Edited by: Klaus Gramann, Technical University of Berlin, Germany
Reviewed by: Anjan Chatterjee, Perelman School of Medicine, USA; Branka Spehar, University of New South Wales, Australia
*Correspondence: Norberto M. Grzywacz
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The Processing Fluency Theory posits that the ease of sensory information processing in the brain facilitates esthetic pleasure. Accordingly, the theory would predict that master painters should display biases toward visual properties such as symmetry, balance, and moderate complexity. Have these biases been occurring and if so, have painters been optimizing these properties (fluency variables)? Here, we address these questions with statistics of portrait paintings from the Early Renaissance period. To do this, we first developed different computational measures for each of the aforementioned fluency variables. Then, we measured their statistics in 153 portraits from 26 master painters, in 27 photographs of people in three controlled poses, and in 38 quickly snapped photographs of individual persons. A statistical comparison between Early Renaissance portraits and quickly snapped photographs revealed that painters showed a bias toward balance, symmetry, and moderate complexity. However, a comparison between portraits and controlled-pose photographs showed that painters did not optimize each of these properties. Instead, different painters presented biases toward different, narrow ranges of fluency variables. Further analysis suggested that the painters' individuality stemmed in part from having to resolve the tension between complexity vs. symmetry and balance. We additionally found that constraints on the use of different painting materials by distinct painters modulated these fluency variables systematically. In conclusion, the Processing Fluency Theory of Esthetic Pleasure would need expansion if we were to apply it to the history of visual art since it cannot explain the lack of optimization of each fluency variables. To expand the theory, we propose the existence of a Neuroesthetic Space, which encompasses the possible values that each of the fluency variables can reach in any given art period. We discuss the neural mechanisms of this Space and propose that it has a distributed representation in the human brain. We further propose that different artists reside in different, small sub-regions of the Space. This Neuroesthetic-Space hypothesis raises the question of how painters and their paintings evolve across art periods.
An important recent theory in art cognition is the Processing Fluency Theory (PFT) of esthetic pleasure, which claims the ease with which the brain processes the perceptual properties of an object contributes to its esthetic value (Reber et al.,
Of the many visual properties studied under the PFT, symmetry, balance, and complexity have received much attention. Numerous studies have shown that individuals prefer objects with greater symmetry (Palmer,
In accordance with the principles of the PFT, we raise the hypothesis that visual artists, especially master painters will show biases toward optimizing fluency variables (i.e., those measuring visual properties like symmetry, balance, and complexity). Although the PFT is a theory for observers, visual artists also function as perceptual agents when performing their work (Bryson,
To test these hypotheses, we first developed computational measures of symmetry, balance, and complexity. We then investigated the statistics of the relationship between these variables in both master paintings and control photographs to study the choices that artists make about these characteristics. Our control photographs consisted of both photos of individuals in controlled poses, as well as quickly taken photos with minimal artistic intent. Comparison of the latter with master paintings allowed us to test whether painters produced art with more symmetry, balance, and complexity than what one would get in spontaneous, quickly snapped photographs. On the other hand, comparison of master paintings with the ideally balanced and symmetric frontally posed controls allowed us to test whether artists optimized their work with respect to these fluency variables. Our investigation adds to previous work that has probed statistical properties of visual art (Graham and Redies,
All images were digitized to a maximum resolution of 1,024 × 1,024 pixels due to computational cost. The minimum number of pixels in the horizontal dimension, i.e., the number of columns was 500. Such a minimum was necessary to allow enough precision in the estimation of the indices of symmetry, balance, and complexity along this dimension. If the number of columns was uneven, one column was detracted from the end of the image to allow precise computation of left-right symmetry and balance in the image. Finally, although the images were originally in color, we converted them into 8-bit grayscale through the colorimetric method (Poynton,
We analyzed 153 portrait paintings of 26 master painters from the Early Renaissance, which we defined as those born between 1370 and 1450. Portrait paintings were only included if they each contained one main individual as the subject. They were painted in oil, tempera, frescos, or a mixture of these materials. All paintings were obtained from the online database, “Artstor Digital Library” (library.artstor.org). If the painting in Artstor had a frame, we removed it before the statistical estimations, except if the painter had painted it.
