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Heterogeneity in chromatic distance in images and characterization of massive painting information gear up

• Byunghwee Lee,
• Daniel Kim,
• Seunghye Sun,
• Hawoong Jeong,
• Juyong Park

x

• Published: September 25, 2018
• https://doi.org/10.1371/journal.pone.0204430

Figures

Abstruse

Painting is an art form that has long functioned as a major aqueduct for the creative expression and advice of humans, its evolution taking identify under an interplay with the scientific discipline, technology, and social environments of the times. Therefore, understanding the process based on comprehensive data could shed light on how humans acted and manifested creatively under changing conditions. Yet, there exist few systematic frameworks that characterize the process for painting, which would require robust statistical methods for defining painting characteristics and identifying human's creative developments, and data of high quality and sufficient quantity. Hither we propose that the color contrast of a painting image signifying the heterogeneity in inter-pixel chromatic distance tin exist a useful representation of its fashion, integrating both the colour and geometry. From the color contrasts of paintings from a large-scale, comprehensive annal of 179 853 high-quality images spanning several centuries we characterize the temporal evolutionary patterns of paintings, and nowadays a deep study of an boggling expansion in creative diversity and individuality that came to ascertain the modernistic era.

Commendation: Lee B, Kim D, Sun S, Jeong H, Park J (2018) Heterogeneity in chromatic distance in images and label of massive painting information fix. PLoS ONE xiii(9): e0204430. https://doi.org/x.1371/periodical.pone.0204430

Editor: Dante R. Chialvo, Consejo Nacional de Investigaciones Cientificas y Tecnicas, ARGENTINA

Received: June 5, 2018; Accepted: September nine, 2018; Published: September 25, 2018

Copyright: © 2018 Lee et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted utilise, distribution, and reproduction in any medium, provided the original writer and source are credited.

Data Availability: All relevant data are within the paper.

Funding: B. Fifty. and H. J. acknowledge the support of National Research Foundation of Korea (NRF-2017R1A2B3006930). (http://www.nrf.re.kr/). J. P. acknowledges the back up of National Research Foundation of Korea (NRF-20100004910, NRF-2013S1A3A2055285 and NRF-2016S1A2A2911945) (http://www.nrf.re.kr/), Ministry building of Science (MSIP-R0184-15-1037) (http://www.msip.become.kr), and BK21 Plus Postgraduate System for Content Scientific discipline (https://bkplus.nrf.re.kr/).

Competing interests: The affiliation with Samsung SDS does not alter our adherence to PLOS ONE policies on sharing data and materials. This commercial affiliation does not alter our adherence to all PLOS One policies on sharing data and materials.

Introduction

Homo have painted to express, record, and communicate ideas and recount experiences since long before the invention of writing [1]. Painting thus has an essential and intimate connection to human history and, as a visual art course borne out of human sensitivity, imagination, and dexterity, is also a product of the human thought, scientific discipline, and technology that make up one's mind the limits of what humans tin can envision and visualize on a physical medium such as a sheet. Such direct, intimate human relationship between painting and science implies that a robust scientific study of painting could produce insights and reveal new answers to many pertinent questions in interdisciplinary field in quantitative and belittling style. To proceed with a scientific research of paintings, we first establish that a piece of fine art can be viewed as a "circuitous system", as information technology is composed of heterogeneous elements that combine to upshot novel emergent phenomena, a hallmark feature of one; in the example of an artwork, the stimulation of the senses the viewer experiences in its presence–be it cerebral, emotional, or physiological–cannot be attributed to a single element of it, for instance a single dot of a certain color, but the collective consequence of all its parts.

