Visual Image Statistics in the History of Western Art

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The history of Western visual art is traditionally divided into a succession of stylistic movements on the basis of the art-historical provenance and visual qualities of artworks. Little is known about how the visual statistics of Western artworks have changed over time, though this data could inform debate about the transitions between art movements. This longitudinal statistical study shows that two measures of the statistics of Western paintings remained relatively stable for 500 years, and similar to the values found in photographic images depicting the same subjects. Dramatic changes began in the late nineteenth century between the years 1878 and 1891, when the statistics of artworks became steadily more variable, and more frequently departed from values that are typical of representational images. This period can be considered as a major turning point that marks the beginning of the Modern Art movement. Statistically, abstract Modern art is more diverse than the representational art of any period. There is only limited evidence that aesthetic responses to paintings bear any relation to their visual statistics.

Abstract

The history of Western visual art is traditionally divided into a succession of stylistic movements on the basis of the art-historical provenance and visual qualities of artworks. Little is known about how the visual statistics of Western artworks have changed over time, though this data could inform debate about the transitions between art movements. This longitudinal statistical study shows that two measures of the statistics of Western paintings remained relatively stable for 500 years, and similar to the values found in photographic images depicting the same subjects. Dramatic changes began in the late nineteenth century between the years 1878 and 1891, when the statistics of artworks became steadily more variable, and more frequently departed from values that are typical of representational images. This period can be considered as a major turning point that marks the beginning of the Modern Art movement. Statistically, abstract Modern art is more diverse than the representational art of any period. There is only limited evidence that aesthetic responses to paintings bear any relation to their visual statistics.

1. Introduction

From the fourteenth to the twentieth centuries Western visual art evolved through a number of different styles, and the 600-year period is commonly divided into movements ranging from the Renaissance in the 1400s to Modernism in the 1900s (Graham-Dixon, 2008; Little, 2004). The defining features of art in different movements are a matter of ongoing debate, and the attribution of an artwork to a given movement can be uncertain. Nevertheless, attribution to a particular movement can have a profound influence on how an artwork is appreciated and analysed. The borders between movements are highly significant because they represent major cultural and aesthetic thresholds in the development of the Western artistic tradition. Art movements are traditionally defined by the art-historical context and visual qualities of artworks (Graham-Dixon, 2008; Little, 2004), such as manifesto statements (e.g. Futurism), broad cultural trends (Romanticism), or retrospective labels (Mannerism). If different movements really do mark significant events in the history of visual art, such as changes in the visual preoccupations of artists or their increasing ability to create life-like and aesthetically pleasing depictions of scenes, then artworks may also differ in their quantitative, statistical properties. Longitudinal analysis of image statistics may therefore shed new light on the transitions between art movements.

Previous research has found that images of natural scenes possess a high degree of regular statistical structure, in terms of the complexity and predictability of variations in tonal and colour values (Burton and Moorhead, 1987; Kersten, 1987; Ruderman, 1997). The human visual system is well-adapted to process these regularities. The receptive fields of visual neurons are tuned to the statistics of natural images (Field, 1987; Knill et al., 1990). Samples of artworks have been found to display the same statistical regularities as natural scenes, leading to proposals that artists reproduce the visual statistics of natural scenes in their paintings because this facilitates their processing by the brain, or makes them aesthetically more attractive (Graham and Field, 2008; Redies, 2007). Although previous work has analysed paintings using pre-defined categories of subject matter (abstract, landscape, portrait and so on) or period (Renaissance, Mannerism, Baroque, Rococo and so on) (Graham and Field, 2008; Hayn-Leichsenring et al., 2017; Redies and Brachmann, 2017; Redies et al., 2007a), there has been no work to track visual statistics longitudinally through a long period of time, yet this data could provide a new way to test theories about transitions between art movements and about visual aesthetics.

This study analysed the visual statistics of a large sample of 542 artworks spanning the period between 1285 and 2008, including examples from the most highly regarded artists in the Western tradition. The paintings were sampled from two datasets of art images, the JenAesthetics dataset (Amirshahi et al., 2013) and the MART dataset (Yanulevskaya et al., 2012), supplemented by additional images to widen coverage. The JenAesthetics and MART datasets also provided subjective ratings of their images, which were compared with statistical measures. A large sample of 245 photographic images was also analysed in order to provide a comparison of the artworks with natural scenes depicting the same range of subjects (landscapes, still life, animals, portraits).

Two widely used measures of visual statistics were calculated for each of the 787 images: Fractal dimension (FD) and Shannon entropy (SE). FD measures the degree to which a picture is broken up or fractured into a spatial pattern or a complex form. Images containing relatively smooth and unbroken spatial forms produce low FD values, whereas intricately detailed, densely fractured patterns produce a high FD value. Many natural forms are known to possess fractal properties (Peitgen and Saupe, 1988). SE measures the degree to which patterns or spatial forms vary unpredictably or randomly across an image (commonly called redundancy). Pictures in which the tonal and colour values at any one location can be predicted very well by the values nearby have a SE value close to zero (highly redundant), whereas highly unpredictable, randomly varying patterns have a high SE value (low redundancy). The brain is thought to exploit the redundancy of natural images in order to maximize the efficiency with which they can be processed (Field, 1987).

