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Do artists use linear perspective to depict visual space?
Robert Pepperell,
Cardiff School of Art & Design,
Cardiff Metropolitan University,
Cardiff, CF24 0SP, UK.
rpepperell@cardiffmet.ac.uk
Manuela Haertel,
Department of General Psychology and Methodology,
Otto Friedrich University Bamberg,
Bamberg, Germany.
Keywords: Linear perspective; visual space; art; photography; visual perception
Abstract: The question of how to accurately depict visual space has fascinated artists,
architects, scientists and philosophers for hundreds of years. Many have argued that
linear perspective, which is based on well-understood laws of optics and geometry, is
the natural way to record visual space. Others have argued that linear perspective
projections fail to account for important features of visual experience, and have
proposed various curvilinear, subjective, and hyperbolic forms of perspective instead.
In this study we compare three sets of artistic depictions of real-world scenes to linear
perspective versions (photographs) of the same scenes. They include a series of
paintings made by one of the authors, a selection of landscape paintings by Paul
Cézanne, and a set of drawings made as part of a controlled experiment by people
with art training. When comparing the artworks to the photographs depicting the same
visual space we found consistent differences. In the artworks the part of the scene
corresponding to the central visual field was enlarged compared to the photograph and
the part corresponding to the peripheral field was compressed. We consider a number
of factors that could explain these results.
1. Introduction
The question of how to accurately depict our visual experience of the world has been
a subject of controversy in the arts, humanities and sciences for over 500 years. A
widely accepted view is that linear perspective is the correct way to do this because it
uses the same geometric laws that govern the behavior of light and the optics of
human sight as defined in Euclid’s Optics (Gombrich, 1960; Pirenne, 1970; Gibson,
1971; Ward, 1976; Rehkämper, 2003). As one prominent advocate of this view argues,
linear perspective is “the only natural system of perspective” that “corresponds to the
way we actually see the world around us.” (Pirenne, 1952)
Linear perspective is a projective technique for representing the three-dimensional
world on a (normally) two-dimensional plane. Among its most important principles
are that parallel lines leading away from the viewer converge at the vanishing point in
line with the viewer’s eye, that objects diminish in size as they recede and increase as
they approach, that parallel lines perpendicular to the horizon line remain parallel, and
that straight lines in nature generally appear straight in the picture (Walters &
Bromham, 1970). Most technologies for depicting reality (photographic and movie
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cameras, computer generated images, etc.) produce pictures with linear perspective
projection that vary depending on the kind of lens or light sensitive plate being used.
Linear perspective is the correct way to represent the visual world, its supporters
argue, because it is “simply a device to send into the eye the same light distribution as
would be sent by the object itself.” (Pirenne, 1952)
But even those artists who enthusiastically pioneered the application of linear
perspective in painting had doubts about its utility as a method of depicting visual
space. Leonardo da Vinci and Piero della Francesca were both aware that strict
application of its rules in making paintings on flat surfaces led to unnatural
distortions, particularly when dealing with wide angle views (Kemp, 1990; Elkins,
1994). And it has often been observed that straight lines in nature can appear curved
in perception, a phenomenon some artists have felt compelled to record for the sake of
truth to appearance and others have cited in support of various subjective, curvilinear,
or hyperbolic theories of perspective (Herdman, 1853; Hauck, 1879; Panofsky, 1927;
Hansen, 1973; Heelan, 1983; Flocon & Barre, 1988).
Scientific studies have shown that linear perspective renderings of objects or scenes
do not always accord with how observers imagine they should look. For example,
Hagen (1986) found that drawings of cubes created using perspective convergence
were judged less realistic, natural, or accurate than renderings with little or no
perspective convergence. Observers in a study by Pont et al. (2012) preferred a
‘template’ rendering of a cube to versions with greater or lesser perspective
foreshortening. Howard and Allison (2011) showed that adults tend to draw real threedimensional cubes in divergent rather than (mathematically correct) convergent
perspective, which is more in keeping with the way three-dimensional objects were
represented in art prior to the Renaissance. Similar findings were reported by
Deregowksi et al. (1994), where the normal projection of a cube was perceived by
observers as having diverging sides when viewed with lateral displacement. This, the
authors argue, is consistent with the way such forms were depicted in so-called
‘Byzantine perspective’.
Other investigations have found a high level of agreement about judgment of angle
size of large objects in real-world scenes and in photographs of the same scenes,
especially at longer viewing distances (Hecht et al. 1999). Watanabe (2006),
meanwhile, compared the geometrical structures of photographic and stereoscopic
depictions of directly perceived physical space. Significant variations in depth
perception between the depicted and the actual scenes were shown, suggesting
photographic space does not reproduce real physical space. On the basis of eye
tracking studies, Franke et al. (2008) reported a preference for, what they called,
‘perceptually realistic’ multi-perspective renderings of scenes compared to the
mathematically correct, camera-like single perspectives views of the same scenes. The
multi-perspective pictures were based on methods used by artists such as Canaletto,
where a number of viewpoints of the same scene are integrated into one picture.
It has also been pointed out that the position of the viewer in respect to the picture can
affect judgments about perceptual accuracy of the projection method used (Juricevic
& Kennedy, 2006; Todorovic, 2009). Tyler (in press) follows Hardy and Perrin (1932)
in arguing that a linear perspective rendering cannot be properly appreciated without
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viewing it at precisely the same point from which the perspective is constructed,
which is usually impossible since it lies too close to the picture surface.
