will func-Fig. 14. This figure illustrates the cast shadows of a ‘‘dumbbell” shaped object cast ont
saddle or hyperbolic paraboloid). One can readily see that the orientation of the object ha
orientation of the object relative to the principal directions of background curvature ha
Please cite this article in press as: Norman, J. F., et al. The perception o
logica (2009), doi:10.1016/j.actpsy.2009.01.007background surface. In this case, the orientation of object features
relative to principal directions of background curvature is impor-
tant and does affect the shape of the resulting cast shadows. Per-
haps, this additional complexity in the behavior of shadows
accounts for the reduced performance of the observers and the
model when they attempted to identify the objects from shadows
cast onto the saddle-shaped background surfaces. In other words,
the shapes of shadows cast onto a hemisphere are influenced by
three factors (the 3-D shape of the object, the hemispherical shape
of the background, and the position of the light source), whereas
the shapes of shadows cast onto a saddle are influenced by four fac-
tors (the 3-D shape of the object, the saddle-like shape of the back-
ground, the exact orientation of the principal directions ofo the curved surfaces used in Experiment 2 (top row – hemisphere, bottom row –
s no effect upon the shape of the shadows cast onto the hemisphere. In contrast, the
s a large effect upon the shapes of the shadows cast onto the saddle.
f 3-D shape from shadows cast onto curved surfaces. Acta Psycho-

background curvature relative to object features, and the position
of the light source).
Kersten, D., Knill, D. C., Mamassian, P., & Bülthoff, I. (1996). Illusory motion from
J.F. Norman et al. / Acta Psychologica xxx (2009) xxx–xxx 11
ARTICLE IN PRESSIn summary, we have shown that deforming and static cast
shadows contain valuable amounts of perceptual information
about solid object shape. The results of Experiment 1 demonstrate
that human observers’ discrimination performance is as good with
deforming cast shadows as with full-cue animation sequences. Our
results (e.g. see Fig. 11) indicate that observers can also perform
well if they are asked to discriminate the shape of objects from
shadows cast onto curved background surfaces. In our Experiment
2, the observers’ ability to discriminate between the various 3-D
object shapes was especially good for those shadows that were cast
onto convex hemispherical backgrounds.
Acknowledgements
We thank James T. Todd for providing the images used in Fig. 1.
We also thank John M. Kennedy, James T. Todd, and an additional
anonymous reviewer for their helpful suggestions during the prep-
aration of the manuscript.
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