A recent development that is proving to have far-reaching implications for a scientific exploration of human actions and beliefs in many social, cultural complex systems is the increasing availability of massive high-quality data that allows a large-scale application of scientific frameworks and verification [2–7]. In the area of culture, subjects on which quantitative pattern-finding accept been performed to a degree include literature [8–12] where Polish linguist Wincenty Lutosławski'due south piece of work on the statistical features of give-and-take usage in Plato'south Dialogue [8] is well known, music [13–17], and painting [18–26]. A landmark scientific report of paintings can be constitute in Taylor et al.'due south characterisation of Jackson Pollock's (1912–1956) drip paintings using fractal geometry to distinguish between accurate Pollocks and those of unknown origins [18], demonstrating that an creative manner tin can be quantified. More contempo examples regarding painting include Lyu et al.'s wavelet-based decomposition of images [20], Hughes et al.'s sparse-coding models for authenticating artworks [21], Kim et al.'s characterization of variations in chiaroscuro technique via the then-called "roughness exponent" from statistical physics [22] and Gatys et al.'due south style representation derived from correlations between the unlike features in different layers in a Convolutional Neural Network [23]. Besides quantification of artistic styles, some studied perceived similarities betwixt different paintings [24], the influence relationships between artworks for quantifying inventiveness in an artwork [25], and the changes in the perception of dazzler using confront-recognition on images from different eras [26].

Upon these progress in scientific analysis of painting, there all the same remains much necessity for a robust, comprehensive effort to overcome the following shortcomings therein: First, they often autumn short of presenting a coherent and robust quantitative framework for analysis of multiple images; second, they do not use the full color data (due to the added complexity); 3rd, they tend to focus on specific artworks or painters, non seeking generality, among others. In this piece of work, we overcome these bug by formulating a framework for analyzing paintings that uses the consummate colour information which at the same time incorporates the geometrical relationships between the colors, two essential edifice blocks of an image. Our proposed quantity tin be computed rapidly on the entire collection of digital images, assuasive us to trace the stylistic evolution of painting throughout different periods, and identify pregnant patterns that characterizes each menses.

Reflecting its ubiquity in nature and intriguing scientific characteristics, colour boasts a long history as a discipline of all-encompassing scientific investigation in many fields such every bit physics (eastward.g., optics), biology (e.g., vision), and especially in the modern times, visual engineering science, to proper name only a few. The beginning of modern quantitative research on color can be attributed to ii groundbreaking investigations by Newton [27] and Goethe [28, 29] who focused on the nature of calorie-free equally the combinations of, and differentiations between, colors that lay foundations to more than modern research on color and vision [30, 31]. Inspired past these works and subsequent developments, here nosotros propose the concept of 'color contrast' every bit a signature of how color has been used in a painting. Equally its name suggests, color contrast refers to the compound outcome of chromatic differentiation originating from different colors in a painting. Well-known examples of paintings with intuitive, easily noticeable color contrast include Vincent van Gogh's (1853–1890) Starry Night (1899) where a bright yellow moon is embedded in the dark bluish sky and Piet Mondrian's (1872–1944) Composition A (1923) where well-divers geometric shapes of distinct colors are juxtaposed to form the so-called 'hard edge' painting, a mode popularized during the twentieth century and became one of its signature styles. These two examples suggest that the sources of color contrast are the colour departure (east.yard., bright yellow versus night bluish) and the geometrical proximity (eastward.g., the juxtaposition of distinct colors generating clear, crisp boundaries). Based on this realization, in this paper we devise a statistical measure of the colour contrast in a painting we label seamlessness Due south, demonstrate that this quantity is indeed a useful indicator for characterizing distinct painting styles, and finally apply it to nearly 180000 digital scans of historical paintings–the largest yet in our type of study–to rail the evolution of painting and narrate how individual painters take developed creatively.

Data clarification

Digital scans of paintings (mostly western) were collected the post-obit three major online art databases: Web Gallery of Fine art (abbreviated WGA) [3], Wiki Art (WA) [4], and BBC-Your Paintings (BYP) [5]. The WGA contains paintings dated pre-1900, while the WA and BYP datasets contain those dated up to 2014 (all datasets are upwards-to-appointment as of Oct 2015). WGA provides 2 useful metadata on the paintings: the painting technique (e.g., tempera, fresco, oil) and genre (e.g., portrait, still life, and 'genre painting'–itself a specific genre depicting ordinary life). BYP is mainly a collection of oil paintings preserved in, and originating from, the U.k.. (We evidence that BYP data notwithstanding exhibits a comparable trend in color dissimilarity with other datasets.) The paintings dated pre-1300s were excluded, as they were besides few. Also excluded were those deemed improper for our analysis or outside the scope of information technology: They include partial images of a larger original, not-rectangular frames, seriously damaged images, photographs, etc. The final datasets used in our analysis comprise eighteen 321 (WGA), lxx 235 (WA), 91 297 (BYP) images for a total of 179 853. A significant bulk of the images considered in this work–99.eight% of WGA, 76.0% of WA, and all of BYP–are 500 pixels or larger in their length of longer side.

