Identification and quantification of colours in children’s drawings Christelle Cocco1 , Raphaël Ceré2 , Aris Xanthos3 , Pierre-Yves Brandt1 1 Institute for Social Sciences of Religions, University of Lausanne, Switzerland 2 Department of Geography and Sustainability, University of Lausanne, Switzerland 3 Department of Language and Information Sciences, University of Lausanne, Switzerland {ccocco, rcere, axanthos, pbrandt}@unil.ch Abstract colour usage in the drawings, e.g. “Which colours are used to draw god?”, “Are the colours used pref- Researchers in social sciences and humanit- erentially to answer the task of drawing god the ies disciplines are confronted with the need same in each country?”, or “Do older children use to analyse increasing amounts of visual a larger array of colours than younger ones?”. An- data, which calls for the development of swering such questions presupposes the ability to new computational methods. This paper fo- identify the colours used in each of the thousands of cuses on the problem of identifying the col- drawings in the “Drawings of gods” database. This ours used in children’s drawings, notably in paper attempts to give a formal characterisation of the perspective of assessing their diversity. this problem, proposes a computational methodo- It describes a simple, effective, and flexible logy for solving it, and discusses the first results of algorithm for performing this task. This its application to a subset of the project’s drawings. methodology is applied to a subset of more Processes for capturing colours and providing than 1000 drawings taken from the “Draw- numerical representations of them have been stand- ings of gods” database. The first results ardised long ago by such institutions as the Com- show that this approach makes it possible mission Internationale de l’Eclairage (CIE). Ar- to address meaningful research questions guably, the most well-known scheme for digital concerning the patterns of colour usage in colour representation is the RGB colour space: a these data. colour is described by a triplet of values, each of which corresponds to the intensity of a primary col- 1 Introduction our light beam (red, green, or blue); each value is Social sciences and humanities (SSH) have a rich encoded with one octet, so that there are 2563 = tradition of using computational methods for ana- 16, 777, 216 possible RGB colour triplets. This lysing text data. In contrast, although visual media representation, which is the one in which the draw- have an increasing importance in many disciplines ings of our dataset are converted by the digitisation and a central role in some of them, researchers in process, is vastly too fine-grained for answering SSH have only just begun to explore the methodo- research questions of the kind stated above, as a logical opportunities offered by computerized im- single pencil stroke on a sheet of paper typically age analysis. Rooted in developmental psychology contains dozens of RGB shades when digitised. and psychology of religion, the “Drawings of gods” The challenge of colour identification, then, con- project1 is an example of an SSH project in which sists in defining a consistent mapping from a stand- image is the primary data type: its main goals are ard digital colour space (in our case, RGB) to a the collection and analysis of drawings of gods pro- much more coarse-grained colour set, adapted to duced by children in various countries and cultures the research purposes of the widest possible range (see, e.g., Brandt et al., 2009; Dandarova, 2013; of SSH disciplines. Dandarova Robert et al., 2016). In this context, an This task is rendered significantly more difficult important class of research questions is related to by the fact that colour perception is a complex phe- nomenon which varies from one person to another 1. This project is supported by the Swiss National Science Foundation (SNSF), grant no. 156383. The database of the on the basis of neurobiological factors, as well as project is available at http://ddd.unil.ch/. cultural factors such as language (Pastoureau, 2017, 11 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) pp. 35 and 87). This was confirmed by a prelimin- ing colour similarity rather than assigning pixels to ary experiment where we asked five human experts predefined colour categories. Colour names have of various languages and cultures to look at 21 also been used in the framework of object recogni- children’s drawings and indicate the presence or tion (see, e.g., Khan et al., 2013), but this task is absence of colours in a list (in French) based on essentially irrelevant for answering SSH research the five principal and the five intermediate hues questions such as illustrated in section 1. Further- of the Munsell colour system (Munsell, 1912) and more, these methods are usually adapted for pro- completed by four colours (namely, brown, black, cessing photographic