This study investigates the projective techniques used by artists when rendering visual
space. We were specifically interested in the extent to which artists use linear
perspective when depicting real world scenes. Do artistic renditions of visual space
conform to linear perspective or do they deviate from it, and if so how? To study this
we compared three sets of artistic depictions of real-world scenes to photographically
generated linear perspective depictions of the same scenes. We used a series of 10
paintings made by one of the authors in which the purpose was to depict the entire
contents of the visual field relative to a given object in fixation, a selection of 18
landscape paintings made by Paul Cézanne in the late nineteenth and early twentieth
centuries, and a set of drawings made by 11 participants with art training under
controlled conditions in which the task was to depict a still life scene.
2. Experiments
2.1.1 Experiment 1: Depicting the full visual field
Around 2011 Robert Pepperell made a series of paintings the purpose of which was to
depict the contents of the entire visual field relative to a certain object of fixation
(Pepperell, 2012). Depending on individual anatomy and lighting conditions the
normal human visual field spans some 180 degrees laterally and 120 degrees
vertically (Gibson, 1950; Hershenson, 1999). Cameras normally capture the central
area of the visual field; typically a standard 50mm camera lens on a 35 mm film or
sensor subtends to 43 lateral degrees. This results in the exclusion or cropping of the
part of the scene that would be visible in an observer’s peripheral field (Hagen et al.,
1978; Cutting, 2003). The task here was to depict the full scope of the visual field, as
illustrated in Figure 1.
It was through making these paintings and comparing them to photographs taken of
the same scenes that variations in the sizes of objects became apparent between the
two forms of representation, with objects located in the centre of the field of view
seeming to occupy more pictorial space in the paintings than in the photographs. To
test the reliability of this observation we decided to measure the way objects appeared
in the paintings as compared to photographs of the same scenes. We hypothesized that
an artistic depiction of a scene will differ from a linear perspective photograph of the
scene due to differences in the way artists perceive and record visual space.
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Figure 1. Illustration of the human visual field, including the area of binocular overlap in the
mid-grey area (after Gibson, 1950), and the typical portion captured by a camera, shown in
the darkened central rectangle, approximating to the central part of the visual field, including
the foveated region.
2.1.2 Methods
An example of the paintings used in this part of the study is shown in Figure 2 and
further examples can be seen online http://www.robertpepperell.com/Studio/
index.html. The paintings are mostly in the medium of oil on canvas, with occasional
use of sand and other matter to add texture around the margins. Different shaped and
proportioned canvasses were used, sometimes oval in shape and landscape in format,
between approximately 500 mm to 1000 mm in width. To produce the paintings a
scene was arranged in the studio, or found in the environment, and an object of
fixation chosen. The task then was to record the entire area visible to both eyes when
maintaining the fixation on the chosen object. Registration points were set at the
extreme top, bottom, left and right of the canvas corresponding to the extreme edges
of the peripheral field. The visible objects were then mapped out on the canvas with
the fixation point, or object, being normally located at or close to the centre,
corresponding to the foveal area of the visual field. Measurements of the relative
positions and sizes of objects were made on the basis of the available impressions,
and the final images corresponded as closely as possible to the visual space observed.
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Figure 2. Studio Painting 3 (White Series). Oil and sand on canvas, 2011. An example of
painting by Robert Pepperell showing everything visible when fixating on the vase, painted
on a canvas approximating the shape of the human visual field as seen in Figure 1. Colour
versions of all images available online.
After each painting was made a photograph was taken of the scene that matched, as
closely as possible, the area of visual space captured in the painting (Figure 3). These
photographs were shot using a Canon 5D Mark II DSLR with a full frame (35 mm)
sensor and wide-angle zoom lens. It is important to note that in order to capture the
same visual space it was not possible in all cases to shoot the scene from the same
vantage point or angle it was painted from. As noted above, a 35 mm camera
equipped with a 50 mm lens records a smaller visual angle of the scene than is
available to a human from the same vantage point, if the entire visual field is taken
into account. It was often necessary, therefore, to move the camera further back from
the artists’ vantage point to match the boundaries of the visual space being depicted.
This meant, however, that while the overall area of visual space captured was similar
the views seen by the artist and the camera were not identical. This is due to
differences in the way camera lenses affect the optical structure of the image at
varying distances from the object being photographed; a given object will appear
larger in proportion to the overall picture size when photographed close up with a
wide-angle lens than with a telephoto lens farther away. In addition, the angle from
which objects were viewed during the painting process often differed from the angle
at which the photograph was taken. This is because the artist alternates between the
view of the scene and the view of the canvas during the recording process, and so was
often viewing the object of fixation obliquely. The result is that the objects of fixation
in the paintings and photographs do not always lie at the same point within the
respective picture frames.
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Figure 3. On the left is a painting of a still life scene (Studio Painting 10) and on the right is a
photograph of the same scene capturing, as closely as possible, the same visual space. In this
case the centre of fixation in the painting was on the uppermost flowers in the vase. Both
pictures represent the same visual space despite being different in shape and the objects in the
scene varying in size and distribution.
To compare the way space was depicted artistically versus photographically we first
overlaid the paintings on the matching photographs to see to what extent the
depictions of the scene matched (Figure 4).
