Perception, 2014, volume 43, pages 395 – 416

doi:10.1068/p7692

Do artists use linear perspective to depict visual space?

Robert Pepperell1, Manuela Haertel2 1

 Cardiff School of Art & Design, Cardiff Metropolitan University, Cardiff CF24 0SP, UK;  Department of General Psychology and Methodology, Otto Friedrich University Bamberg, Bamberg, Germany; e‑mail: [email protected] Received 19 January 2014, in revised form 29 March 2014, published online 14 May 2014 2

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 correct 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 with 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 with 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 with the photograph, and the part corresponding to the peripheral field was compressed. We consider a number of factors that could explain these results. Keywords: linear perspective, visual space, art, photography, visual perception

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 behaviour of light and the optics of human sight as defined in Euclid’s Optics (Gibson, 1971; Gombrich, 1960; Pirenne, 1970; Rehkämper, 2003; Ward, 1976). 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, page 170). Yet even major authorities of perspective theory have recognized perspectivally correct images do not always appear correct to the viewer. Thomas Malton (1775), who wrote a widely used handbook of perspective for artists and architects in the 18th century, had to admit: “it is evident that there is manifest difference between the Representation of an Object on a Plane and its true Appearance” (page 22). 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 cameras, computer-generated images, etc) produce linear perspective projections. 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, page 180).

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But some of the artists who pioneered the use of linear perspective in painting, such as Leonardo da Vinci and Piero della Francesca, soon realized its limitations as a method of depicting visual space. They were aware it produced unnatural distortions when wide-angle views were projected onto a plane (Elkins, 1994; Kemp, 1990). And it has frequently 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 (Flocon & Barre, 1988; Hansen, 1973; Hauck, 1879; Heelan, 1983; Herdman, 1853; Panofsky, 1924). 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 three-dimensional cubes in divergent rather than (mathematically correct) convergent perspective, which is more in keeping with the way three-dimensional objects were represented in much European art prior to the Renaissance. Similar findings were reported by Deregowksi, Parker, and Massironi (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, van Doorn, & Koenderink, 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’ multiperspective renderings of scenes compared with the mathematically correct, camera-like single-perspective views of the same scenes. The multiperspective 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; Todorović, 2009). Tyler (in press) follows Hardy and Perrin (1932) in arguing that a linear perspective rendering cannot be properly appreciated without 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 with 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 late19th and early-20th centuries, and a set of drawings made by eleven participants with art training under controlled conditions in which the task was to depict a still-life scene.

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2 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 180–190° laterally and 120–130° vertically (Gibson, 1950; Hershenson, 1999). A camera pointing at a real-world scene will normally capture only a portion of the total area visible to a human viewer from the same vantage point, this portion equating roughly to the central area of the visual field and including the foveated region. Typically, a standard 50 mm camera lens on a 35 mm film or sensor captures an area that subtends to 43° laterally. This results in the exclusion or cropping of the part of the scene that would be visible in an observer’s peripheral field (Cutting, 2003; Hagen, Jones, & Reed, 1978). The task in making the paintings discussed here was to depict the full scope of the visual field, as illustrated in figure 1.

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.

It was through making these paintings and comparing them with 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 appearing 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 with 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. 2.1  Methods An example of the paintings used in this part of the study is shown in figure 2, and further examples can be seen in colour 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 and 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 region.

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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.

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(b) Figure 3. (a) A painting of a still-life scene (Studio Painting 10 ); (b) 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.

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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 artist’s 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 (Cooper, Piazza, & Banks, 2012). 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 alternated 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. 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 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 analyzed.

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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.

2.2  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 with 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. While the results support 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—

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Figure 6. The proportion, expressed as a percentage, of the total pictorial area occupied by the object of fixation in the paintings compared with 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.