2. Materials and Methods

2.1. Image Samples

2.1.1. Art

A sample of 542 digital images was compiled from four sources. The images depicted artworks dating from 1285 to 2008:

JenAesthetics dataset (Amirshahi et al., 2013). This dataset contains information about 1625 Western paintings by 410 artists, drawn from images in the Google Art Project. The JenAesthetics dataset includes file download links from the Wikimedia Commons website. 375 paintings were selected for inclusion in the sample on the basis that: (i) Only one work was included for each artist; (ii) the download link was still active. The selected works cover the period 1435–1925.

MART dataset (Yanulevskaya et al., 2012). This source contains information and images relating to 500 abstract paintings from the Museum of Modern and Contemporary Art of Trento and Rovereto (MART). Many artists were represented by more than one painting in the image set, so 74 paintings were selected for inclusion in the sample on the basis that: (i) Only one work was included for each artist; (ii) the image size was at least 256 pixels on its shorter side. The selected works cover the period 1918–2008.

Wikimedia Commons website. The JenAesthetics dataset was lacking in terms of representation by certain well-known artists and periods, so 50 images were downloaded from the Wikimedia Commons website to fill the gaps, based on artists and paintings highlighted in Graham-Dixon (2008) as particularly significant in the history of art (https://commons.wikimedia.org/wiki/Category:Art). The selected works cover the period 1285–1984.

Tate Gallery. Similarly the Modern art represented in the MART dataset was lacking in representation by certain artists, so 43 images were downloaded from the Tate website (www.tate.org.uk) to fill the gaps, based on artists and paintings highlighted in Graham-Dixon (2008) as particularly significant in the history of art. The selected works cover the period 1905–1983.

2.1.2. Photographs

A sample of 245 digital photographs was compiled from two sources, depicting a range of subjects similar to those in the sample of artworks:

McGill calibrated colour image database (Olmos and Kingdom, 2004). Four groups of images were selected: 66 pure landscape scenes (no artificial structures or humans); 33 images containing animals; 90 images containing flowers or foliage; 36 images containing fruits and vegetables.

Pixabay.com. Portraiture is an established genre in painting, but was not represented in the McGill database. Portraits can contain either single figures or groups, from half-length to full-length. Twenty photographs were selected from pixabay.com (an online free-to-use image source) that contained a mixture of such photographic portraits.

2.2. Image Statistics

2.2.1. Procedure

Original images were first cropped and re-scaled to remove variations in their pixel dimensions and aspect ratio (see below). Each image was first cropped to the largest central square region (the length of each square side of the cropped image was equal to the length of the shorter side in the original image), and then re-scaled to 1024 × 1024 pixels using cubic interpolation (Matlab R2015a imresize() function).

Original images were encoded in sRGB colour. The cropped/scaled images were converted into Lab format using the Matlab R2015a makecform(‘srgb2lab’) function. Image statistics were then computed separately on the eight-bit (0–255) ‘L’ (luminance) ‘a’ (red–green), and ‘b’ (blue–yellow) planes. Results reported show only the luminance statistics, but the same trends in the data were observed in both of the colour planes.

Three image statistics were calculated on each of the three planes of the prepared images using Matlab R2015a: Fractal dimension, Shannon entropy, and Fourier amplitude spectrum slope. The results of the latter calculation are not reported because the same trends in the data were observed as seen in the other two statistics. Data for all three colour planes and statistical measures are included in supplementary materials.

2.2.2. Fractal Dimension

Fractal dimension was calculated using a three-dimensional box-counting algorithm (Jin and Ong, 1995; Li, Du, and Sun, 2009; Liu et al., 2014), in which image content is represented as a surface in a three-dimensional volume (two spatial axes, x and y, and an intensity axis, i). The algorithm divides the xyi volume of an image into many equal-sized boxes, and the number of boxes that intersect the image surface is counted. The count is repeated across a range of box sizes (b), and the proportion of filled to unfilled boxes at different sizes is given by b D. Images with uniform intensity (a flat two-dimensional plane in the xyi space) yield a value of the exponent D equal to 2.0 because only one 2-D sheet of boxes in the xy plane intersects with the image surface. Highly intricate patterns that fill the entire 3-D volume (such as a dense forest of fine luminance spikes) yield a value of D approaching 3.0 because nearly all boxes in the xyi space intersect with the image surface. The exponent D corresponds to the box-counting measure of fractal dimension for a given image. D was estimated using the differential box-counting algorithm (Jin and Ong, 1995), implemented as a custom function (‘CBC.m’) in Matlab R2015a, with the addition of more recent refinements to the algorithm (Li et al., 2009; Liu et al., 2014). This function is available in supplementary materials.

2.2.3. Shannon Entropy

The Shannon Entropy (SE, (Shannon, 1948)) of an image is defined as:

SE = − Σp.log2 p

where p contains the histogram of intensities in the image (quantized into a number of bins). In the case of the eight-bit images used in the present study, p had 256 bins. SE was calculated using the built-in ‘entropy’ function in Matlab R2015a. SE can be considered as the number of bits required to encode an image (Kersten, 1987). Eight-bit images that are highly redundant (large areas having similar pixel values) have a SE value close to 0, whereas highly unpredictable eight-bit images have a SE value close to the maximum value of 8.