Figure 4. An illustration of process whereby paintings were overlaid on their respective
photographs to compare the relative area occupied by each. The painting lies inside the
boundary of the photograph.
Knowing that each painting had been created by reference to a central object of
fixation, we then compared the size of this object relative to the total picture area. To
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do this a rectangle was drawn around the object of fixation on the painting and around
the same object in the photograph (Figure 5). The size of this rectangle was calculated
as a percentage of the total image size. The relative proportions were then compared
in each of the 10 painting-photograph pairs analysed.
Figure 5. In each painting the area occupied by the object of fixation was bounded by a
rectangle. The same object in the photograph was also bounded by a rectangle, shown here in
white.
2.1.3 Results and discussion
Our measurements revealed that although there was good correspondence between the
shape of the objects of fixation in the paintings and the photographs the global
structure of the painting did not correspond to the linear perspective version. The
proportion of the total pictorial space occupied by the object of fixation was
consistently larger in the paintings than in the photographs. As can be seen in Figure
6, the painted objects of fixation accounted for a greater percentage of the total picture
area than their photographic equivalents. At the same time, the objects around the area
of fixation were often depicted smaller than in the photographs. This was revealed by
comparing the overall dimensions of the paintings to the photographs once they had
been rescaled so the size of the object of fixation matched in both cases. On this
measure the paintings occupied between 8% and 72% of the area of the equivalent
photographs.
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Percentage of total picture area occupied by the object
of fixation
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16
Photo
14
Painting
12
10
8
6
4
2
0
Figure 6. Here is shown the proportion, expressed as a percentage, of the total pictorial area
occupied by the object of fixation in the paintings compared to the photographs. The data
show a pattern in which the objects in the paintings occupy a larger percentage of the area
than in the photographs.
While the results show support for the hypothesis it should be acknowledged that the
data collection lacked control in several important respects. First, as noted above, the
paintings and the photographs were not always made from identical vantage points.
Had this been done — perhaps with the use of an ultra-wide-angle lens — then the
object of fixation in the paintings and photographs may have corresponded much
more closely in size. Future studies will investigate this factor more fully, along with
the issue of oblique viewing angle. It should also be noted that the paintings
themselves were, with one exception, representations of a binocular visual field while
the photographs were monocular. This may have accounted for some of the
discrepancy between the painted and photographic depictions in terms how the space
was structured, particularly with objects that were close to the viewpoint where the
differences between the two eyes are more marked. So while these results are
interesting they do not provide conclusive evidence of the hypothesized effect of
enlargement of the area of fixation in painted views. To test whether this effect was
observable in other situations where artistic depictions of scenes are compared to
photographs we carried out two further experiments.
2.2.1 Experiment 2: Cézanne’s depictions of landscapes
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Paul Cézanne (1839-1906) was one of the most influential artists of the modern era
(Rewald, 1986; Danchev, 2012). He produced paintings and drawings on a range of
subjects, including still life, portrait, figure composition, and landscape. His landscape
paintings have held a special fascination for other artists, critics, and philosophers.
The literature on Cézanne contains frequent references to the sensation of depth
engendered by his landscapes and a number of theories have been advanced to explain
this, including his method of rendering solid objects as modulated planes of colour
(Fry, 1927), the way he subordinated the forms on the canvas to the compositional
demands of the picture plane (Novotny 1948), his attempts to accommodate the
binocular features of human vision (Friedenwald, 1955), his application of ‘subjective
curvature’ (Turner, 1981), his use of a form of ‘perceptual perspective’ that
corresponds more closely to human visual experience (Rauschenbach, 1982), or his
use of ‘parallel projection’ to convey the effect of objects seen by a mobile viewer
(Smith, 2013). A frequent subject of debate in such literature is the extent to which
Cézanne obeyed or flouted the laws of linear perspective.
Interest in the way Cézanne produced his landscape paintings, and in particular the
way they often seem to deviate from linear perspective, has led several art historians
to seek out the locations in which they were made in order to photograph them from
the same vantage point (Rewald, 1944; Loran, 1963; Machotka, 1996). The purpose,
among other things, was to analyse the composition of the paintings to understand
how Cézanne arrived at his unique depictions of space. As noted above, because
photographic images conform to linear perspective they can be used to gauge how
closely the artist adhered to its laws. While these analyses have focused on certain
stylistic tendencies, they have discovered no underlying explanation for the so-called
‘distortions’ that appear repeatedly in his art, nor have they led to any consensus about
how he achieved his effects of heightened depth.
2.2.2 Methods
In this experiment we took a sample of 18 from the 70 or so currently available
photographs taken from viewpoints that Cézanne depicted and compared them to the
respective paintings (Figure 7). Our criteria for selecting the sample images were,
first, that they covered the span of the artists’ career in its mature period from the
1870s until his death in 1906, second, that we were able to clearly match the depicted
space in the painting to that in the photograph and, third, that they had an identifiable
‘motif’, or main subject. We chose a chronological spread of paintings in order to
detect if there were any effects of stylistic changes over time. Many of the available
photographs were excluded either because they didn´t allow for accurate enough
alignment between the painted and photograph space or because they overrepresented
a particular part of his career.