Results

Characterizing colour contrast of a painting from inter-pixel colour difference distribution

Colour contrast represents the effect brought on by the differences in color between different points in a painting. It therefore can play a key role in characterizing the results of how a painter places dissimilar colors on a sheet in various positions, in other words, paintings. Homo sense of color dissimilarity between two colors in a painting (the pixels in instance of a digital epitome) would be afflicted nigh strongly by two factors, the divergence between the colors themselves and the geometrical separation—the more than unlike the colors and the closer they are in real infinite, the more pronounced the consequence of color contrast will be. Quantifying colour contrast with such a belongings thus requires two elements: A measure of the chromatic divergence between two colors that agrees with homo perception, and the spatial separation between the ii.

Quantifying the difference between two colors starts by placing them on a three-coordinate organization called 'color space'. A color space is named according to what the three coordinates measure. Ordinarily used ones include the RGB (Red, Green, Blueish) space, the HSV space (Hue–position on the colour bicycle, Saturation, Value–brightness), and the CIELab infinite (the full nomenclature existence 1976 CIE L* a* b*) for Fifty* (lightness between 0 for black and 100 for white), a* (running the gamut betwixt cyan and magenta, but no specified numerical limits), and b* (between blue and yellow, similar). To measure the color contrast we utilize the CIELab, as it was designed so that the human perception of the deviation between two colors and would exist proportional to the the Euclidean distance between the 2, [32]. And in the present work, we take the simplest arroyo of because the colour distances betwixt side by side pixel pairs, which yields a full of ∼iiN pixel pairs in a rectangular image of Due north pixels to consider. Fig ane(a) and 1(d) visualize the differences between next pixel colors for 2 paintings, Piet Mondrian'due south Composition A and Claude Monet'south H2o Lilies and Japanese Bridge.

Fig i. Quantifying the colour contrast of a painting from the color distances betwixt adjacent pixels.

The altitude is visualized as height d along the z-centrality overlaid on the corresponding paintings, Piet Mondrian's Composition A ((a)–(c)) and Claude Monet'due south H2o Lilies and Japanese Bridge ((d)–(f)). (a) In the Mondrian, a number of large d correspond to the conspicuous walls betwixt regular patches of uniform colors. (b) Such pattern can be shown in more detail via the distribution π(d) ('o'), plotted in log-log scale. (c) The epitome size-dependent raw distributions can exist rescaled into a unmarried curve. (d) The Monet, meanwhile, lacks the crisp patchy structure of the Mondrian, indicative of heavily intertwining brushstrokes using complex color mixtures of the impressionism, resulting in high average d but few extreme values. (east) The Monet'southward π(d) accordingly shows a more quickly decaying tail. (f) The distribution once again collapses onto a single characteristic curve, regardless of paradigm size. All images are obtained from Wiki Art and in the public domain.

https://doi.org/10.1371/periodical.pone.0204430.g001

We label the distribution of color difference betwixt the ∼ 2Due north neighboring pixel pairs in a painting its 'inter-pixel color difference distribution' π(d). While the measured π(d) is paradigm-resolution dependent (Fig 1(b) and ane(e)), rescaling information technology past (1) where is the mean, caused distributions collapse into a single curve (Fig 1(c) and 1(f)), demonstrating its size-contained universal characteristic.

In Fig ane(c) and 1(f), we see that the shapes of π(d)s from the 2 paintings are significantly unlike. In the Mondrian, a number of large d stand for to the conspicuous walls between regular patches of compatible colors resulting in a heavy-tailed distribution of π(d) compared to an exponential. The Monet, meanwhile, lacks the crisp patchy structure of the Mondrian, indicative of heavily intertwining brushstrokes using complex color mixtures of the impressionism, resulting in loftier average d but few extreme values. The Monet's π(d) accordingly shows a more than rapidly decomposable tail.