sources rather than drawings. white and grey).2 Recognizing the difficulty (if not However, other studies in computer vision have the impossibility) to define universal human colour proposed promising descriptors such as colour his- categories, we settled in this work on a set of 10 tograms (see, e.g., Sun et al., 2006), colour names categories (red, orange, yellow, green, cyan, blue, acquired using machine learning techniques (Van de purple, pink, white, and achromatic) which proved Weijer et al., 2009; Lindner and Süsstrunk, 2013), relevant for addressing the “Drawings of gods” re- or parametric models for automatic colour nam- search questions, and which our method is able to ing, where each colour category is modelled as a identify consistently. Most colours in this set are fuzzy set with a parametric membership function also present in those proposed by Berlin and Kay (Benavente et al., 2008). In both cases of colour (1969) and Pastoureau (2017). The main differ- naming, colour palettes are learned from annotated ences with those lie in the absence of brown, which data collected from Google Images for the former the proposed method fails to identify consistently, and from psychophysical experiments for the latter. the fusion of black and grey, whose distinction is These palettes could be used as the starting point not relevant for characterizing the drawings of our of the method presented in section 3.2, although dataset, and the addition of cyan. It is worth noting, they are too fine-grained for our purpose. however, that this particular colour set is but one The K-means algorithm is often used to find col- possible configuration of the method, which can be our groups (see, e.g., Yendrikhovskij, 2001; Kony- easily adapted to fit different user needs. ushkova et al., 2015; Hu and Lee, 2007). However, The remainder of the paper is organized as fol- there are two main drawbacks with this method: lows. Section 2 offers a brief overview of related (i) it is necessary to define a priori the number of work in the computer vision literature. After a syn- clusters (K), i.e. the number of colours; (ii) the thetic presentation of the data used in this study (a output of the method is the mean colour (i.e. the sample of about 1200 drawings extracted from the centroid) of each cluster, which can be difficult to “Drawings of gods” dataset), section 3 proposes a relate to predefined colour categories. The article detailed, formal account of the proposed algorithm of Konyushkova et al. (2015) provides an example for colour identification, and describes two ways of the application of this technique to the analysis of quantifying colour diversity based on the results of the “Drawings of gods” images. of colour identification. Section 4 discusses the Finally, Kim et al. (2007) describe a method for results of colour identification and colour diversity identifying colours in drawings which is very sim- quantification applied to our data, and section 5 ilar to the one proposed here. The main differences draws a brief conclusion. are that their method starts with images in another colour space, namely HVC (“hue–value–chroma”, 2 State of the art also known as the Munsell colour system) and, Research about colours in computer vision mostly more importantly, that it does not rely on a formal focuses on image segmentation (see, e.g., Cheng distinction between micro- and macro-colours (see and Sun, 2000; Chen et al., 2005; Hanmandlu et al., section 3.2), since they define macro-colours dir- 2013) and image retrieval (see, e.g., Deng et al., ectly and classify each pixel into one of these col- 2001; Rao et al., 2015; Zhang et al., 2016). In ours. either case, the problem typically consists in assess- 3 Method 2. The agreement between annotators for each colour, as measured by Fleiss’s Kappa (Fleiss, 1971), varied between 3.1 Data and preprocessing 0.0512 and 0.876. It was even negative for white, since part of the subjects did not consider the background of the page as The dataset used in this study is a subset of N = a colour. 1211 drawings collected in three countries (Japan, 12 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) Switzerland and Russia) between 2003 and 2016 plained at the end of this section. and extracted from the complete “Drawings of Achromatic gods” database (which contains over 6600 draw- Red ings from nine countries and which is constantly growing). Small groups of compulsory school aged children were sat in a way that discouraged copying from each other and were asked to draw “god”, according to the procedure described in Dandarova Robert et al. (2016). Specifically, each child received a blank A4 paper sheet, a grey pen- cil, a ten-colour set of wax pastels and an eraser. In some cases, such as in Russia, children employed ordinary coloured pencils due to the lack of avail- able material. Orange Green Blue Pink Each drawing k ∈ 1, . . . , N has been digitised