2.2.4. Validation

To test whether the CBC function produces valid estimates of fractal dimension, it was applied to a set of 90 random fractal patterns that were generated using a spectral synthesis algorithm (Saupe, 1988). Digital eight-bit grey-level images with a range of nominal FD and equivalent Fourier amplitude spectral slope values were created (2.1 to 2.9 and −1.9 to −1.1, respectively). The correlation between the output of the custom CBC function and the nominal fractal dimension of the patterns was very high (r = 0.998). Measured SE values across all the random fractals varied between 7 and 8, commensurate with the random nature of the patterns.

In the photographic images used in the main study there is likely to have been a nonlinear relation between luminance sensed by the camera and stored pixel intensity, known as image gamma. In digital cameras, for example, pixel luminance is usually proportional to sensed luminance raised to the power 1/2.2, and this can be corrected in a reproduction by raising pixel luminance to the power 2.2. However, it was not possible to establish whether gamma correction had already been applied to any of the sample images. So rather than apply a correction, the approach taken here was to test the effect of different gamma values on the measured statistics. Visual statistics were calculated from the random fractal images after applying a gamma exponent of 1.0 (no gamma correction), and also after applying an extreme exponent of 2.5. Measured FD changed between the two gamma exponents by an average of 0.17%. Measured SE changed on average by 7.1%. Thus the inability to correct for unspecified gamma effects may have added a relatively small amount of ‘noise’ to the measured statistics but should not have introduced errors that would invalidate the conclusions. Results are reported using a gamma exponent of 1.0.

As mentioned above, all images were re-scaled and cropped to have the same pixel dimensions. This ensured that statistics were not influenced by variation in pixel dimensions from image to image. To test whether re-scaling itself affected calculations, 20 random fractal images were generated using the method described above so as to have a nominal FD of 2.5 (spectral slope −1.5), 10 images at a resolution of 4096 × 4096, and 10 images at 256 × 256. They were all re-scaled to 1024 × 1024 (so half were down-scaled and half were up-scaled). The mean estimated FD of the images changed by 0.36% after down-scaling, and −5.36% after up-scaling. The mean SE of the images changed by −0.02% after down-scaling, and −0.001% after up-scaling. Re-scaling thus made little difference to these measured statistics (by contrast, spectral slope values were seriously affected by up-scaling; mean estimated slope steepened by over 60% from −1.49 to −2.4).

2.3. Calculation of Moving Average and Variability

In order to visualise and analyse trends over time, the Figures plot the moving average value and variability of the statistics as a function of date. The moving average value plotted for a given year represents the mean across all artworks dated within a time window of +/− 25 years. Similarly the moving variability for a given year represents the standard deviation across all artworks dated within a time window of +/− 25 years. In both cases values are plotted only if the sample window contained more than eight artworks (all dates after 1485 satisfied this rule).

3. Results

Each small circle in Fig. 1 (upper) plots the FD of a single artwork in the sample at the date assigned to it. The solid line represents the moving average value of FD over time. The dashed horizontal line shows the average FD found in the sample of photographic images. Figure 1 (lower) shows corresponding data for SE. Both graphs show that, on average, the values of FD and SE changed relatively little over a period of almost 800 years, and close to the values found in photographic images. On the other hand, the graphs also show that the scatter of the statistics varied quite markedly over time. This trend is more apparent in Fig. 2, which shows the variability (moving standard deviation) of the two statistics over time. FD variability is plotted in blue (left-hand axis), and SE variability is plotted in red (right-hand axis). Although the FD and SE values of individual paintings are only moderately correlated (r = 0.367; Coefficient of Determination or C d = 0.135), the two statistics show very similar trends in terms of their variability across paintings. Variability remained relatively stable up to the middle of the nineteenth century, even declining slightly, but at a certain point in the late 1800’s it began to increase steadily, and this trend continued into the twentieth century.

Figure 1.
Figure 1.

Upper: Scatterplot of the fractal dimension of 542 Western artworks created during the period 1400–2008. The solid line represents the moving average fractal dimension at each date (mean of artworks within +/− 25 years of the date). The dashed line represents the mean fractal dimension of 245 photographic images of the same range of subjects. Lower: Scatterplot of the Shannon entropy of 542 Western artworks created during the period 1400–2008. The solid line represents the moving average Shannon entropy at each date (mean of artworks within +/− 25 years). The dashed line represents the mean Shannon entropy of 245 photographic images of the same range of subjects.

Citation: Art & Perception 6, 2-3 ( 2018) ; 10.1163/22134913-20181092

Figure 2.
Figure 2.

The variability of Shannon entropy and fractal dimension in 542 Western artworks over time. The red points and right-hand vertical axis represent Shannon entropy; the blue points and left-hand vertical axis represent fractal dimension. Variability at each date corresponds to the standard deviation of artworks within +/− 25 years of the date. The straight lines represent best-fitting linear segments according to piecewise linear regression analysis, for SE (red) and FD (blue).