To run across what types of painting a given π(d) represents, we generate artificial images that possess the π(d) of a existent painting as input. The procedure starts by randomly relocating the pixels of the input image, then updating the image stepwise using the Metropolis-Hastings algorithm until the original painting's π(d) is reconstructed, and inspecting the resulting paradigm. To employ the Urban center-Hastings algorithm nosotros define the energy East of an interim image I to be the Kolmogorov–Smirnov (G-S) statistic between the π(d)'s of the acting epitome and the original (ii) where Π _I (x) and Π(x) are the cumulative distributions of their π(x), and sup _x denotes the supremum of the set of distances. The K-S statistic quantifies a altitude between two cumulative distributions and is useful for nonparametric methods for comparing two sample distributions. Other statistical distances such every bit Jensen-Shannon divergence and Bhattacharyya altitude may also exist used for this purpose. Our Urban center-Hastings process is as follows:

1. Initialize: The pixels of the original prototype are completely randomly shuffled, resulting in the initial configuration we label I ₀.
2. Generate a candidate configuration I′ by randomly choosing two pixels from the current configuration I then switching their locations.
3. Calculate the energy departure between I and I′.
4. Accept the new configuration with a probability .
5. Continue to next time step t = t + 1, and repeat the processes 2–iv until the target π(d) is accomplished.

Temperature T can exist tuned to aid escape local free energy minima and assistance in convergence, and various techniques including simulated annealing could be employed to find approximate global energy minima [33]. Fig 2 shows the method applied to Pieter Bruegel the Elder's Census at Bethlehem (1566) and the final images obtained from using image generation process (see Fig 2(c) and ii(d)) using a reduced grayscale version (Fig two(b)) for a faster simulation. The π(d)s of the original and the reconstructed epitome are shown in Fig 2(eastward). The reconstructed images using simulation, with identical π(d), exhibits clusters of similar sizes and colors every bit the original, i.e. color contrast. This does demonstrate that π(d) indeed characterizes the colour contrast of a painting. Merely π(d) can be bothersome to employ, then we devise a simpler measure derived from π(d) itself, inspired by the relationship between the shapes of π(d) and paintings shown in Fig one. The long- and short-tail distributions tin exist conveniently compared past the coefficient of variation , where and σ _d are the mean and the standard divergence of π(d). A further desirable belongings of this quantity is that information technology is invariable under scaling of Eq one. Other characterizing measures using higher moments of the distribution such as skewness or kurtosis also could be used every bit they are independent of location and calibration parameters. The value of the coefficient of variation ranges between 0 and ∞, 0 for completely regular distributions such as a delta office (σ _d = 0), ane for an exponential or Poisson distribution ( ), and ∞ for heavy-tailed distributions with an infinite variance. For convenience, it is commonplace to use instead a quantity (3) which takes the range [−1, ane] of values. This quantity has establish a wide range of employ in various scientific fields, for instance in the study of inter-event time distributions such as analysis of earthquake occurrence patterns [34], heartbeats of human subjects [34, 35], advice patterns of individuals [36], and human being behavioral dynamics online and offline [37, 38], etc. We do the same here, and we label this quantity the seamlessness of a painting, to exist further explained below.

Fig two. Generating a reconstructed fake image with the same inter-pixel color difference distribution as an input painting.

(a) The input painting The Demography at Bethlehem by Pieter Bruegel the Elder (1566). The paradigm is obtained from Wiki Art and in the public domain. (b) For a faster simulation we used a rescaled (20x20) grayscale version. (c) The reconstructed image from a completely randomized version of the original. While the locations of the patches of like colors have inverse, they are of similar sizes every bit the original paradigm. (d) The simulated prototype where xxx% of the pixels were maintained fixed in the original image. (e) π(d) of the rescaled original image (b), reconstructed (c), and the randomly shuffled images.