Yellow Cyan Purple White and, for the purpose of this study, resized using the imresize module of the scipy.misc Python Figure 1: Set of 117 colours aggregated in 10 package, in such fashion that the length of the groups. For each colour, the three values represent drawing’s longest side is normalised to 320 pixels. the RGB components. Note that with this procedure, there remains a small amount of variability in the length of the drawings’ Formally, let ~cl := {cRl , cGl , sBl } with l ∈ 1, . . . , L shortest side. denote each micro-colour. For each pixel ~si j in an In what follows, each normalised drawing is rep- image, we find the micro-colour whose squared resented formally as a matrix S := (~si j ) of I × J Euclidean dissimilarity with the pixel is minimal: pixels (~s), where each pixel is a triplet of values corresponding to red, green, and blue intensity re- c(~si j ) := argmin k~si j −~cl k2 (1) l∈[1,L] spectively, i.e. ~s := {sR , sG , sB }. The pixel is then associated with one out of G = 3.2 Identification of colours 10 macro-colours, according to the groupings of The proposed colour identification method draws micro-colours delineated in Figure 1. This macro- on the work of Kim et al. (2007), who associate colour, denoted by C(~si j ), is ultimately considered each pixel of an image with the most similar colour to be the pixel’s colour. of a set of colours that they defined in the Munsell For each colour g ∈ 1, . . . , G we then define a colour system. Besides the adoption of another binary matrix Bg := (bgij ), of the same dimensions colour space3 and of another colour set, the partic- as the considered drawing and whose components ularity of our approach is that it uses a two-stage are 1 iff g is the colour assigned to the pixel in assignment process. Each pixel is first associated question: 5 with a “micro-colour” (represented by one of the 117 small rectangular areas in Figure 1), which bgij := 1(C(~si j ) = g) (2) in turn belongs to a “macro-colour” (red, orange, This enables us to define the pixel count (i.e. the yellow, green, cyan, blue, purple, pink, white, and number of pixels) of each colour g in a given image achromatic).4 Decomposing colour identification as: in this way offers two advantages. First, micro- ng := ∑ bgij (3) colours are more fine-grained and permit thus to ij grasp more shades of each colour. Secondly, it Pixel counts can be used to compute the proportion is possible to create a new set of macro-colours of each colour in a given image or in a set of im- without modifying the set of micro-colours as ex- ages, in order to answer the first type of research 3. Using the RGB colour space instead of the Munsell colour questions mentioned in section 1. In section 4.1 system allows us to avoid an additional transformation step. below, we show the resulting proportions for the 4. The Python source code implementing our method is available at https://github.com/ChrisCocco/ddd_ 5. Here and in the sequel, 1(A) denotes the indicator function colours. of event A, taking on the value 1 if A is true, and 0 otherwise. 13 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) N = 1211 drawings of our sample, along with the a drawing, and the Shannon entropy of the colour decomposition into binary matrices of a couple distribution. drawings. In the case of variety, an additional prepro- It is important to note that while the set of cessing step is performed: in order to reduce the L = 117 micro-colours used in this study is defined amount of noise – anomalous pixels resulting from by a particular RGB colour chart, 6 it could have the digitisation process – a median filter of 3 × 3 been easily substituted with another one. The same pixels is applied to each binary colour matrix Bg . holds for the set of G macro-colours used here, The filtered matrix, B̃g , is then used to compute new which is the result of discussions in the “Drawing counts ñg := ∑i j b̃gij , which in turn make it possible of gods” project’s team. Since it is complicated for to calculate the colour variety as: computers and for human to differentiate black and V := ∑ 1(ñg > 0) (4) grey (or which pencil was used by the children), g they were grouped into a single “achromatic” cat- Following Shannon (1948), the colour entropy egory. Moreover, this distinction is not necessary is defined as: to study a child’s colour choice. Brown, which is considered as a colour of the second rank by Pas- H := − ∑ f g log f g (5) g toureau (2017) and not as a principal or intermedi- ate hue in the Munsell colour system for instance, where f g := ng / ∑k nk stands for the (unfiltered) is not included in the colour list. Indeed, brown is a colour relative frequency (computed on the basis shade of red or orange (eventually green) in colour of Bg ). H varies between 0 and log G: H = 0 spaces such as HSV or HSL, with a high saturation corresponds to a deterministic configuration where and a relatively