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Figure 7. Example of (left) a scene depicted by Cézanne (Well and Grinding Wheel in the
Forest of the Château Noir, Well: Millstone and Cistern Under Trees (Meule et citerne sous
bois), 1892, Oil on canvas, The Barnes Foundation, Merion, Pennsylvania) and (right) a
photograph of the same scene by John Rewald (from Loran, 1963). Both pictures show the
same physical space, although the passage of time between them (some 30 years in this case)
has led to some alterations, notably in the size although not the position of the trees.
We first overlaid the paintings on the photographs, as in Experiment 1, as a simple test
to determine the extent to which they corresponded in their depiction of the same
scene and reveal any immediate differences (see Figure 8). It is worth stressing that,
as with Experiment 1, our aim here was to compare two renditions of the same visual
space as accurately as we could with the available material. In some cases this meant
cropping parts of the paintings or photographs in order to line up the same edges in
each.
Figure 8. An illustration of the process in which the painting is overlaid on the photograph of
the same scene to compare the structure of the depicted space. Here the painting has been
shown with a white border overlaid on the photograph at 50% transparency.
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Next we identified an object, or set of objects, within each painting that corresponded
to the motif, or main subject, of the painting. The criteria for choosing the objects
were, first, that they were more or less centrally located within the image, and second,
that the outlines of the objects matched when the pictures were resized and overlaid
(see Figure 9).
Figure 9. An example of selecting the motif, or main subject, of the painting using the images
in Figure 7. A group of objects were chosen from the centre of the painting (top left) that
could be clearly identified in the corresponding photograph (top right), and then overlaid to
check alignment (bottom). In this illustration the area from the painting is overlaid with 50%
transparency.
We repeated the procedure used in Experiment 1, and drew a rectangle around these
objects in both the paintings and the photographs, taking care to match them as
closely as possible (See Figure 10). We then calculated the size of these ‘motif’ areas
as a proportion of the total image size in both the paintings and the photographs and
expressed these as a percentage.
Figure 10. Illustration showing the placing of bounding rectangles (in white) around the
motif, or objects constituting the main subject of the painting, and around the same objects in
the photograph.
2.2.3 Results and discussion
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As in experiment 1, when the paintings were overlaid on the photographs there were
substantial differences between the way space was depicted in each case, suggesting
the artist was not systematically applying the laws of linear perspective to the scene as
a whole.
Measurement of the proportion of pictorial space occupied by the motif in the
painting compared to the photograph produced the results shown in Figure 11. In all
the examples measured the motif object or objects occupied a larger proportion of the
pictorial space in the painting than in the equivalent photograph. This value varied
across the sample but there was no pattern to suggest it was linked to the
chronological changes style over the period studied. As we saw in the previous
experiment, the artist was not only enlarging the area of the central motif but also
compressing the space around it. When the paintings were resized so that the
bounding boxes matched those in the photographs they occupied between 26% and
96% of the area of the photograph, despite depicting the same visual space.
Percentage of total picture area occupied by
the object of fixation
35
Photograph
30
Painting
25
20
15
10
5
0
1867
1906
Figure 11. Shown is the proportion, expressed as a percentage, of the total pictorial area
occupied by the central motifs in the paintings compared to the photographs. The data shows
a clear trend in which the motifs in the paintings occupy a larger percentage of the pictorial
area than in the photographs.
As with experiment 1, the fact that the materials we used were created for artistic
rather than scientific purposes made them less suitable for precise or consistent
measurement. We were not able to independently verify that the photographs were
taken from exactly the same station from which the paintings were made, or indeed if
the paintings were made from a single viewpoint (Smith 2013). Even in the cases
where the paintings and photographs matched well there were some minor variations
between the areas of physical space depicted in each, often due to the passage of time.
In addition, our decisions about which motif objects to measure and where to place
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the bounding boxes and how to crop the images were a matter of judgment. For these
reasons the trends shown in the data must be treated with caution as they are based on
a number of approximations.
However, if Cézanne did indeed represent visual space according to these
organizational principles, knowingly or intuitively, then it would be consistent with
observations made elsewhere about his style, and also with comments the artist
himself made. The author of one of the most important surveys of Cézanne’s
composition methods notes on several occasions the tendency of the artist to enlarge
the motif relative to the space around it, although he attributes this to decorative rather
than perceptual imperatives (Loran 1963). The author of a more recent publication
comparing (freshly taken) photographs to Cézanne’s paintings recognised the same
tendency toward enlargement of the motif but denied it represented any deviation
from traditional perspective. Rather, he argues the artist was making adjustments that
served the pictorial balance of the painting concerned (Machotka 1996).
Cézanne’s motive for consistently enlarging the objects in the central area of his
paintings, and whether he did so in accordance with or despite the laws of linear
perspective, continues to be the subject of debate. But we get some hint of his views
from a comment he made to fellow artists in 1905, which acknowledges his lack of
adherence to conventional academic methods: ‘I am a primitive, I have a lazy eye. I
applied twice to the Ecole des Beaux-Arts, but I can’t pull a composition together. If a
head interests me, I make it too large.’ (in Doran, 2001)
Despite Cézanne’s self-deprecating remarks, our study also revealed his remarkable
skill as a draftsman in being able to closely follow the local form of his motifs, as
compared to the photographs, even if the global structure of the paintings varies
significantly. This becomes clear when his paintings are resized and overlaid on the
photographs, as can be seen the two examples shown here in Figure 12. It suggests
that any global distortions or deviations from perspectival norms in these works were
not due to observational deficiencies or lack of artistic ability. The present study
supports the conclusion of Rauschenbach (1982) that the perspectival ‘oddities’ notes
by many experts on Cézanne are the result of his attempt to represent in paint his
perception of space and not an inability to accurately render what he saw.