https://doi.org/10.1371/journal.pone.0204430.g002

In Fig three we evidence sample randomly generated grayscale images with Due south taking the two farthermost values and one the middle: (a) A power-law π(d) ∼ d ^−α with power exponent α = 1 (S = 1), (b) an exponential π(d) ∼ exp(−λd)) with λ = 1/40 (South = 0), (c) a Gaussian distribution ( ) with a modest width (σ _d = one) (Southward ≈ −ane). In Fig 3(a), nosotros see that the images with a power-police π(d) (big Due south) exhibit interfaces of abrupt color change betwixt extensive patches of similar colors to accommodate a large inhomogeneity in d, giving rise to a potent sense of overall color contrast. Then in Fig 3(b) we run across a weakened such issue: compared with (a), hither the pixel-to-pixel color transitions are more gradual and relatively lack particularly sharp boundaries. Finally in Fig 3(c) nosotros see a lack of sizable patches of uniform colors, resulting in blurred boundaries with a small Due south. This observations is as well origin of our nomenclature 'Seamlessness': A college Due south (Fig 3(a)) implies the image appears as if made upwardly of a smaller number of patches (simply each one existence larger), requiring less seams (if 1 were to stitch them). A smaller South (Fig 3(c)) means many smaller patches of different colors are intertwined, resulting in more seams.

Fig iii. 3 distinct probability distributions π(d) and fake images.

(a) Power-police distribution π(d) ∼ d ^−one (Due south = 1) with (b) Exponential distribution (π(d) ∼ exp(−d/xl)) (Due south = 0). (c) A narrow Gaussian distribution with mean and σ _d = 1 (South ≈ −ane). As we get from big S (left) to modest (correct), the cluster of like colors become smaller, showing signs of lower color dissimilarity.

https://doi.org/ten.1371/journal.pone.0204430.g003

We further deport a cluster size analysis on the simulated images to quantify our visual inspection. To exercise so we measure the colour difference between adjacent pixel pairs (taking a value between 0 and 1 in a grayscale prototype) and link the pixels that are of 0.1 or a smaller value. And so the set of pixels that are connected via those links are considered to ascertain a cluster of like colors. We measure the size of the largest cluster and the boilerplate size of clusters to characterize each image. The generated images from the three dissimilar π(d)southward in Fig three prove quantitatively unlike characteristics. The largest cluster size of the images (whose full size is 20×20), generated from a power-law distribution is 85.v and the average cluster size is 7.01 on average (Fig 3(a)). The images following an exponential distribution (Fig 3(b)) have the largest cluster size as 62.75 and the boilerplate cluster size is 4.68 on average. Lastly, the largest cluster size of the images generated from a gaussian distribution is eleven.0 and the average cluster size is 1.45 on boilerplate (Fig 3(c)). The divergence in the size of largest clusters and the boilerplate cluster size of iii distinct π(d)s shows that different π(d)s indeed exhibit different characteristics.

Mapping the evolution of color contrast from massive painting data sets

S measured from the data ready is presented as a besprinkle plot in Fig 4(b) with the date of production in the 10-axis. Clearer statistical patterns of changes in color contrast are presented in Fig 4(c) to 4(m). First, in Fig four(c) to 4(g), the average and standard departure in S have more often than not increased over time (with the exception of a temporary dip in the 18-19th centuries for the average S). These changes can be plant to correspond to notable and well-understood developments in painting technique and apparatuses. For example, the increase in S around the fifteenth century coincides with the adoption of oil every bit pigment binder medium (Fig 5(a)) [1, 39]; Earlier then, tempera (using egg yolk as folder medium) and fresco (watercolor painted directly on moisture plaster; Michelangelo's Sistine Chapel ceiling painting is a famous example) were the virtually mutual. The very physical characteristic of oil–high viscosity and the longer time to dry–provided painters with an opportunity to try new techniques that resulted in high contrast (Fig 5(b)), most notably chiaroscuro (noted past gradations between dark and light that create the effect of highlighting the discipline [39]) during the Renaissance period, and tenebrism (representing a dramatic dissimilarity betwixt lite and dark [39]) made popular during the Bizarre flow by such painters every bit Caravaggio (1517–1610).

Fig 4. The evolution of S showing the development of paintings over time.