low lightness or value. It would be a single colour occurs with relative frequency f g = possible to group some of the 117 micro-colours 1, while the maximum H = log G is reached when into a new “brown” group, however there was no the colour distribution is uniform (∀g : f g = 1/G). consensus in the project team on how to do so. In section 4.2 below, we will discuss the results In summary, the proposed method for identifying obtained when applying these two ways of quantify- colours can be configured in various ways, depend- ing colour diversity to the drawings of our sample. ing on two levels of choice, first regarding micro- In particular, we will show how they can be used colours and secondly regarding macro-colours; the to characterise the strategies adopted by children particular configuration described in this paper and for the task of drawing god, which is an important used for producing the results presented in section 4 result for the psychologists of the project’s team. below is the result of discussions with the “Draw- ing of gods” project’s team and it is specifically 4 Results adapted to this project’s research purposes. In this section, we present the first results obtained by applying the methods for colour identification 3.3 Quantification of colour diversity and colour diversity assessment described in sec- There are a number of ways of quantifying the di- tion 3 to the selected subset of the “Drawings of versity associated with a discrete distribution, such gods” database. as the distribution of colours in a drawing obtained 4.1 Colour identification with the identification method described in sec- tion 3.2 above. All diversity measures are, to a The first outcome of the proposed colour identi- certain extent, dependent on the size of the sample fication method is the decomposition of each im- from which the considered distribution has been age into a set of G binary matrices, one matrix obtained (see, e.g., Tweedie and Baayen, 1998), Bg := (bi j ) per colour g. One way of visualising however the impact of this dependence is lessened these matrices consists in using them as an inver- in our case by the (partial) normalisation of draw- ted “mask”, in the sense of image processing, and ing size (see section 3.1 above). In the present applying them to the original image. Formally, for study, we experiment with two diversity measures, each colour g, we construct a new image Sg := (~sigj ), namely the variety or number of distinct colours in where each pixel is defined as: ( ~si j if bgij = 1 6. Namely the one available at https://www.rapidtables. ~sigj := (6) com/web/color/RGB_Color.html (0, 0, 0) otherwise 14 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) White Red Orange Yellow Green Cyan Blue Purple Pink Achromatic White Red Orange Yellow Green Cyan Blue Purple Pink Achromatic White Red Orange Yellow Green Cyan Blue Purple Pink Achromatic Figure 2: Visualising the results of the colour identification method. Top: Japanese drawing. Middle: Russian drawing. Bottom: Swiss drawing. Drawings in this figure are children’s productions under copyright. 15 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) The result is a set of G images filled with black and 3- to 4-year old children) are the most preferred except for the pixels that have been identified as colours, while the least preferred ones are yellow belonging to a given colour g. Figure 2 shows and orange (and sometimes red). The distribution three examples of this way of visualising the colour of identified colours in our data shows that children configuration detected in an image. certainly do not use their preferred colours to draw These examples were selected to illustrate vari- god, but specific colours for this task. Assuming ous (and decreasing) degrees of concordance that they employ blue to depict the sky and yellow between the automated colour identification and for the light or the sun, the results are compatible the human intuition. In the first example, all col- with the hypothesis that children imagine god as ours are identified as expected by the project’s team, something or someone shining in the sky. The pro- which is what visual inspection of the results gener- posed method will also make it possible to compare ally reveals. All colours are also identified correctly the colour distribution across countries, age groups, and as expected in the second example, considering and so on, and thus to test various psychological that brown is not part of the selected colour set; as hypotheses. a result it is divided into orange and red. Also, and 4.2 Quantification of colour diversity it is coherent, the mixing of blue and yellow around the centre of the drawing creates nuances that are 4.2.1 Variety and entropy identified as green. The third example illustrates a P ercentage of drawings (N = 1211) weakness of the method, namely the identification 18.33% 18.50% 16.93% 16.93% of colours with a low saturation and a low lightness, in particular green. 