Citation: Art & Perception 6, 2-3 ( 2018) ; 10.1163/22134913-20181092

The variability data in Fig. 2 appear to split into two approximately linear regions having different slopes. Piecewise linear regression analysis was used to identify the optimum date at which to split the data into two parts. Each year during the period 1502–1967 was treated as a possible split date between the two linear segments (with at least 16 points in each segment). The Coefficient of Determination (C d) of each segmented linear regression was calculated as follows:

C d = 1 – [ Σ(yY r)2 / Σ(yY a)2 ]

where y is an obtained value of y, Y r is the expected value of y obtained from segmented regression, and Y a is the average of all obtained y values. The year that maximised the C d for the piecewise fit was taken as the optimum date at which to split the variability data into two parts. As a check on the validity of the analysis, these optimum fits were compared against those returned by Matlab’s ‘Shape Prescriptive Modeling’ toolkit. The two piecewise fits produced exactly the same split dates.

The FD data were fitted optimally (C d = 0.93) using a split date of 1878, while the SE data were fitted optimally using a split date of 1891 (C d = 0.86). In both cases, fit quality declined steadily using splits at earlier or later dates. The lines in Fig. 2 show the best-fitting piecewise regressions for FD (blue) and SE (red). The optimal fits are remarkably similar despite the modest correlation between the two image statistics. The slopes of the linear functions before and after the split dates are significantly different.

In line with the regression analysis, Levene’s test for equality of variance showed that the variance of FD scores was significantly higher after 1878 than before this date (F = 63.8; df = [1, 540]; p < 0.0001), though there was no significant difference between mean FD values before and after 1878 (t = 0.184; df = 294.8; p = 0.85). Levene’s test also showed that the variance of SE scores was significantly higher after 1891 compared to before this date (F = 48.4; df = [1, 540]; p < 0.0001). SE scores were significantly lower on average after 1891 (7.04) compared to before this date (7.23) according to a Wilcoxon test (used because SE values were not normally distributed; Z = 4.52; p = 0.02). This effect may be due to a ceiling effect in SE scores (which cannot exceed 8), so that increased variability will tend to bias the mean towards lower SE values.

Subjective beauty ratings were available for 451 of the 542 paintings in the dataset. For images from the JenAesthetics database, participants had rated each painting for ‘beauty’, with data recorded on a 100-point scale (Amirshahi et al., 2015). For images from the MART database, participants had rated their emotional response to each painting on a seven-point scale (1 representing a highly negative emotion and 7 representing a highly positive one; Sartori, 2014). On the assumption that the latter scores bear some relation to beauty, they were re-scaled onto a 100-point scale and combined with the JenAesthetics ratings.

Figure 3 (upper) plots 451 beauty ratings as a function of year. The solid line represents the moving average value of beauty over time. There is a general linear trend for beauty scores to rise significantly over time (t = 5.51; df = 449; p < 0.0001). The vertical dashed lines indicate the best-fitting split dates from the analysis of statistical variability in FD (blue line) and SE (red line). There is no obvious change in beauty ratings that aligns with either split date. Figure 3 (lower) plots variability (moving standard deviation) of beauty scores over time, again with vertical lines indicating the split dates according to FD and SE. Unlike the single inflection point evident in the statistics (Fig. 2), the variability of beauty ratings rises and falls repeatedly over time, before and after the split dates.

Figure 3.
Figure 3.

Upper: Scatterplot of beauty ratings of 451 paintings from the JenAesthetics and MART datasets. The solid line represents the moving average value of beauty over time. The vertical dashed lines mark the best-fitting split dates from the analysis of statistical variability in FD (blue line) and SE (red line). Lower: Variability (moving standard deviation) of beauty ratings over time. The vertical dashed lines mark the best-fitting split dates from the analysis of statistical variability in FD (blue line) and SE (red line).

Citation: Art & Perception 6, 2-3 ( 2018) ; 10.1163/22134913-20181092

There were significant (though low) correlations between beauty ratings prior to 1878/1891, and the FD/SE values of the paintings (FD: r = 0.151, p = 0.01; SE: r = 0.19, p = 0.006), as shown in the scatterplot of Fig. 4. There were no significant correlations between beauty ratings after 1878/1891 and FD/SE values (FD: r = −0.074, p = 0.352; SE: r = −0.145, p = 0.103).

Figure 4.
Figure 4.

Scatterplots of beauty ratings of artworks prior to 1878 against FD (blue points and left-hand axis), and of artworks prior to 1891 against SE (red points and right-hand axis). R-squared values were 0.023 for FD and 0.036 for SE.

Citation: Art & Perception 6, 2-3 ( 2018) ; 10.1163/22134913-20181092

4. Discussion

A striking aspect of the longitudinal data on visual statistics is the steady increase in the variability of FD and SE that began in the late nineteenth century and continued into the twentieth century. The Modern Art period is widely acknowledged to have its roots in the late 1800s, but there has been continuing debate about the most appropriate date to assign as the starting point of Modern Art. Brettell (1999) takes the date of the Great Exhibition at Crystal Palace in 1851 as the start of Modernism. Other possible dates in the late 1800s have also been suggested, including 1855 (the date of Courbet’s manifesto painting, The Studio of the Painter, A Real Allegory), 1863 (the exhibition of Manet’s Dejeuner sur l’Herbe), and 1874 (the exhibition of the first Impressionist paintings; Phillips, 2012). The present longitudinal data provide a statistical estimate of the transition between pre-Modern and Modern Art, namely the period between 1878 and 1891. The paintings in the image set offer some insight into the art movements associated with this transition. The works immediately prior to 1878 include paintings by Renoir (La Promenade), Sisley (La Route de Versailles), Corot (Le View Pont), Menzel (Das Ballsouper), and Eakins (Portrait of Dr. D. Gross), who are regarded as members of the Realist and Impressionist movements. On the other hand, the works dated soon after 1878 are by artists associated with Neo-Impressionism and Post-Impressionism, including Camille Pissarro (Conversation), Cezanne (Morning View of Estaque against the Sunlight), Seurat (La Luzerne Saint-Denis), Signac (Breakfast), Gaugin (Washerwomen), and Van Gogh (Starry Night). Thus in a statistical sense Impressionism marked the end of the pre-Modern period, whereas the Modern Art period began with Neo- and Post- Impressionism.