(a) The number of paintings in the 3 datasets (WA, WGA, BYP) used in this study. (b) Besprinkle plot of Due south from 1300 CE to 2014 CE. We find an increase in the average and the variance of S, almost noticeable in the mid-nineteenth century. (c) Changes in average S over time, along with the standard error of the mean. (d) Each individual painter'southward standard difference of Due south tends to grow, showing the widening diversity in way of works produced past a painter. Each gray dot indicates an artist. (east)—(g) The changing variances of Due south over time (WA, WGA, and BYP). The distributions get the broadest in the modern era. (The WGA dataset contains paintings only upward to 1900.)

https://doi.org/x.1371/periodical.pone.0204430.g004

Fig 5. Evolution of Due south in paintings of diverse techniques and genres.

(a) The number of paintings of various techniques in the WGA dataset. (b) Historical changes of S in different painting techniques, with the standard fault of the mean indicated. Kolmogorov-Smirnov tests on the shaded area ostend that the distribution of South of dissimilar techniques are significantly different (P < x⁻¹¹ betwixt every pair). (c) Number of paintings in various genres in the WGA dataset. (d) Evolution of S in various genres, with the standard fault of the hateful indicated.

https://doi.org/10.1371/periodical.pone.0204430.g005

The emergence of such novel painting techniques is besides closely related to the rise of novel painting genres: The ability to highlight the bailiwick is credited for the ascent in demand for portraits, for case (Fig 5(c)). Still life, on the other hand, shows notable changes during the sixteenth century, reaching its peak in the seventeenth century (Fig 5(d)). The increase of Southward in still life in the sixteenth century coincides with the changes in themes and subjects: In the offset half of the century, Dutch painters such as Pieter Aertsen (1508–1575) and Joachim Beuckelaer (1533–1573) intentionally combined nevertheless life with detailed and vivid depictions of biblical scenes in the groundwork, while in the 2d half artists began to highlight notwithstanding objects by incorporating chiaroscuro previously heavily used in portraits, resulting in high South [39].

The most significant evolution occurred in the nineteenth century (Fig 4(c) and 4(d)) when artists began to perceive paintings as a means of expressing one's individuality and originality more strongly than before [40]. The pursuit of a wide range of dissimilar interpretations of the earth gave rise to new techniques for expressing nature [ane]. In the beginning of the nineteenth century, the pursuit of fleeting impressions of light onto nature and landscapes replaced the dramatic, bogus lighting effect of the previous era, probable causing S to drop. The arrival of those "impressionists" were also helped past the railroad and the portable paints that enabled traveling to distant areas, leading to the surge in popularity of landscape paintings in the nineteenth century [41] (Fig five(c)). Towards the end of the nineteenth century modern abstract art began to emerge, noted for an fifty-fifty more drastic difference from realism [1]. After the turn down in South during the impressionist era, such uncomplicated and geometric abstraction led to a rapid increase in S (Fig four(c)). We notation that, in addition, the increase in mean Due south was accompanied past a significant increase in variance of S, indicating heightened diverseness in style of paintings produced. The virtually notable growth in variance occurs between the nineteenth and the twentieth centuries (Fig 4(b)). Fig iv(e) to 4(yard) shows this in more detail: in earlier periods, the distribution of South is narrow around the mean, simply information technology becomes increasingly broader equally we approach the modern times, rendering it less and less valid to talk of a 'typical' way. Next nosotros delve into the origin of this increased diversity in more than detail.

Characterizing the individuality of painters in the modern era

The patterns of Due south shown in Fig 4(e) to 4(thou) are aggregate, i.east. over all the paintings contained in our data set. It thus cannot teach us about how varied the private painters' styles may be, since two opposite explanations–painters having clear individual styles (therefore the heterogeneity coming from at that place existence many different painters), or painters themselves exhibiting diverse styles–could lead to the same patterns. While in reality there would be both types of painters, nosotros find that many modernistic painters take produced works that span a wide range of Southward, equally shown in Fig iv(d). This culture of experimentation and embodiment of diverse stylistic possibilities are in good understanding with the characteristic of the modern era mentioned above [1]. This prompts us to investigate the nature of individual stylistic diversity for the mod painter. Here nosotros propose ii distinct yet complementary aspects of stylistic individuality and explore them to better characterize the modern era, namely the individual painter's stylistic (one) development over their career that nosotros call metamorphosality, and (2) uniqueness relative to the popular styles of the mean solar day that nosotros phone call singularity.

Private evolution: Metamorphosality.