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perhaps with the use of an ultra-wide-angle lens—the object of fixation in the paintings and photographs may have corresponded 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 of 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 with photographs, we carried out two further experiments. 3 Experiment 2: Cézanne’s depictions of landscapes Cézanne (1839–1906) was one of the most influential artists of the modern era (Danchev, 2012; Rewald, 1986). He produced paintings and drawings of 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 (Loran, 1963; Machotka, 1996; Rewald, 1944). The purpose, among other things, was to analyze 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 highlighted certain stylistic tendencies, they have discovered no underlying explanation for the so‑called ‘distortions’ that appear repeatedly in Cézanne’s art. Nor have they led to any consensus about how he achieved his effects of heightened depth. 3.1  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 with the respective paintings (figure 7). Our criteria for selecting the sample images were, first, that they covered the span of the artist’s career in its mature period from the 1870s until his death in 1906; second, that we were able to 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 did not allow for accurate enough alignment between the painted and photograph space or because they overrepresented a particular period of his career.

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(b) Figure 7. (a) An example of a scene depicted by Paul Cézanne, Millstone and Cistern under Trees (La Meule et citerne en sous-bois), 1892–4, oil on canvas, 25⅝ × 31⅞ inches (65.1 × 81 cm) as shown in Loran (1963) and reproduced here by kind permission of the Barnes Foundation (Image © The Barnes Foundation). (b) A photograph of the same scene from Cézanne’s Composition: Analysis of His Form with Diagrams and Photographs of His Motifs, by Erle Loran (© 1971 by Erle Loran, published by the University of California Press). Both pictures show approximately the same physical space, although the passage of time between them (some 30 years, in this case) has inevitably led to some alterations.

We first overlaid the paintings on the photographs, as in experiment 1, to determine the extent to which they corresponded in their depiction of the same scene (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 edges. 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).

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Figure 8. An illustration of the process in which the painting is overlaid on the cropped photograph of the same scene to compare the structure of the depicted space. Here the painting has been shown schematically with black lines, while the photograph is shown with grey lines.

Figure 9. An example of selecting the motif, or main subject, of the painting and photograph in figure 7, represented here schematically. A group of objects were chosen from the centre of the painting (left) that could be clearly identified in the corresponding photograph (right).

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 9). 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.

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3.2  Results and discussion Measurement of the proportion of pictorial space occupied by the motif in the painting compared with the photograph produced the results shown in figure 10. 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 in 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 approximately the same visual space. 35

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Figure 10. The proportion, expressed as a percentage, of the total pictorial area occupied by the central motifs in the paintings compared with the photographs. The data show a 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 did not allow for precise or consistent measurement. We were not able to independently verify that the photographs were made from exactly the same vantage point as the paintings, 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 still 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, where to place the bounding boxes, and how to crop the images were a matter of judgment. It is also likely that some of the reproductions of Cézanne’s paintings included less of the picture area than was actually painted; they may have been photographed in frames that overlapped the edges, which were subsequently cropped out. For these reasons the data must be treated with caution. 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

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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 with Cézanne’s paintings recognized 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).

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(b) Figure 11. (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 figure 11a and the objects located in the lower left of figure 11b 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.

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Cézanne’s motive for 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, continue 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, page 86). 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 with 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 in the two examples shown in figure 11. 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’ noted 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. 4 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 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 and location of vantage point. 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 with 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 that participants would choose the centrally located object (a brass teapot) as the main motif and depict it larger than it would appear in the equivalent photographs. 4.1  Methods 4.1.1  Participants. There were eleven participants (six male, five female), all of whom were undergraduate or graduate students at the Cardiff School of Art and Design with general art training but no formal instruction in linear perspective methods. Ages ranged from 20 to 45 years (M = 28.36 years; SD = 8.34 years). 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. 4.1.2  Procedure. We created a still-life scene consisting of everyday objects (figure 12). 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 12. Participants were given a sheet of white paper (size 841 × 594 mm), a drawing board, and charcoal. The paper was identical in aspect ratio

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Figure 12. 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.

to the still-life scene, and its edges were also marked off with black tape. A chair was set up in a fixed position 2.3 m from the still life scene, and all participants were seated as they drew. The first six 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. 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 13). A further five 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 followed common photographic practice by using a rectilinear 50 mm lens on a camera (Canon 5D Mark III) with a 35 mm sensor (Cooper et al., 2012). We cropped the photographs to fit the size of the marked-off area in the scene. 4.1.3  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.