Abstract art is closely associated with Modernism, and a recent study (Redies and Brachmann, 2017) reported greater variability in the statistics of abstract art compared to representational art, consistent with the present results. However, the turning point in 1878-1891 cannot be attributed solely to the introduction of abstract art. The first abstract painting in the image set dates from 1915 (Malevich’s “Suprematism, 18 th Construction”), 37 years after the inflection in FD variability and 24 years after the inflection in SE variability. There are 94 representational paintings in the image set dated between 1878 and 1915 from movements such as Pointillism and Fauvism. So the trend towards diversification began before the appearance of abstract art, which can thus be seen as part of a Modern movement away from traditional representational depictions rather than a quantum shift in art (Elger, 2017). This view is in agreement with those arguing that the boundaries between traditional representational painting and abstraction are indistinct, because all painting is in some respect an abstraction from reality (Gombrich, 1972). The painter Maurice Denis famously remarked that “A picture, before it is a picture of a warhorse, a naked woman, or some anecdote or other, is essentially a flat surface covered with colours in a particular arrangement” (Denis, 1890).

To assess the extent to which Modern art departs from the stable statistical parameters set by pre-Modern art, statistical outliers in the entire dataset were identified using limits set by pre-Modern art. An outlier was defined as any painting whose FD (or SE) fell more than 1.5 times the interquartile range above the third quartile or below the first quartile of values in pre-Modern art. In the case of FD, only 3 of 323 pre-Modern paintings (<1%) were identified as outliers, whereas 34 of 219 Modern paintings (15.5%) were identified as outliers. Five of the Modern outliers were representational, and 29 were abstracts. Turning to SE, only 9 of 361 pre-Modern paintings (2.5%) were outliers, whereas 37 of 181 Modern paintings (20.4%) were identified as outliers, all except one being abstracts. Pre-Modern outliers were mostly portraits or still life paintings. The Appendix lists details of all outliers. Furthermore, according to Levene’s test for equality of variance, the variance of Modern abstract paintings in the dataset is significantly higher than that of Modern representational paintings (FD: F = 31.6, df = [1, 217], p < 0.0001; SE: F = 36.3, df = [1, 179], p < 0.0001).

The present analysis therefore supports the view that Modern artists explored more radical depictions than their pre-Modern counterparts. The greater number of outliers found in the Modern period, particularly among abstract paintings, bears out the argument that Modern art is marked by a greater divergence from natural statistics. Nevertheless, it must also be acknowledged that many Modern paintings are not classified as statistical outliers.

(Ruderman, 1994) pointed out that:

“Natural images are distinctive because they contain particular types of structure. …The images we encounter every day comprise a very sparse subset of all possible images.” (pp. 517–518)

Two characteristic regularities in the statistics of natural images that were identified by Ruderman (1994) are their scale invariance and their redundancy. FD and SE statistics are employed in the present research because they measure these two properties. Many studies of natural images have reported regularities in these and other image statistics (see, for example Burton and Moorhead, 1987; Kersten, 1987; Ruderman, 1997). Likewise many studies of artworks have reported corresponding regularities in their statistics (Graham and Field, 2007, 2008; Redies et al., 2007a, b). The simplest null hypothesis for the similarity between the two image sets is that statistical regularities in artworks just reflect the regularities found in natural images, because they depict the same kinds of non-random features and structures. Representational art depicts natural forms such as rocks, fields, clouds, lakes, animals and so on, which can be expected to generate similar image statistics to those observed in photographic images of these forms. With a few rare exceptions, abstract art is also highly non-random, being composed of selected spatial features such as edges, lines, and shapes (Kandinsky’s ‘point, line and plane’), so will also generate non-random image statistics (such as a Fourier amplitude spectrum with a negative slope). A number of studies have argued in favour of an alternative hypothesis: Artists have a universal preference for images that are ‘super-regular’ in some sense compared to equivalent control images (Graham and Field, 2008; Mather, 2014; Redies and Brachmann, 2017; Redies et al., 2007a; Schweinhart and Essock, 2013; Spehar et al., 2003). There are two variants of the universal preference hypothesis (Graham and Field, 2008); the ‘perceptibility’ hypothesis and the ‘affect’ hypothesis. The perceptibility hypothesis proposes that artists create paintings that are readily visible to the human eye, and can be processed more efficiently by the visual system (Graham and Field, 2007). In some sense they are ‘super-regular’ — very well matched to the natural image statistics that the visual system evolved and developed to process. The affect hypothesis, on the other hand, proposes that images with super-regular statistics are inherently aesthetically more pleasing (Redies, 2007; Spehar et al., 2003).