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A
B
Figure 12. A and B are schematic outlines of two of the Cézanne paintings used in the
experiment illustrating the way his depictions of the central motifs correspond closely to the
photographs of the scenes. The darker outlines show the objects as painted by Cézanne and
the lighter outlines show the same objects as they appear in the photographs. The smaller inset
rectangle shows the area of the painting. Note that the right hand edge of the central form in A
and the objects located in the lower left of B line up well, despite the variance in size between
the painting and photograph in each case. This suggests the deviations from linear perspective
were not arbitrary or accidental.
2.3.1 Experiment 3: Controlled drawing study
Given the similarities in the way visual space was depicted in the two cases above we
wanted to see whether depictions by other people with art training would show the
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same tendency. We designed an experiment in which participants drew a still life
scene. Unlike in the previous two experiments, here we were able to control a range
of variables such as the dimensions of the scene, location of viewing station, etc.,
which allowed more robust and accurate data gathering.
In this experiment we were interested to discover, first, to what extent participants
would produce pictures that conformed to linear perspective. Second, we investigated
whether being directed to pay attention to a central object or motif within the scene
would affect participants' judgments about size and position of the objects they drew.
We know that the paintings used in experiment 1 were made by reference to a specific
fixation point or central object, and we suspected the same function was served by the
motif in the Cézanne paintings. Finally, we looked at whether the inclusion of objects
at the edges of the scene would affect the depicted size and position of the central
motif. Having a wider distribution of objects in the scene poses different challenges in
terms of ‘fitting everything in’ to a given space compared to a scene with more
centrally arranged objects. Again, we used photographs to generate the correct linear
perspective views. On the basis of the preceding experiments we predicted
participants would chose the centrally located object (a brass teapot) as the main motif
and depict it larger than it would appear in the equivalent photographs.
2.3.2 Methods
2.3.2.1 Participants
There were 11 participants (6 male, 5 female) all of whom were undergraduate or
graduate students at Cardiff School of Art and Design with general fine art training
but no formal instruction in linear perspective methods. Ages ranged from 20 to 45
years (M= 28.36; SD=8.34). All had normal or corrected-to-normal vision. They were
recruited on the basis they were taking part in a ´drawing study’ but were told nothing
about the purpose of the experiment. No payment or credits were offered for
participation and they gave informed consent.
2.3.2.2 Procedure
We created a still life scene consisting of everyday objects (Figure 13). The objects
varied in size, the smallest being on the left of the scene and the tallest on the right. A
rectangular area was marked off in black tape on the wall behind the objects
corresponding to the area shown in Figure 13. Participants were given a sheet of white
paper (size 841 x 594 mm), a drawing board and charcoal. The paper was identical in
aspect ratio to the still life scene and its edges were also marked off with black tape. A
chair was set up in a fixed position 2.3m from the still life scene, and all participants
were seated as they drew.
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Figure 13. The still life scene drawn by participants in group 1. The black line shows the area
they were required to draw, which corresponded in aspect ratio to the sheet of paper they were
given to draw on.
The first 6 participants (group 1) were asked to draw as accurately as they could what
they could see in the marked off area (condition A). This instruction was designed to
elicit the most direct transcription of their visual experience of the scene, and to avoid
them being concerned with artistic style or other aesthetic issues. They were given no
time limit, but each took approximately 10-15 minutes. Then the same participants
were asked to make a new drawing, but this time they were directed to pay attention
to the brass teapot in the centre of the scene (condition B). We wanted to see whether
fixating on a specific object or motif, rather than taking in the scene ‘as a whole’,
affected the result.
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Figure 14. The still life scene drawn by participants in group 2. The addition of outlying
objects was to test whether the depiction of the scene would change once a wider distribution
of objects had to be fitted onto the paper.
We then modified the still life by including outlying objects at the left and right of the
scene to test the effect of having to accommodate a wider spread of objects within the
same pictorial area (Figure 14). A further 5 participants (group 2) then drew this
scene, first being asked to draw it as accurately as they could (condition A), and then
being asked to pay attention to the teapot and draw the scene again (condition B) in
the same way as group 1.
A photograph was taken of both scenes with the camera located at the same distance
from the scene as the participants, and in line with the eye of a person of average
height. We used a rectilinear 50mm lens on Canon 5D Mark III with a 35mm sensor
and cropped the photograph to fit the size of the marked off area in the scene.
2.3.2.3 Method of measurement
As with the experiments above, we first overlaid the drawings on the photographs,
this time knowing exactly the areas being compared, to ascertain the extent to which
the drawings conform to linear perspective. Next we drew a bounding rectangle
around the teapots in the drawings and photographs and calculated the size of this area
relative to the total area of each. Finally, we measured the absolute area occupied by
one of the outlying objects drawn by group 2 (the bag) in order to compare its size
between the different conditions.
2.3.3 Results and discussion
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Figure 15. Samples of drawings produced by participants. In the top row are drawings by
group 1 and in the lower row by group 2, all in condition A.
