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Pattern Recognition Letters 28 (2007) 703–709

Computer analysis of Van Gogh’s complementary colours

Igor Berezhnoy *, Eric Postma, Jaap van den Herik

IKAT/Computer Science, Maastricht University, Faculty of Humanities and Sciences, Tongersestraat 6, 6211 LN Maastricht, Netherlands

Available online 20 September 2006

Abstract

Traditionally, the analysis of visual arts is performed by human art experts only. The availability of advanced artificial intelligencetechniques makes it possible to support art experts in their judgement of visual art. In this article currently available image-analysis tech-niques are applied. Our aim is (1) to determine how successful the usage of complementary colours was in the oeuvre of Vincent VanGogh and (2) whether this characteristic may make his paintings identifiable in time. It is commonly acknowledged that, especially inhis French period, Van Gogh started employing complementary colours to emphasize contours of objects or parts of scenes.

This article proposes a new method called MECOCO1 to measure complementary-colour usage in a painting by combining an oppo-nent-colour space representation with Gabor filtering. To achieve the aim, (1) we defined a novel measure called the opponency value thatquantifies the usage of complementary-colour transitions in a painting and (2) we studied Van Gogh’s painting style. MECOCO’s anal-ysis of a dataset of 145 digitised and colour-calibrated oil-on-canvas paintings confirms the global transition pattern of complementarycolours in Van Gogh’s paintings as generally acknowledged by art experts. In addition, MECOCO also provides an objective and quan-tifiable way to support the analysis of colours in individual paintings.� 2006 Elsevier B.V. All rights reserved.

Keywords: Image analysis; Color analysis; Automatic painting analysis; Gabor filters; Opponent colors; CIELab space

1. Introduction

Attempting to mimic and amplify the perceptual impactof natural scenes, Vincent Van Gogh used complementarycolours as a means to emphasize contours and to enhancethe vividness of natural colours (Hulsker, 1996). Whereasearly in his artistic career, Van Gogh refrained from usingcomplementary colours, in his later career, while residing inParis and the South of France, he made abundant use ofcomplementary colours (Maffei and Fiorentini, 1999). Artexperts analysing the paintings of Van Gogh are very inter-ested in his usage of colours. In particular, they study thepresence of complementary colours in his paintings (see,e.g., Badt, 1981). Nowadays Artificial Intelligence (AI)techniques may have the potential to aid the art expert indetermining the colours in Van Gogh’s oeuvre (Postma

0167-8655/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.patrec.2006.08.002

* Corresponding author. Tel.: +31 43 38 84897.E-mail address: I.Berezhnoy@cs.unimaas.nl (I. Berezhnoy).

1 MECOCO stands for Method for the Extraction of COmplementaryCOlours.

and van den Herik, 2000). Moreover, the same techniquesmay even be used by the art experts to test hypotheses onthe artistic development of Van Gogh. We believe thattechniques that support the art expert in his/her decisionmay be considered as an intelligent technique; thereforewe call it an AI technique. To investigate the viability ofapplying AI techniques to support the study of paintings,we address the following problem statement: can we estab-lish an increase of complementary colours as used by VanGogh in his paintings over his most active period (i.e., from1885 to 1890)? To provide an answer to this question weperformed a digital analysis of 145 of Van Gogh’s oil-on-canvas paintings in an attempt to quantify and detect thetransition in his usage of complementary colours.

The outline of the remainder of this contribution is asfollows. Section 2 is a concise introduction to colour andcolour perception. Section 3 presents our methodMECOCO that analyses complementary colours in digitalreproductions of paintings. In Section 4 we provide theresults of applying the method to a considerable part ofVan Gogh’s oeuvre. In Section 5 we present to some extent

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a verification of our findings and discuss two critical factorswhich have a considerable impact on the results. Finally,Section 6 gives answer to the problem statement in theform of a conclusion and points to future work.

2. The perception of complementary colours

The perception of colours can be best explained with thehelp of the colour circle and the notion of colour comple-ments. The colour circle is a circular arrangement of thespectral colours. Fig. 1 shows an example of circularlyarranged hues. The small circles arranged along the perim-eter of the large colour circle represent hues that match astandard set of colour cards, the so-called Munsell cards(Munsell, 1923; Levine, 2000). The perceived colour differ-ences correspond to distances along the perimeter of thecolour circle. Colours on opposite sides of the colour circlehave the largest perceptual distance and are called comple-mentary colours. The colour pairs red–green and yellow–blue are well-known complementary colours. As can beseen in Fig. 1, these colour pairs occupy approximatelyopposite sides of the colour circle. Kuehni (2004) collectedresults on human variability in unique-hue perception forover 600 observers. The shaded circle segments illustratethe approximate variability of hues that were identifiedby human observers as the corresponding basic colour.Although unique-hue variability is quite large, the rangesfor the complementary pairs ‘‘red’’–‘‘green’’ and ‘‘yel-low’’–‘‘blue’’ still occupy opposite segments of the circleas can be clearly seen in Fig. 1. The results indicate that dif-ferent observers may assess the colours in a painting quitedifferently, whereas the same observers will largely agree oncomplementary-colour pairs.