A complete list of the paintings and controls in this paper appears in the
Six graduate students and three professors from Georgetown University were chosen as volunteers for these controls. Photographs of the volunteers were taken while sitting at frontal, 45°, and 90° poses. Thus, we obtained 27 posed-control photographs (three each of nine subjects). Our control posed photographs had the direction of the face, shoulders/chest, and eyes fully congruent, and always rotated around a vertical axis. These well-controlled conditions served to reduce statistical variability in the fluency variables in this group, allowing us to use a relatively small number of photographs. To reduce variability further, all the photographs were taken indoors with identical lighting conditions by using a Canon EOS 700D/Rebel T5i camera fitted with an EF-S 18-55 mm F3.5-5.6 IS STM lens (Canon USA, Inc., Melville, New York, USA).
Each volunteer signed a written consent based on an approved Institutional Review Board protocol.
To compare these controls with the master paintings more directly, we attempted to classify the poses in the latter. Such a classification in artistic paintings could only be approximate. Artists varied at least three different variables within the pose structure, including rotating the face, shoulders/chest, and the eyes separately. Furthermore, these three variables were occasionally modulated parametrically along both the vertical and the horizontal axes. Artists most likely exploited these modulations to increase complexity in their works (Pope-Hennessy,
We wanted the last set of controls to be images in which no deliberate artistic effort existed. Therefore, instead of using publicly available photographs that may contain artistic intent, we selected photographs from a collection of casual, quickly snapped, and as-unposed-as-possible photographs taken by the authors with their iPhone 6 (Apple, Cupertino, California, USA). Rejection criteria were similar to those of portrait paintings and posed controls, i.e., photographs had to contain one main, recognizable subject and not be more than 90° in pose. We also rejected photographs with any blurred portions. Two of the authors blindly selected appropriate photographs from a pool of 230 images. After consensual selection, only 38 survived the rejection criteria, thus having minimal posing, framing, and artistic effort. Each of the subjects signed a written consent to have his or her photograph used in this study based on an approved Institutional Review Board protocol.
All control photographs, posed or quickly snapped, are available upon request.
We developed computational measures of symmetry, balance, and complexity, and analyzed them statistically using MATLAB R2015a (MathWorks, Natick, Massachusetts, USA), using scripts developed specially for this project.
To make the reading of the following sections on the computational measures more accessible, we begin each text with a paragraph that provides the physical intuition of the proposed calculations. We hope that these paragraphs will allow the reader to understand the rationale even by skipping the equations. These, in turn, appear after the introductory paragraphs.
Symmetry in images has previously been defined in a variety of manners. The definitions include different types of symmetry, especially rotational, reflectional (along different axes), or translational. While many algorithms exist for these measurements, our method is similar in nature to the ones concerning vertical bi-lateral symmetry (O'Mara and Owens,
Let Ik, j be the intensity of the pixel in Row k and Column j. Let the number of rows and columns be
We define the overall (medial vertical) asymmetry index from this equation as:
This asymmetry index is what appears in
The main idea behind pictorial balance is that features of the image have a spatial distribution that is as homogeneous as possible. Because portraits are vertical, one reasonable measurement of balance is along the horizontal dimension, which is what we do here. There are multiple definitions of pictorial balance, from which we consider three prominent ones. The first is suggested by the bodies of literature from Art, and History and Psychology of Art (Ross,
Let the
The physicalist-imbalance index is similar to Equations (2) and (3), except that it weighs the intensities with the distances to the balance line, i.e.:
Similarly, the mean-imbalance index is as in Equations (2) and (3), except that it uses the mean instead of the integrals, i.e.:
As for the integral-balance index, the physicalist- and mean-balance indices are one minus the corresponding imbalance indices.
Finally, in order to determine the optimal balance lines, we seek positions that minimize the imbalance indices, i.e.:
In this paper, we looked for the columns achieving these minima. Both Λ
The balance and imbalance indices quantify how similar the two sides of a balance line are overall. However, similarity may be achieved by compensating a feature on, say, the top right of an image, with something in the bottom left. If so, although the image may have left-right balance overall, the balance may be imperfect at different heights of the image. We wanted to quantify how careful master painters were about this fine balance. For this purpose, we first determined the best balance position row by row in the painting. We then measured the error in these positions relative to the horizontal size of the image.