Figure 15 shows some sample drawings made during the experiment. As can be seen
in Figure 16, we found the same tendency in this as in the two previous experiments
in which the central object, or motif, was depicted larger in the drawings than it was
in the photographs. This was true of all the drawings made.
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30
Condition A
Condition B
Area of picture occupied by teapot in %
25
20
15
10
5
0
Photo
Group 1
Group 2
Figure 16. Showing the amount of picture area occupied by the brass teapot in the
photographs and in the drawings done by group 1 (no outlying objects) and group 2 (with
outlying objects). Condition A required participants to draw the scene accurately while
condition B required them to pay attention to the teapot. The size of the teapot is calculated as
a mean percentage of the total picture size.
To determine any differences between the results generated by group 1 (who drew the
scene without outlying objects) and group 2 (who drew the scene that included
outlying objects) we used the non-parametric Mann-Whitney-U-Test. This revealed
no significant differences between the groups 1 and 2 for conditions A and B.
However, the teapot in condition A for group 2 was depicted as somewhat smaller
than in other cases, probably due to the additional constraint imposed by the outlying
objects. This effect was negated, however, when participants were asked to attend to
the teapot (condition B). To determine the significance of any differences between
conditions A (where participants were asked to draw the scene accurately) and
condition B (where they were asked to pay attention to the teapot) we used the nonparametric Wilcoxon signed-rank test. This revealed no significant difference between
the conditions (p= .131). As with the two previous experiments, the drawings were
smaller than the photographs when resized so that the teapots matched. Expressed as
mean values, the drawings done by group 1 were 41% of the size of the photographs
under condition A and 34% under condition B, while the figures for group 2 were
48% for condition A and 33% for condition B.
Despite the lack of statistically significant differences between the groups and the
conditions the results were consistent with the previous two experiments and in line
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Revised version 3 March 2014
with the prediction that participants would tend to enlarge the central motif object
compared to the linear perspective photograph. Also as expected, participants chose
the centrally located teapot as the main object or motif, even before being directed to
pay attention to it. The fact that the relative size of the teapot was not significantly
altered by the direction to attend to it seems to corroborate this. Moreover, the teapot
was not the largest object in the original scene (the vase of flowers on the right was
taller) so it was probably chosen as prominent because of its position rather than its
size.
Lastly, we found a tendency to depict an outlying object as smaller in the drawings
than in the photographs, as can be seen in Figure 17. This is consistent with the earlier
two cases, where objects at the periphery of the visual field were shown smaller than
their photographic equivalents.
Area of picture occupied by bag in %
100
90
80
70
60
50
40
30
20
10
0
Photograph
Condition A
Condition B
Figure 17. Showing the area occupied area by the outlying bag (in square cm) in the
photograph and in condition A (draw the scene) and B (pay attention to the teapot) expressed
as a mean value of all samples.
We found no significant difference between the size of the bag in condition A
compared to the photograph. However, under condition B the bag was significantly
smaller in the drawings and was rendered smaller as the size of the teapot grew. This
is indicative of the same peripheral shrinking effect seen in experiments 1 and 2.
Finally, it should be noted that in this experiment the eye heights of participants
would have varied due to differences in height, although as not subjects were
abnormally tall or short we believe these variations would have a negligible impact on
their performance.
20
Revised version 3 March 2014
3. General discussion
Throughout history artists have used many different projective techniques to depict
visual experience and only relatively rarely have they strictly conformed to linear
perspective (Hagen, 1986); there are countless ways to portray the visual world. So, it
is not surprising that the artworks studied here deviated from its rules. What is
interesting, however, is that they deviated from linear perspective a particular and
consistent way. Across the three sets of pictures we found a tendency to substantially
enlarge the area of the scene corresponding to the central visual field and diminish the
periphery compared to the linear perspective rendering. What could account for these
tendencies?
It has long been known that under certain conditions visual space can appear curved
or bulged. Helmholtz (1867) psychophysically investigated the way objectively
curved lines in a checked pincushion pattern can appear subjectively straight on close
monocular viewing (Oomes et al. 2009). And in an influential essay, in which he
advanced a theory about the inability of linear perspective to depict the essentially
curved experienced of visual perception, the art historian Panofsky (1924) noted the
reverse effect in which a chessboard appears to ‘swell out like a shield’ when
approached. A more recent study of the same ‘bulging grid’ phenomena acknowledges
it still lacks explanation (Foster and Altschuler, 2000). Other historic experiments,
such as those conducted by Blumenfeld (1913) in which participants were presented
with pairs of rows of lights, viewed binocularly, that were adjusted until they
appeared to form a parallel alley, provided evidence that we judge some curved lines
to be straight. On the basis of these and other experiments Luneberg (1947) proposed
that all visual space is hyperbolic, that is, curved. And this led to further proposals
about the advantages of depicting 3-dimensional space in hyperbolic geometry rather
than projective geometry as it approximates more closely to visual experience (Finch,
1977).
There is evidence that attention can affect the way visual space is perceived. Suzuki
and Cavanagh (1997) showed that perception of space is distorted around the focus of
attention, effectively expanding the perceived space at this point. This builds on
earlier research showing shrinkage the receptive field toward the focus of attention
(Desimore et al. 1990), possibly contributing an enhancement of visual processing for
the attended area. In experiments using moving stimuli Anton-Erxleben and
colleagues (2007) also reported a correlation between attention and increase in
perceived size of the stimulus, an effect they attributed to distortion in the retinotopic
distribution of receptive fields. A more recent study using distance estimation tasks
also found perceptual expansion around the locus of attention (Wardack et al., 2011).