29.04% 9.91% 9.08% P roportion of pixels 22.35% 19.94% 3.96% 4.21% 1.73% 0.41% 9.46% 1 2 3 4 5 6 7 8 9 10 8.09% Colour variety 6.07% 4.13% 0.33% 0.59% Figure 4: Distribution of colour variety. P ink P urple Cyan Green Red Orange Blue Y ellow Achro. Based on the output of the colour identifica- tion method, the variety and entropy of colours were computed as described in section 3.3. Fig- Figure 3: Distribution of identified colours. ure 4 shows the distribution of colour variety in the dataset, which reveals that a majority of draw- Besides the visualisation of colour decomposi- ings (about 70%) have between 5 and 8 identified tion, the method allows us to compute the propor- colours. The distribution deviates slightly from tion of each colour g in the selected dataset, based normality, in the sense that drawings with 7 and 8 on the summation of each colour’s pixel counts colours are particularly frequent, and there is also (with the exception of white) over all drawings. a small peak of drawings with a single non-white The resulting histogram, represented in Figure 3 colour (V = 2). The box plots in Figure 5 depict the shows that the most frequently identified “colour” variability of colour entropy for a given amount of is achromatic, followed by blue and yellow. Or- colour variety. While the median of entropy is con- ange, red, green and cyan have a moderate repres- sistently increasing with variety, as expected, the entation, while pink and purple are clearly under- spread of individual entropy values is quite large represented. Studies on colour preference (see, e.g., regardless of the corresponding variety. Granger, 1955; Zentner, 2001; Jonauskaite et al., In order to get a better idea of the interpretation 2016) have shown that shades of blue and green, of colour entropy variations for a given amount of such as cyan, as well as red (especially for female variety, we have designed a visualisation in which 16 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) only two of them mentioned white, this colour was removed altogether (both in human and automated 1.5 colour identification results). The colour variety Colour entropy perceived by an annotator in a drawing was then 1.0 defined as the number of non-empty areas on their sheet. Thus, if an annotator described a colour us- 0.5 ing several colour or shade names in a single area, it was counted as a single colour. Figure 7 shows that the difference between the 0.0 1 2 3 4 5 6 7 8 9 10 colour variety V (k̃) automatically detected in a Colour variety drawing k̃ and the average V h (k̃) of the correspond- ing human-perceived variety over the five experts Figure 5: Colour entropy box-plots as a function is no greater than 2. This result is quite impress- of colour variety. ive considering the limitations of the automatic attributions discussed previously as well as the hu- man perception bias. The scatter plot in Figure a sample of drawings are plotted on a grid with 9 8 confirms that there is a considerable degree of rows corresponding to colour variety (between 2 concordance between V (k̃) and V h (k̃). and 10, excluding empty drawings) and 5 columns Figure 9 shows the range of disagreement corresponding to specific points in the distribution between the two variety estimates using the so- of colour entropy (minimum, first quartile, median, called Bland and Altman graphic (Bland and Alt- third quartile, and maximum), as represented in man, 1986). For each drawing k̃, the difference Figure 6. In practice, this visualisation was con- d(k̃) := V (k̃) − V h (k̃) (on the vertical axis) is structed one row after another, by extracting all represented as a function of their mean d(k̃) := drawings with a given amount of colour variety in V (k̃)+V h (k̃) 2 (on the horizontal axis). The more d(k̃) the dataset, then finding in this subset the draw- is distant of 0, the higher the disagreement between ings with the minimum and maximum colour en- the two variety estimates, and d := 1/Ñ ∑k̃ d(k̃) = tropy as well as those that are closest to the desired 0 indicates a perfect concordance between them if quantiles. This representation shows that colour d(k̃) = 0 ∀ k̃, i.e. 1/Ñ ∑k̃ d(k̃) = 0. In this case, al- entropy seems to correspond well with the intuitive though the sample is too small to be representative, notion of drawing completeness: the higher the en- the mean disagreement d = −0.74 is reasonably tropy, the more the colours are covering the page. low (1/Ñ ∑k̃ d(k̃) = 1.3). That more colours are Also, entropy and variety seem to concur to create a found by humans than by the algorithm on average gradual distinction between drawings with a white is consistent with the fact that brown is not part of background and single object or character (bottom- the automatically identified colour set and that grey left) and drawings representing one or more objects and black are aggregated. in a more contextualised fashion (top-right). Thus, besides operationalising the basic notion of colour 5 Conclusion diversity, colour variety and entropy enable us to characterise certain aspects of drawing strategy and In this paper, we have introduced a simple and ef- of the spatial organisation of colours in a drawing. fective method for the identification of colours in children’s drawings (and other types of images). 