For the sake of brevity, we only show here how the calculation is performed for the integral balance since the methods are identical for the other forms of balance. We begin by adapting (Equations 2, 3, and 7) to be row by row, getting:
This function is illustrated for different images in
This measure looks at the overall distribution of intensities in a given image, with a greater spread in the distribution equating to greater complexity of order 1. Therefore, a very complex image would have a wide range of intensities such as white noise. In contrast, the simplest image would be a blank canvas with only one type of intensity. Figure
Let pixels have intensities [0, …, I*] (from 0 to 255 in our collection). For Image Q, let intensity l have Ml occurrences in histograms such as those in Figures
From this equation, we define Entropy of Order 1 for Image Q as:
In practice, if
To create an index of complexity out of this entropy, we divide it by its largest possible value given any arbitrary image. This largest value comes from large images for which every pixel has an intensity randomly picked from all possible values. Thus,
Dividing
By the definition of
A limitation of Complexity of Order 1 is that it does not capture the change in complexity due to spatial organization. If one scrambles the positions of the pixels in a painting, it looks more complex. However, because the distribution of intensities remains the same upon scrambling, the Complexity of Order 1 does not change. To capture the observed change of complexity, one must ask, “Given the intensity of a pixel, can one predict the intensity in another?” For nearby pixels, the answer is typically yes, because they often represent portions of the same surface (Field,
To define Entropy of Order 2 for Image Q and Isometric Transformation T, we begin by letting
From this definition, we define Entropy of Order 2 for Image Q and Transformation T as:
The maximal value of Entropy of Order 2 occurs when the pixels are independent of each other. Thus,
We wished to determine the balance definition (integral, physicalist, or mean) best capturing what artists used for their portraits. For this purpose, we compared the optimal balance lines (Equation 7) to important features in the face. We wrote a special MATLAB function to perform this comparison. This function first determined the positions of the primary eye (the eye closer to the center of the canvas, Tyler,
In this study, we developed computational measures of symmetry, balance, and complexity, and investigated the relationship between these variables to probe the choices that artists of the Early Renaissance made about these quantities when painting portraits. Of these visual properties, the understanding of balance has perhaps been the most highly debated. Based on this debate, we have identified three different definitions of balance. They are the integral balance, physicalist balance, and mean balance (Equations 3, 5, and 6 respectively). Consequently, we began this study by determining which of these definitions matched best what we observed in portrait paintings. To do this, we first determined the positions in paintings in which each definition resulted in the greatest amount of vertical balance, or least imbalance (Equation 7). Not surprisingly, we found statistically significant positive correlations between these positions according to the different definitions of balance. For example, the Pearson linear correlation coefficients were 0.96 and 0.94 when plotting the best position of integral balance against those for the physicalist and mean balances respectively. We observed similar correlations for posed controls and quickly snapped photographs. These correlations make intuitive sense. They arise from the mathematical overlap of the definitions. However, a correlation between two definitions of balance does not mean that one of them is not better when inspected in detail. An illustration of the best positions obtained with the different definitions of balance can be seen in Figures
As suggested by Figures
Therefore, we conclude that the integral definition of balance captures what artist do better than the physicalist and mean ones. Hence, all of our subsequent analyses use the integral definition of balance.