One way to test the perceptibility hypothesis empirically is to compare the visual statistics of paintings against those of control images such as photographs, and test for super-regularities in the former. The issue is complicated because it can be very difficult to identify the most appropriate set of control images that should, under the null hypothesis, produce identical image statistics to the artworks. However, some studies have reported ‘super-regularities’ in representational artworks that are consistent with the perceptibility hypothesis. For example, Schweinhart and Essock (2013) found that artists under-represent oblique orientations in their paintings at all but the largest spatial scales. Several studies also report that the range of spectral slopes found in artworks is narrower than that in natural scenes (Graham and Field, 2008; Mather, 2014; Redies et al., 2007a; Schweinhart and Essock, 2013). The average statistics of the paintings in the present dataset stay close to those of the photographs, and over time there is a trend for the variability of both FD and SE to fall slightly, at least up to the late 1800s. This trend could reflect increasing conformity with natural statistics. However, after the late 1800s the trend reverses, suggesting that the Modern artists were not so concerned with reproducing natural statistics.

A direct way to evaluate the affect hypothesis is to compare preference ratings for paintings with their image statistics. There is limited evidence in the literature for a universal aesthetic preference driven by statistics (Aks and Sprott, 1996; Spehar et al., 2003), but the present results do not offer much support for the hypothesis. There is a significant (though very weak) correlation between visual statistics and beauty for pre-Modern paintings, but not for Modern paintings. While the variability of FD and SE statistics steadily increased during the twentieth century, the variability of beauty scores declined over most of this time. Perhaps Modern art is often judged on its non-visual, conceptual qualities rather than its visual aesthetics. Recent research on aesthetics appears to have moved on from the appealingly simple notion of a universal aesthetic preference that is shared by all participants, in favour of identifying clusters of participants who prefer different constellations of image statistics (Güçlütürk et al., 2016; Hayn-Leichsenring et al., 2017; Spehar et al., 2016).

5. Conclusion

Visual statistics reveal that a significant change in the visual content of Western art occurred in the latter half of the nineteenth century. This change in visual statistics can be viewed as marking the beginning of the Modern Art movement. Statistically, abstract Modern art is more diverse than the representational art of any period. There is only limited evidence that aesthetic responses to paintings bear any relation to their visual statistics.

Supplementary Materials

The spreadsheets containing details of artworks, photographs and statistics, as well as Matlab scripts for the calculation of the statistics, are available in the Open Science Framework:

Mather, G. (2017, December 19). Visual Statistics in Perception and Art. Retrieved from osf.io/9u36z. doi: 10.17605/OSF.IO/9U36Z

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  • Graham D. J. and Field D. J. (2008). Variations in intensity statistics for representational and abstract art, and for art from the Eastern and Western hemispheres, Perception 37, 13411352.

    • Search Google Scholar
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  • Graham-Dixon A. (2008). Art: The Definitive Visual Guide. Dorling Kindersley, London, UK.

  • Güçlütürk Y. , Jacobs R. H. A. H. and Lier R. van (2016). Liking versus complexity: Decomposing the inverted U-curve, Front. Hum. Neurosci. 10, 112. http://doi.org/10.3389/fnhum.2016.00112.

    • Search Google Scholar
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  • Hayn-Leichsenring G. U. , Lehmann T. and Redies C. (2017). Subjective ratings of beauty and aesthetics: correlations with statistical image properties in Western oil paintings, iPerception 8, 2041669517715474. http://doi.org/10.1177/2041669517715474.

    • Search Google Scholar
    • Export Citation
  • Jin X. C. and Ong S. H. (1995). A practical method for estimating fractal dimension, Pattern Recognit. Lett. 16, 457464.

  • Kersten D. (1987). Predictability and redundancy of natural images, J. Opt. Soc. Am. A 4, 23952400.

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  • Li J. , Du Q. and Sun C. (2009). An improved box-counting method for image fractal dimension estimation, Pattern Recognit. 42, 24602469.

    • Search Google Scholar
    • Export Citation
  • Little S. (2004). - isms: Understanding Art. Bloomsbury, London, UK.

  • Liu Y. , Chen L. , Wang H. , Jiang L. , Zhang Y. , Zhao J. , Wang D. , Zhao Y. and Song Y. (2014). An improved differential box-counting method to estimate fractal dimensions of gray-level images, J. Vis. Commun. Image Represent. 25, 11021111.

    • Search Google Scholar
    • Export Citation
  • Mather G. (2014). Artistic adjustment of image spectral slope. Art Percept. 2, 1122.

  • Olmos A. and Kingdom F. A. A. (2004). A biologically inspired algorithm for the recovery of shading and reflectance images, Perception 33, 14631473.

    • Search Google Scholar
    • Export Citation
  • Peitgen D. and Saupe H. (1988). The Science of Fractal Images. Springer-Verlag, New York, NY, USA.

  • Phillips S. (2012). …isms. Understanding Modern Art. Bloomsbury, London, UK.

  • Redies C. (2007). A universal model of esthetic perception based on the sensory coding of natural stimuli, Spat. Vis. 21, 97117.