4.2.2 Concordance with human judgement We have shown how the results of this method To conclude this section, we discuss the results of can be used, in conjunction with classical diversity an attempt to compare the colour variety obtained measures, to tackle meaningful research questions using the proposed colour identification method in the context of “Drawings of gods”, a large SSH with the human perception of colour variety. We project. The proposed methodology will be sys- asked five human experts (the same ones as men- tematically employed in future research within this tioned in section 1) to write down all the colours framework to address various research questions they saw in each drawing k̃ in a sample of Ñ = 10 based on such features as children’s age, gender, or drawings. Annotators had at their disposal a paper country of residence. Unlike the inter-rater meth- sheet with 15 areas for writing colour names. Since odology traditionally used in psychology, which 17 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) 10 9 8 7 Colour variety 6 5 4 3 2 min. 1st quartile median 3rd quartile max. Colour entropy Figure 6: Sample of drawings illustrating selected points in the distribution of colour entropy (columns) as a function of colour variety (rows). Drawings in this figure are children’s productions under copyright. 18 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) 12 ● 10 ● ● ● 10 ● ● ● 8 Number of colours ● Mean numbers of colours (humans) 8 ● ● ● 6 ● 6 ● ● ● ● ● 4 ● ● 4 Mean numbers of colours (humans) ± sd 2 ● Number of colours (algorithm) ● 1 2 3 4 5 6 7 8 9 10 2 Drawings 0 Figure 7: Comparison of automatically detected 0 2 4 6 8 10 colour variety with human-perceived variety. Number of colours (algorithm) requires human experts to annotate the data (a te- Figure 8: Relationship between automatically de- dious and error-prone task), the proposed method tected colour variety and average human-perceived has the advantage of being objective and being able variety. to provide consistent results on large visual data- bases. Moreover, as illustrated in section 4.2.1, the methodology allows us to explore complex re- Number of colours (algorithm) − Mean numbers of colours (humans) search questions such as the characterisation of 4 children’s strategies for the task of drawing god, e.g., filling the entire page versus drawing only a 2 main character or object without background. ● ● The proposed colour identification method has ● 0 also the advantage of being adaptable, as explained ● in section 3.2, since the set of micro- and macro- ● ● ● −2 colours can be easily modified to fit different re- ● ● ● search purposes. For instance, as suggested in sec- tion 2, one of these colour sets could be replaced by −4 a set acquired using machine learning techniques. While the methodology was illustrated on data 4 5 6 7 8 9 extracted from the “Drawings of gods” project, it Mean number of colours between humans and algorithm is in principle applicable to a wide range of visual databases in other areas of digital humanities, such Figure 9: Bland and Altman graphic showing the as film studies, art history, and so on. For instance, range of disagreement between automatically de- it would be possible to study the colours used by tected colour variety and average human-perceived a painter during various periods of their life; or to variety. monitor the evolution of colour variety in cover pages of a magazine across the seasons. Thus, standardising colours by area could be use- As a next step, it would be interesting to apply ful to avoid underestimating a particular colour’s a filter at the beginning of the process, such as representation. the Mumford-Shah regulariser proposed by Erdem and Tari (2009), which transforms a set of noisy Acknowledgements pixels to a uniform patch. Indeed, when children (or adults) fill in an area of the sheet with one col- We would like to thank the reviewers for their con- our, the application is not regular and consequently structive feedback. We would also like to thank only part of the pixels of this area are coloured. Zhargalma Dandarova Robert, Grégory Dessart, 19 Proceedings of the Workshop on Computational Methods in the Humanities 2018 (COMHUM 2018) Olga Serbaeva and Zahra Astaneh for their help in Fleiss, Joseph L (1971). Measuring nominal scale the definition of the set of macro-colours, as well as agreement among many raters. 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