A prediction of the PFT is that master painters would show biases toward optimizing balance in their portrait paintings. However, even if the PFT were right, artists might not optimize balance independently of other fluency variables. Our next goal was to get an understanding of exactly how well artists were balancing their paintings. We used two procedures to achieve this goal. In the one covered in the next section, we measured the imbalance index for all paintings. Here, we wanted to determine the precision of balance at different vertical heights of the image. To carry out this determination, we calculated the optimal position of balance as previously indicated, however in a row-by-row analysis. The result is a line of balance points (Equation 8) for each row as seen in Figure
Figure
However, Early Renaissance artists might not have balanced their paintings as well as they could. The balance points of the frontally posed photograph had much less variation (Figure
A quantitative analysis of 153 portrait paintings, 38 quickly snapped photographs, and 9 frontally posed images confirmed that artists worked to balance their paintings but not to perfection. In this analysis, we compared the precision of balance in the three different categories of images. For each image, we calculated the line thickness (Equation 9). The analysis showed that portrait paintings yielded a lower line thickness than the quickly snapped photographs (Figure
Do master painters also show biases toward high symmetry and complexity, but not optimize them independently of the other fluency variables? To answer this question, we quantified symmetry and complexity. In addition, we studied the relationship of these fluency variables with balance. Here, we begin with the quantification of the Indices of Asymmetry (Equation 1) and Imbalance (Equation 4) for all the images in our study (Figure
Figure
One reason for painters not to optimize balance and symmetry independently was that these variables showed a degree of correlation. A weak positive correlation between the Indices of Asymmetry and Imbalance was apparent for both portrait paintings and quickly snapped photographs in Figure
We additionally looked at the population of artists to determine if they showed individuality and choice in terms of these variables. An illustration of the individuality encountered in our data is shown in Figure
Next, we looked at the different measures of complexity to test whether master painters showed biases to increasing it, tried to optimize it, or made individual choices about it. In addition, we investigated the relationship between different indicators of complexity and the Index of Imbalance (Equation 4). One of the indices of complexity that we studied was that of Order 1, which captured the richness of the distribution of intensities (Equation 11). We also studied Complexity of Order 2 (Equation 12). This index captured how much spatial organization reduced the amount of information in the painting. As Equation 12 indicates, Complexity of Order 2 is a function of the Transformation T. Because an infinite number of such transformations are possible, Complexity of Order 2 is not just a simple index (Figures
The results in Figure
Unlike the Index of Asymmetry that correlated with the Index of Imbalance (Figure
Finally, we investigated whether master painters made individual choices about complexity, as they did for asymmetry and imbalance (Figure
Further evidence of individuality with respect to complexity came from an analysis of the correlation between Complexity of Order 1 and Δ Complexity. This analysis revealed a statistically significant negative correlation of −0.47, (
We have seen that when separated by artist, the distribution of the values of the fluency variables is not homogenous (Figures
If two fluency variables are interdependent, they may force the artist to choose, because increasing fluency through one variable may reduce fluency through another. We saw an example of interdependence in the positive correlation between symmetry and balance (Figure
Figure
We observed similar results when subjectively classifying poses in portrait paintings (Figure
External factors, such as the painting medium that artists must use also force them to make choices. During the Early Renaissance, artists mainly had a choice between a handful of media (Bambach,
Our analysis showed that the artists' works were influenced by the painting medium. For example, both oil and mixed paintings were statistically significantly more imbalanced than frescos and tempera paintings (two-sided Kruskal-Wallis test, 153 degrees of freedom, χ2 = 11.9,
In this study, we examined whether master portrait painters from the Early Renaissance Period showed esthetic biases according to the PFT. The theory posited that increased perceptual fluency was associated with a greater esthetic response. Therefore, one would expect that the painters created their works in a way to maximize the fluency of perceptual variables. In particular, painters might try to optimize balance, symmetry, and complexity in their works. These biases might be the result of conscious intent or occur unconsciously. Overall, we found that painters were indeed displaying esthetic biases toward increasing fluency. The painters' work exhibited more symmetry and balance than quickly snapped, non-artistic controls (Figures
To explain why master painters may not be optimizing all of their fluency variables independently, we propose to extend the PFT with the Neuroesthetic-Space Principle. This principle begins by proposing that during an esthetic judgment, the brain decomposes an image into its fluency variables. Our equations give possible definitions for some of these variables, but their exact details depend on the neural mechanisms performing the computations. In this work, we explore three such variables, namely, balance, symmetry, and complexity, but the Space is likely much more complex, being highly multi-dimensional. Our results suggest that the possible values that these variables may attain are not likely boundless. Instead, they may reside in a certain limited space. Cross sections of this space are illustrated by the scatterplots in Figures