  • Redies C. and Brachmann A. (2017). Statistical image properties in large subsets of traditional art, bad art, and abstract art, Front. Neurosci. 11, 593. http://doi.org/10.3389/fnins.2017.00593.

    • Search Google Scholar
    • Export Citation
  • Redies C. , Hänisch J. , Blickhan M. and Denzler J. (2007a). Artists portray human faces with the Fourier statistics of complex natural scenes, Network 18, 235248.

    • Search Google Scholar
    • Export Citation
  • Redies C. , Hasenstein J. and Denzler J. (2007b). Fractal-like image statistics in visual art: similarity to natural scenes, Spat. Vis. 21, 137148.

    • Search Google Scholar
    • Export Citation
  • Ruderman D. L. (1994). The statistics of natural images, Network 5, 517548.

  • Ruderman D. L. (1997). Origins of scaling in natural images, Vis. Res. 37, 33853398.

  • Sartori A. (2014). Affective analysis of abstract paintings using statistical analysis and art theory, in: Proceedings of the 16th International Conference on Multimodal Interaction - ICMI ’14, V(212), Istanbul, Turkey, pp. 384388. http://doi.org/10.1145/2663204.2666289.

    • Search Google Scholar
    • Export Citation
  • Saupe D. (1988). Algorithms for random fractals, in: The Science of Fractal Images, Peitgen D. and Saupe H. (Eds), pp. 71136. Springer-Verlag, New York, NY, USA.

    • Search Google Scholar
    • Export Citation
  • Schweinhart A. M. , and Essock E. A. (2013). Structural content in paintings: Artists overregularize oriented content of paintings relative to the typical natural scene bias, Perception 42, 13111332.

    • Search Google Scholar
    • Export Citation
  • Shannon C. E. (1948). A mathematical theory of communication, Bell Syst. Tech. J. 27, 379–423, 623656.

  • Spehar B. , Clifford C. W. G. , Newell B. R. and Taylor R. P. (2003). Universal aesthetic of fractals, Comput. Graph. 27, 813820.

  • Spehar B. , Walker N. and Taylor R. P. (2016). Taxonomy of individual variations in aesthetic responses to fractal patterns, Front. Hum. Neurosci. 10, 350. http://doi.org/10.3389/fnhum.2016.00350.

    • Search Google Scholar
    • Export Citation
  • Yanulevskaya V. , Uijlings J. , Bruni E. , Sartori A. , Zamboni E. , Bacci F. , Melcher D. and Sebe N. (2012). In the eye of the beholder: Employing statistical analysis and eye tracking for analyzing abstract paintings categories and subject descriptors, in: Proceedings of the 20th ACM International Conference on Multimedia, Nara, Japan, pp. 349358. http://doi.org/10.1145/2393347.2393399.

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Appendix

Table of outliers based on the statistics of pre-Modern art. The upper half of the table shows FD outliers, and the lower half shows SE outliers. Dates in italics identify abstract artworks. See text for details of outlier calculations.

T000001
*

To whom correspondence should be addressed. E-mail: gmather@lincoln.ac.uk

If the inline PDF is not rendering correctly, you can download the PDF file here.

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  • Gombrich E. (1972). The Story of Art, 13th ed. Phaedon, Oxford, UK.Graham, D. J. and Field, D. J. (2007). Statistical regularities of art images and natural scenes: Spectra, sparseness and nonlinearities, Spat. Vis. 21, 149164.

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  • Graham D. J. and Field D. J. (2008). Variations in intensity statistics for representational and abstract art, and for art from the Eastern and Western hemispheres, Perception 37, 13411352.

    • Search Google Scholar
    • Export Citation
  • Graham-Dixon A. (2008). Art: The Definitive Visual Guide. Dorling Kindersley, London, UK.

  • Güçlütürk Y. , Jacobs R. H. A. H. and Lier R. van (2016). Liking versus complexity: Decomposing the inverted U-curve, Front. Hum. Neurosci. 10, 112. http://doi.org/10.3389/fnhum.2016.00112.

    • Search Google Scholar
    • Export Citation
  • Hayn-Leichsenring G. U. , Lehmann T. and Redies C. (2017). Subjective ratings of beauty and aesthetics: correlations with statistical image properties in Western oil paintings, iPerception 8, 2041669517715474. http://doi.org/10.1177/2041669517715474.

    • Search Google Scholar
    • Export Citation
  • Jin X. C. and Ong S. H. (1995). A practical method for estimating fractal dimension, Pattern Recognit. Lett. 16, 457464.

  • Kersten D. (1987). Predictability and redundancy of natural images, J. Opt. Soc. Am. A 4, 23952400.

  • Knill D. C. , Field D. J. and Kersten D. (1990). Human discrimination of fractal images, J. Opt. Soc. Am. A 7, 11131123.

  • Li J. , Du Q. and Sun C. (2009). An improved box-counting method for image fractal dimension estimation, Pattern Recognit. 42, 24602469.

    • Search Google Scholar
    • Export Citation
  • Little S. (2004). - isms: Understanding Art. Bloomsbury, London, UK.

  • Liu Y. , Chen L. , Wang H. , Jiang L. , Zhang Y. , Zhao J. , Wang D. , Zhao Y. and Song Y. (2014). An improved differential box-counting method to estimate fractal dimensions of gray-level images, J. Vis. Commun. Image Represent. 25, 11021111.