Mondrian, founder of De Stijl motion and known for iconic abstractionism, in fact produced paintings that span a wide range of S (Fig vi(d)). And it is reflected in how he progressed gradually from traditional manner (small S) to abstractionism (large South) that matured in the 1920s (Fig half-dozen(a) and 6(d)). Pierre Auguste Renoir (1841–1919), leader of early on impressionism, exhibited the opposite trend: his S decreases over time, as he transitions to more free-flowing brush strokes of impressionist techniques to generate boundaries that fuse softly with the background (Fig vi(b) and six(e)). Other prominent impressionists such as Claude Monet (1840–1926) and Edgar Degas (1834–1917) demonstrate like trends.

Fig 6. Characterizing individual painters.

(a, b) Growth in S of Mondrian's and Renoir's paintings, respectively, over the normalized careers of each painter. The gradient a of the linear fit (dashed carmine lines) is 0.62 for Mondrian and −0.10 for Renoir. (c) The histogram of the linear slopes {a} of 1 326 mod artists who produced paintings in at least five singled-out years. A few notable artists are indicated. The dashed line indicates the average slope ( , a slight tendency towards abstract paintings). (d, due east) Painting samples by Mondrian and Renoir, respectively, highlighting their stylistic changes over their careers (All images are obtained from Wiki Art and in the public domain). (f) Singularity of paintings past seven select artists. The darker ring indicates the range −i ≤ z ≤ 1. (grand) Histogram of the singularity of 330 artists with more than xl paintings. The dashed line indicates the average gradient ( ).

https://doi.org/x.1371/periodical.pone.0204430.g006

These observations prompt us to quantify such stylistic evolution of a painter using the charge per unit of changes in S, given as the slope a of the linear fit over 1's career normalized to 1. For case, nosotros find a = 0.62 for Mondrian and a = −0.ten for Renoir (Fig half-dozen(c)). The distribution of a for the 1 326 modern painters whose median of the product year is 1800 or later, (who produced paintings in v or more distinct years) resembles a Gaussian. Given this observation and that the quality of an creative person is more than reasonably measured in relation to others (as an absolute measure of creative quality is not readily available), we define the metamorphosality μ of a painter as the z-score of the painter's a, where is the average, and σ _a is the standard deviation. In Fig 7(a) we show the top 100 artists in terms of metamorphosality, fifty with increasing S fifty with decreasing S. On the positive side the American painter Howard Mehring (1931–1978) shows the largest μ = iv.07. Appropriately, Mehring's early works are reminiscent of such figures equally Pollock or Mark Rothko (1903–1970) and Helen Frankenthaler (1928–2011), employing scattered colors with vague boundaries [42]. His later on works, on the other hand, brainstorm to characteristic geometric compositions of vivid colors with sharp transitions, similar to Mondrian's difficult-border paintings. At the other extreme with the most negative μ is Swiss-French painter Félix Edouard Vallotton (1865–1925), member of the post-impressionist avant-garde group Les Nabis. Initially having gained fame for forest cuts featuring extremely reductive flat patterns with strong outlines (high Southward), he produced classical-fashion paintings such equally landscapes and still life in later life (low S) for μ = −5.59.

Fig vii. Modern painters with the highest metamorphosality or singularity.

(a) The 100 artists with the strongest metamorphosality μ (fifty positively, l negatively). American painter Howard Mehring made the most significant shift from low-S to loftier-Southward during his career (acme), while Felix Vallotton was the contrary (bottom). (b) The 100 artists with the strongest singularity ν (50 positively, 50 negatively). Qi Baishi'south works comprise the highest fraction of singularly loftier-South paintings, while Kolomon Moser was the reverse.

https://doi.org/ten.1371/journal.pone.0204430.g007

Uniqueness amidst contemporaries: Singularity.