Why did master painters exhibit individuality within the Neuroesthetic Space? We already mentioned that painters could use different painting media. However, the choice of these media was sometimes imposed by the artists' patrons and sometimes dependent on accessibility. For example, in the Early Renaissance, some artists had to do frescos, while others could use oil or tempera (Paoletti and Radke,
Another reason for individuality in the Neuroesthetic Space is that some fluency variables show interdependence. If all the variables were independent, then painters could manipulate them individually; nonetheless, with interdependence, the optimum of one variable might not be the optimum of another. Thus, artists had to choose. An example of a mild interdependence affecting artists' choice was the weak correlation between symmetry and balance (Figure
Therefore, because of media constraints, fluency-variable interdependence, or other reasons, portrait painters must exert individual choice. The difference in choices undoubtedly has innate, physiological, and personal experience components. For example, studies of preference for complexity show that different people lie in distinct portions of an inverted “U” curve (Jacobsen and Höfel,
An innovation of our paper is the introduction of computational methods to begin outlining the relationship between multiple fluency variables in a Neuroesthetic Space. Other definitions of the same fluency variables are possible and exist, of course (Dakin and Watt,
As for refining the definition of the fluency variables, a process such as the one that we used for balance suggests a path to follow. Balance is widely attributed as necessary to the appreciation of an image. Experiments have shown that lack of balance can be detected in the order of just tens of milliseconds (Locher and Nagy,
To test further whether the integral definition of balance was meaningful, we measured the quality, i.e., the precision, of the ensuing balance lines. The results of a row-by-row analysis in Figure
However, although we gained confidence about the integral balance, we know that our definition is probably not as good as it could be. If it were, we would expect the bar plots in Figure
Finally, how confident can we be of our definitions of complexity? The debate regarding a good psychophysical definition of visual complexity has remained unresolved thus far. Most existing definitions are grounded in some manner in information theory (Shannon and Weaver,
The focus of our study is primarily regarding the exteroceptive variables of perception, termed “outer psychophysics” by Fechner (Fechner,
What are the possible neural mechanisms of the PFT and the Neuroesthetic Space? We begin with the latter. Models of esthetics usually account for dual levels of processing, e.g., a “lower” sensory and a “higher” cognitive route. The latter which includes semantic and emotional content (Chatterjee,
We now turn our attention to the possible mechanisms of the PFT. To understand them, we reiterate that the computation of the location of the sensory input within the Neuroesthetic Space is distributed. Consequently, multisensory integration is required for the estimation of overall fluency and thus, esthetic processing. While the idea that an esthetic judgment involves distributed computations and subsequent integration is largely accepted, its mechanisms are unclear (Redies,
In this study, we propose the principle of a Neuroesthetic Space. This space is composed of complex, interdependent perceptual variables. Furthermore, the shape of the boundaries of the space may have complex geometries (Figures
Another question that we face about the principle of Neuroesthetic Space pertains to its temporal dynamics. How do painters and their paintings evolve across art periods? Art could move inside a fixed Neuroesthetic Space, or its boundaries could drift slowly across time or jump abruptly from period to period. We began our analysis focusing on the period when portraiture first emerged. This focus allowed uncovering fundamental fluency variables. By tracking their dynamics over time, we may effectively measure how this art forms and its Neuroesthetic Space changes from period to period (Spehr et al.,
This study was carried out in accordance with the recommendations of Human Subjects Guidelines, Georgetown Institutional Review Board with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Institutional Review Board at Georgetown University.
HA was involved in the design of the project, developing and using programming scripts for data gathering and analysis, carrying out the measurements with participants, interpreting results, and writing and revising the manuscript. IC-H was involved in the design of the project, selecting the paintings, collecting data, carrying out the measurements with participants, and revising the manuscript. NG was involved in the design of the project, developing the mathematical equations, creating and using programming scripts for data gathering and analysis, interpreting the results, and revising and approving the manuscript for publication.
This work was partially funded by the Training Grant T32NS041231 from the National Institutes of Health to the Interdisciplinary Program in Neuroscience at Georgetown University.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We would like to thank Ms. Meg Oakely, Director of Copyright and Scholarly Communication at Georgetown University Library for her assistance in obtaining the rights to images used in this publication. We would also like to thank Prof. Anjan Chatterjee for his helpful comments on a preliminary conference presentation of this work, specifically related to the Processing Fluency Theory as it applies to an artist. In addition, IC-H would like to thank the Consejo Superior de la Universidad Nacional de Colombia for authorizing his sabbatical year at Georgetown University.
The Supplementary Material for this article can be found online at:
1The attribution of this painting has been in dispute by connoisseurs like Morelli, Springer, and Müntz (Pagden,