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Figure 13. 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.

4.2  Results and discussion Figure 14 shows some sample drawings made during the experiment. As can be seen in figure 15, 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.

Figure 14. 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.

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Figure 15. 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 nonparametric 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 condition 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 = 0.131). 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 with the prediction that participants would tend to enlarge the central motif object compared with 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 16. This is consistent with the earlier two cases, where objects at the periphery of the visual field were shown smaller than their photographic equivalents.

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Figure 16. The area occupied 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 with 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. 5 General discussion Throughout history, artists have used many different projective techniques to depict visual experience, and only relatively rarely have they strictly applied the laws of linear perspective (Hagen, 1986). It is not necessarily surprising, therefore, that the artworks studied here deviated from its rules; there are countless ways to depict the visual world. What is interesting, however, is that the works studied here deviated from linear perspective in 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 with the linear perspective rendering. What could account for this? It has long been known that under certain conditions visual space can appear curved or bulged. Helmholtz (1867/1962) psychophysically investigated the way objectively curved lines in a checked pincushion pattern can appear subjectively straight on close monocular viewing (Oomes, Koenderink, van Doorn, & de Ridder, 2009). And in an influential essay, in which he advanced a theory about the inability of linear perspective to depict the way straight lines can appear curved in 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 & Altschuler, 2001). Other historic experiments, such as those conducted by Blumenfeld (1913) in which participants were presented with pairs of rows of lights, viewed binocularly, which 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 (1949) proposed that all visual space is hyperbolic—that is, curved. And this led to further proposals about the advantages of depicting three-dimensional space in hyperbolic geometry rather than projective geometry as it approximates more closely to visual experience (Finch, 1977).

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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 of the receptive field toward the focus of attention (Desimone & Duncan, 1995), possibly contributing an enhancement of visual processing for the attended area. In experiments using moving stimuli, Anton-Erxleben and colleagues (Anton-Erxleben, Heinrich, & Treue, 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 (Wardak, Denève, & Hamed, 2011). This led the authors to doubt that subjective representations of space corresponded to objective external space. On the basis of 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” (page 1601). Vickery and Chun (2010) 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 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, was 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 with the peripheral area, and is thought to be linked to the greater acuity and resolution of foveal vision (Daniel & Whittenridge, 1961). Recent neuroscientific studies have investigated the link between cortical magnification and size perception (Schwarzkopf, Song, & Rees, 2011). However, Strasburger, Rentschler, and Harvey (1994) have showed that cortical magnification applies to only 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 19th century. The effect was replicated with different apparatus by Schneider, Ehrlich, Stein, Flaum, and Mangel (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, Ropar, Ackroyd, and Rajendran (2005) found that errors in copying drawings could be exacerbated by size

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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 was an untrained artist, 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, page 8). Some studies have sought to link skill in artistic depiction to accuracy in judging visual angles (Carson & Allard, 2012; Carson, Quehl, Aliev, & Danckert, 2014). Using drawings of still-life scenes, as in the present study, the researchers measured the ability of both expert and nonexpert artists (defined by years of experience) to ‘correctly’ depict angles and proportions in the scene compared with 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 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 effect 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 11). 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 (1776–1837), 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, 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 with 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, page 53). But even if artists who depict the world in this way are accurately depicting their experience of visual space, does it follow that nonartists 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).

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Although there have been suggestions that 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; 16th-century architectural drawings of planned fortifications in perspective sometimes required supplementary three-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 localized 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 19th century. This implies it is not an obvious or natural way to represent visual space (Deregowski et al., 1994; Hagen, 1986). 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 with 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 more comfortable station points. 6 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 with 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 good local correspondences in object shape between artworks and photographs, the global structures diverge. This suggests that 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 questions 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 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)?

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