Another fashion to characterize a potent stylistic individuality would to measure how unique, or singular, a painting is. It is once again sensible to measure it in relation to other works, in this case especially among those made effectually the same time, since a fashion that is an outlier at one point in time may be mainstream at another, and vice versa. This tin be achieved by computing the z-score of a painting's S amid its contemporary (defined as having been produced within five years of information technology). We and so phone call a painting highly singular if its |z| > z _c , a threshold value which we ready to be 1 in this paper. In Fig half dozen(f) we show the z-scores of paintings of seven select painters every bit a scatter plot where those within the lightly-shaded areas represent the highly singular paintings (|z| > z _c ). The figure teaches united states of america that painters produced dissimilar ratios of highly singular works, indicating their conventional or unorthodox nature, and the styles they belong to (positive or negative S). The singularity ν of an creative person is divers equally the divergence between the fractions of their works in z > 1 and z < −1. Such definition of singularity give united states of america the benefit of identifying those who tended to produce singular paintings and their preferred style (loftier or low S) simultaneously. For example, 45% of Mondrian's paintings are in z > 1 (singularity loftier-South) and six% in z < −1 (singularly low-South) giving ν = 0.39, apparently consistent with his role in loftier-South paintings. The histogram of the ν of 330 mod painters (who produced more than twoscore paintings for sufficient data) of Fig 6(g) shows us the range of singularities amongst painters, including those even more singular than Mondrian. A more comprehensive listing of the most singular painters (50 for ν > 0 and fifty for negative) of Fig 7(b) contains many names who plough out to be highly regarded in fact for their groundbreaking and unique styles: Examples include Qi Baishi (1864–1957), Chinese-built-in but very popular in the West for witty and brilliant watercolors [43], has the largest singularity (ν = 0.92), followed by Max Bill (1908–1994) known for geometric paintings that came to symbolize the so-called 'Swiss design' (ν = 0.79). On the opposite side nosotros find Koloman Moser (1868–1918), founding member of the Vienna Secession movement and known for complex repetitive motifs inspired by classical Greek and Roman art (ν = −0.91), followed closely by Eugène Leroy (1910–2000) known for numerous works featuring thick brush strokes in unlike colors, resulting in obscure and not readily identifiable imagery [44], to name but a few.

Word

This piece of work presents a written report to characterize the creative deportment of humans from a massive, loftier-quality cultural data spanning several centuries upwards to the modern era. To accomplish it nosotros devised a theoretical and computational framework for quantifying color contrast based on the human relationship betwixt the colors and geometry of the paintings. We proposed quantifying the overall color dissimilarity of a painting by the seamlessness statistic S derived from the full distribution of the inter-pixel color differences, and using the Monte Carlo sampling methods from thermodynamics we demonstrated that South is a consistent representation of color contrast.

Measurements of S on the information were shown to capture in numerical terms multiple historically important developments (scientific, technological, technical, aesthetic, etc.) in that impacted the evolution of painting techniques, genres, and subjects. This has allowed united states to present the stylistic development over human history and how it relates to the conditions of the times brought on by scientific, technological, cognitive innovations in a coherent and quantitative way.

To understand the greatly increased stylistic diverseness of painting in the modernistic era, we profiled the individual qualities of painters using two criteria, metamorphosality (the variability of i's styles over a career) and singularity (uniqueness of style against one'south contemporaries). Nosotros found that the stylistic multifariousness of painting in the modern era is due not to in that location being only more painters, but to the emergence of painters actively evolving stylistically and producing original paintings that defied the established norms of the day.

We believe that our work shows a robust scientific methodology for modeling and analysis of complexity in visual artifacts using large-scale data. Our work could likewise be fruitfully applied to a variety of art forms which tin clearly be converted to data representing its components and the relationship amongst them that allow us to discover interesting patterns and information that can lead to new understanding of humans' creative process.

Based on our current investigation we can imagine multiple interesting directions for future research. Outset, more intricate assay using S would exist possible and desirable in the immediate future to account for the possible biases across time and place due to the specific information set we used. Venturing further, not-western European or American fine art including Asian, Hindu, and Islamic painting art take been largely untouched in our piece of work; large-scale analyses of these subjects would also be of firsthand, universal interest. Also, integrating an analytical study using stylometric measures such as ours with object detection and sectionalisation techniques from machine learning could lead to a deeper understanding of art that incorporates both the styles and contents of paintings [26, 45, 46]. For example, how the same objects or motifs accept been portrayed differently over time would shed light on changes in tastes likewise as style. Going beyond the painting course, our work tin too find use in understanding sculpture, architecture, visual design, moving picture, blitheness, typography, etc.

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Source: https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0204430

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