This led the authors to doubt that subjective representations of space corresponded to
objective external space. Based on their experiments, Liverence and Scholl (2011)
also report a disparity between the structure of objective space and the way we
perceive it, showing that selective attention can stretch and squeeze the
“representational fabric of space in counterintuitive ways”. Vickery and Chun (1994)
demonstrated a somewhat different but related effect in which the perception of
objects distorted or ‘warped’ the appearance of space such that distances within
objects appear larger than objectively equivalent distances seen on a ground. The
authors attribute the effect, at least in part, to the role of attention. However, not all
the evidence is conclusive in this regard. Masin (1999) obtained results when the
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Revised version 3 March 2014
effects of attention on estimation of line length were studied, with some participants
showing a tendency to see the line as larger, while some saw it as smaller. None of
these studies, we should stress, were conducted using natural scenes, and at this stage
it is not clear to what extent their findings are applicable to the pattern found in the
present study, which used only natural scenes.
Even putting aside the influence of attention the perceived enlargement effect may be
due, in part at least, to the so-called cortical magnification factor (Anstis, 1998). In
primates a greater amount of the visual cortex is dedicated to processing information
from the central area of the visual field as compared to the peripheral area, and is
thought to be linked to the greater acuity and resolution of foveal vision (Whitteridge
1961). Recent neuroscientific studies have investigated the link between cortical
magnification and size perception (Schwarzkopf et al. 2013). However, Strasburger at
al. (1994) have showed that cortical magnification applies only to some visual
discrimination processes and not all, and so it is not clear that this anatomical feature
could entirely account for the effect found in the present study.
There is also evidence that the corollary of the central field enlargement effect — the
relative shrinkage of objects in the peripheral field — may be a basic feature of
human vision. Newsome (1972) showed that the perceived size of peripherally-seen
objects decreases with eccentricity, a phenomenon that both Helmholtz and James had
noted in the nineteenth century. The effect was replicated with different apparatus by
Schneider et al. (1978) and Thompson and Fowler (1980).
Another source of difference between artistic and linear perspective depictions of
scenes could be that we misperceive, and hence misrepresent, the visual world.
Gombrich (1984) noted the way artists, especially untrained artists, relied on idealized
memories, or schema, of objects when depicting them, in spite of what might be
visually present. To explore this further Cohen and Bennett (1997) looked at several
possible causes of the inability of most people to accurately draw what they see. They
conducted a series of experiments in which they asked participants to copy images
and measured how accurately they had done so. They concluded the reason most of
the drawings were very inaccurate was that the participants had deluded themselves
about what exactly they were looking at, relying on schematic memories of the
objects rather than direct observation. In a related study Mitchell et al. (2005) found
that errors in copying drawings could be exacerbated by size constancy and
perspective illusions, showing perceptual distortions can interfere with the task of
accurately replicating what is seen. In the present study, however, we think the effect
of reliance on schema is minimal given that none of the participants were untrained
artists, and all were tasked with depicting as accurately as they could what they saw.
Cézanne explicitly declared his desire to faithfully record visual impressions of nature
rather than idealized forms: “I paint as I see, as I perceive” (in Rewald, 1954).
Some studies have sought to link skill in artistic depiction to accuracy in judging
visual angles (Carson and Allard, 2012; Carson et al., 2013). Using drawings of still
life scenes, as in the present study, the researchers measured the ability of both expert
and non-expert artists (defined by years of experience) to ‘correctly’ depict angles and
proportions in the scene compared to a photograph. Deviations from the photograph
were classified as ‘errors’, and the photograph was spoken of in terms of a ‘ground
truth’. In both studies the researchers found the ability of participants to accurately
22
Revised version 3 March 2014
copy a scene varied across the picture, being closer to the photograph in some areas
than others. They attributed this variation to the level of experience of the artist and
the affect of top-down, contextual knowledge. We found similar variations in our
experiments in which some shapes in the artworks matched closely those in the
photographs even if they deviated in size (see Figure 12). However, our study
suggests deviations from photographs may not necessarily be the result of error or
inability but a consequence of the fact that artists are recording features of their visual
experience not adequately captured in photographs. This raises an important
methodological point that has a bearing on all studies that attempt to measure artistic
skill by comparison with photographs. We have apostrophised the terms ‘correctly’,
‘error’ and ‘ground truth’ because the evidence collected here challenges the
assumption the photographic depiction of the scene represents accurately what the
participants would have visually experienced. Humans, after all, are not cameras.