    • Search Google Scholar
    • Export Citation
  • Mather G. (2014). Artistic adjustment of image spectral slope. Art Percept. 2, 1122.

  • Olmos A. and Kingdom F. A. A. (2004). A biologically inspired algorithm for the recovery of shading and reflectance images, Perception 33, 14631473.

    • Search Google Scholar
    • Export Citation
  • Peitgen D. and Saupe H. (1988). The Science of Fractal Images. Springer-Verlag, New York, NY, USA.

  • Phillips S. (2012). …isms. Understanding Modern Art. Bloomsbury, London, UK.

  • Redies C. (2007). A universal model of esthetic perception based on the sensory coding of natural stimuli, Spat. Vis. 21, 97117.

  • Redies C. and Brachmann A. (2017). Statistical image properties in large subsets of traditional art, bad art, and abstract art, Front. Neurosci. 11, 593. http://doi.org/10.3389/fnins.2017.00593.

    • Search Google Scholar
    • Export Citation
  • Redies C. , Hänisch J. , Blickhan M. and Denzler J. (2007a). Artists portray human faces with the Fourier statistics of complex natural scenes, Network 18, 235248.

    • Search Google Scholar
    • Export Citation
  • Redies C. , Hasenstein J. and Denzler J. (2007b). Fractal-like image statistics in visual art: similarity to natural scenes, Spat. Vis. 21, 137148.

    • Search Google Scholar
    • Export Citation
  • Ruderman D. L. (1994). The statistics of natural images, Network 5, 517548.

  • Ruderman D. L. (1997). Origins of scaling in natural images, Vis. Res. 37, 33853398.

  • Sartori A. (2014). Affective analysis of abstract paintings using statistical analysis and art theory, in: Proceedings of the 16th International Conference on Multimodal Interaction - ICMI ’14, V(212), Istanbul, Turkey, pp. 384388. http://doi.org/10.1145/2663204.2666289.

    • Search Google Scholar
    • Export Citation
  • Saupe D. (1988). Algorithms for random fractals, in: The Science of Fractal Images, Peitgen D. and Saupe H. (Eds), pp. 71136. Springer-Verlag, New York, NY, USA.

    • Search Google Scholar
    • Export Citation
  • Schweinhart A. M. , and Essock E. A. (2013). Structural content in paintings: Artists overregularize oriented content of paintings relative to the typical natural scene bias, Perception 42, 13111332.

    • Search Google Scholar
    • Export Citation
  • Shannon C. E. (1948). A mathematical theory of communication, Bell Syst. Tech. J. 27, 379–423, 623656.

  • Spehar B. , Clifford C. W. G. , Newell B. R. and Taylor R. P. (2003). Universal aesthetic of fractals, Comput. Graph. 27, 813820.

  • Spehar B. , Walker N. and Taylor R. P. (2016). Taxonomy of individual variations in aesthetic responses to fractal patterns, Front. Hum. Neurosci. 10, 350. http://doi.org/10.3389/fnhum.2016.00350.

    • Search Google Scholar
    • Export Citation
  • Yanulevskaya V. , Uijlings J. , Bruni E. , Sartori A. , Zamboni E. , Bacci F. , Melcher D. and Sebe N. (2012). In the eye of the beholder: Employing statistical analysis and eye tracking for analyzing abstract paintings categories and subject descriptors, in: Proceedings of the 20th ACM International Conference on Multimedia, Nara, Japan, pp. 349358. http://doi.org/10.1145/2393347.2393399.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Upper: Scatterplot of the fractal dimension of 542 Western artworks created during the period 1400–2008. The solid line represents the moving average fractal dimension at each date (mean of artworks within +/− 25 years of the date). The dashed line represents the mean fractal dimension of 245 photographic images of the same range of subjects. Lower: Scatterplot of the Shannon entropy of 542 Western artworks created during the period 1400–2008. The solid line represents the moving average Shannon entropy at each date (mean of artworks within +/− 25 years). The dashed line represents the mean Shannon entropy of 245 photographic images of the same range of subjects.

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    The variability of Shannon entropy and fractal dimension in 542 Western artworks over time. The red points and right-hand vertical axis represent Shannon entropy; the blue points and left-hand vertical axis represent fractal dimension. Variability at each date corresponds to the standard deviation of artworks within +/− 25 years of the date. The straight lines represent best-fitting linear segments according to piecewise linear regression analysis, for SE (red) and FD (blue).

  • View in gallery

    Upper: Scatterplot of beauty ratings of 451 paintings from the JenAesthetics and MART datasets. The solid line represents the moving average value of beauty over time. The vertical dashed lines mark the best-fitting split dates from the analysis of statistical variability in FD (blue line) and SE (red line). Lower: Variability (moving standard deviation) of beauty ratings over time. The vertical dashed lines mark the best-fitting split dates from the analysis of statistical variability in FD (blue line) and SE (red line).

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    Scatterplots of beauty ratings of artworks prior to 1878 against FD (blue points and left-hand axis), and of artworks prior to 1891 against SE (red points and right-hand axis). R-squared values were 0.023 for FD and 0.036 for SE.

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