It is interesting to note that other major artists have shown the same tendency as
reported here, including Jean-Dominique Ingres (1780-1867), John Constable (17761837), and Vincent van Gogh (1853-1890). Although Ingres and Constable were
active before the invention of photography some scenes drawn and painted by these
artists have subsequently been photographed. (Rewald, 1942; Rewald, 1943)
Constable left a series of remarkable drawings made by tracing the outline of objects
seen through a glass plate with one eye while restraining the position of his head
(Fleming-Williams, 1990). These drawings are effectively correct in linear perspective
and can be compared to the final paintings he made on the same spot, often on the
same day. On the basis of the limited material available from these artists, and using
the same methods as above, we have found identical tendencies of spatial depiction as
reported elsewhere in this study, although further work will be needed to analyze
these examples systematically. In addition, we find other examples of artists reporting
the same enlarging effect of the object of fixation that we saw in the quote from
Cézanne above. The sculptor Alberto Giacometti gave a intriguing account of the
apparently strange proportions in some of his sculpted figures, noting that the more he
worked on any piece of the clay used to represent a part of a body the bigger it looked
(in Sylvester, 1994). And David Hockney, a major British artist with a deep interest in
perception, said: “If I glance at the picture of Brahms on the wall over there, the
moment I do he becomes larger than the door. So measuring the world in a
geometrical way is not that true.” (in Gayford, 2007).
But even if artists who depict the world in this way are accurately depciting their
experience of visual space does it follow that non-artists perceive space in this way
too? The limited evidence available so far is inconclusive: some have found
heightened perceptual skills due to the training in drawing artists often receive
(Kozbelt & Seeley, 2007, Perdreau & Cavanagh, 2013a). But there are also
suggestions that artists have no special access to their low level vision (Perdreau &
Cavanagh 2013b).
Although there have been suggestions it existed in antique times in some form
(Edgerton, 1975; Tyler, in press) the full development of linear perspective occurred
quite late in the history of human image making; initially it spread slowly and only
within a very confined geographical region (Veltman, 1986). There is evidence that
not all viewers could readily appreciate early examples of linear perspective; sixteenth
century architectural drawings of planned fortifications in perspective sometimes
23
Revised version 3 March 2014
required supplementary 3-dimensional models to help potential clients visualise the
structures being represented (Veltman, 1979). In the context of the vast history and
diversity of ways humans have represented the visual world the relatively recent and
localised occurrence of linear perspective seems, if anything, to be an anomaly rather
than the norm — certainly prior to the industrial development of lens-based imaging
devices in the nineteenth century. This implies it is not an obvious or natural way to
represent visual space (Hagen, 1986; Deregowski, 1994).
Lastly, while not directly addressed in the present study, the issue of viewing position
in relation to the scene and in relation to the depiction of the scene is likely to be
important to further work in this area. As noted above, linear perspective projections
assume an ideal viewing point at the ‘centre of projection’ that, in the case of most
pictures, is practically impossible to adopt, being too close to the picture surface for
normal vision (Tyler, in press). Given that we usually see paintings and photographs a
long way removed from the centre of projection it may be that some of the
discrepancies between the projective techniques used by artists and those seen in
linear perspective depictions are compensations for the fact that the works are viewed
from some distance away. Key features of a composition that an artist wants to
emphasize will be more prominent if enlarged than if rendered at the mathematically
correct size when viewed from a distance. Likewise, a mathematically correct
rendition of a key feature viewed at the ideal distance would appear far more
prominent in the visual field of the viewer compared to the surrounding matter. The
fact that true linear perspective images can rarely, if ever, be observed under ideal
conditions may have contributed to the artistic search for alternative projective
techniques that better represent our experience of visual space when the results are
viewed from normal distances.
4. Conclusion
Our study showed that artistic depictions of real world scenes by two professional
artists and a group of art students tended to enlarge the area in the scene
corresponding to the central visual field and diminish the size of areas corresponding
to the peripheral visual field compared to photographs of the visual space. Both these
tendencies deviate from the rules of linear perspective, which require receding objects
(often located in the picture centre) to diminish while approaching objects (such as the
ground or walls close to the viewer seen in the peripheral field) grow. While there are
local correspondences in object shape between artworks and photographs the global
structures diverge. This suggests artists are using a different kind of projective
technique from linear perspective, but one that may more closely represent how the
visual space is experienced from the vantage point being depicted, or how best to
record that space on a given surface from a given point of view.
A number of interesting question remain. If the projective technique attributed to the
artists discussed here more accurately depicts our experience of a given visual space
then do the resulting pictures appear more natural, realistic, or spatially convincing
than their linear perspective counterparts? If so, this may help to explain why
Cézanne’s landscapes are so acclaimed for their evocation of depth. On the other
hand, would such artistic depictions of subjective effects merely fall foul of the El
Greco Fallacy in which attributions of distortions in pictures to perceptual distortions
24
Revised version 3 March 2014
in the ‘eye’ of the artist are seen as erroneous on the grounds that the effect would be
distorting again what is already distorted (Firestone & Scholl, 2013)?
Unfortunately these intriguing problems are beyond the scope of this paper, but they
suggest a promising line of future research in which the kinds of tools recently
developed for measuring perceived depth in pictures (Koenderink et al. et al. 2011)
could be usefully employed. If we were to find that pictures produced according to the
principles discussed here were rated more positively than those produced by linear
perspective in terms of perceived depth, or proximity to visual experience, or even
aesthetic merit, then it would be significant for both art and the science of perception.
Acknowledgments
Thanks to Anja Ruschkowski for help in preparing the study, to Claudia Muth, Claus
Christian Carbon and Heiko Hecht for valuable suggestions on the manuscript, to Jon
Clarkson for bringing Constable’s perspective drawings to our attention, and to an
anonymous reviewer for helpful comments and suggestions.
This work was supported by the Cardiff Metropolitan University Research &
Enterprise Investment Fund and the Erasmus exchange programme of the European
Union.
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