Our analysis of Van Gogh’s paintings is guided by neu-roscientific knowledge about the way how the humanvisual system processes complementary colours (Living-stone, 2002). Given the importance of complementary col-

Fig. 1. The colour circle (reproduced from Kuehni, 2004).

ours in Van Gogh’s work and in the present study, webriefly discuss, in Section 2.1, opponent channels whichform the biological basis of complementary-colour percep-tion. Then, in Section 2.2 we describe the colour represen-tation used in our study. Section 2.3 shows howcomplementary-colour transitions are determined in ouranalysis.

2.1. Opponent channels

Colour is a mental construct (see, e.g., Mollon, 1990).Therefore, when digitally analysing colour, the brain mech-anisms responsible for generating a colour experience haveto be taken into account (insofar as possible). The humanvisual system processes chromatic signals using three typesof retinal cone photoreceptors. The neural transformationof the signals yields an opponent-colour representation inwhich chromatic information is expressed in three chan-nels: a red–green channel, a yellow–blue channel, and ablack-white (luminance) channel (Wandell, 1995; Zeki,1999). The red–green and yellow–blue channels are verysensitive to complementary-colour pairs. For instance,the red–green channel is very sensitive to complementary-colour pairs that include red and green. Experimental evi-dence suggests that the opponent channels arise naturallyin artificial neural networks (Usui et al., 1994) or as theindependent components of natural images (Lee et al.,2002;. Biological studies have revealed that individual neu-rons in the visual system respond to opponent-colours (DeValois and De Valois, 2000).

2.2. Opponent-colour space representation

Each of the three opponent channels can be regarded asforming the representation of an axis in an orthogonalthree-dimensional colour space. The values on the axisrange from a minimum value representing one fully satu-rated colour (e.g., green) to a maximum value representingits fully saturated opponent-colour (red). Halfway betweenthese extremes, the value represents a shade of grey. Severalopponent-colour spaces have been defined (see, e.g., Wan-dell, 1995). The biological plausibility of opponent chan-nels as the basis for the perception of complementarycolours leads us to employ the CIELab colour representa-tion in our method of analysis in Section 3.

2.3. Opponent-colour transitions

As stated in the introduction, Van Gogh used comple-mentary colours to emphasize contours in his paintings.Determining the usage of complementary colours requiresa visual filter that responds to complementary-colour con-tours. In the brain, neural cells that process colours exhibita Gabor-like response sensitivity whereby the positive partof the Gabor function corresponds to one colour of theopponent pair (e.g., red) and the negative parts correspondto the other colour (green; De Valois and De Valois, 2000).

Fig. 2. Illustration of an idealised response profile of a red–green sensitivecell in the visual system.

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Fig. 2 is an illustration of an idealised response profile of ared–green sensitive cell encountered in biological studies. Itshows the response profile in the two-dimensional (image)plane against the red–green axis. The associated cell givesa maximal response when it is stimulated by a red–greencontour in the proper orientation. In our analysis weemploy Gabor filters in combination with the opponent-colour space representation yielding an opponent-colourGabor filter. In order to detect contours at several scaleswe define such Gabor filters at four different scales (cf. Jainand Healey, 1998; see Section 3.3).

3. The analysis of complementary colours

The first aim of our analysis is to determine how success-ful the usage of complementary colours was by Van Goghover his most productive period. To achieve this aim, wedefine a measure called the opponency value that quantifiesthe usage of complementary-colour transitions in a paint-ing. The analysis of complementary colours is performedon digitised reproductions of oil-on-canvas paintings ofVan Gogh. This section discusses the data set (in Section3.1), the transformation of the data (in Section 3.2), andthe method of analysis used to determine opponency valuesfor each painting (in Section 3.3).

3.1. The data set

The digital analysis of colours from paintings dependscritically on the quality of the data set. The appearanceof colours in a digital reproduction of a painting is crucial.The two most important factors are: (1) the characteristicsof the photosensitive film or CCD element in the camera,and (2) the specific effects of the subsequent processes. Ingeneral, each operation (capture, reproduction, scanning)introduces distortions that may introduce a bias in theanalysis. To minimize the effect of these distortions we useda high-quality colour-calibrated data set consisting of ekta-chromes provided by the Van Gogh Museum Amsterdam.Each ektachrome contains a frontal photograph of a paint-ing with a colour calibration chart attached to it. The chart

contains fully saturated reference colours for our analysis:red, green, blue, yellow, and white. The data set consists of145 digitised ektachromes of oil-on-canvas paintings madeby Van Gogh during his stay in Antwerp (6), Paris (72),Arles (32), Saint-Remy (26), and Auvers-sur-Oise (9). Allimages were stored in uncompressed format and rescaledto a standard size. In the standard size, each pixel corre-sponds to a surface area of approximately 0.4 mm2.

3.2. Data transformation

The RGB-coded images contained in the data set aretransformed into CIELab colour-space format that isbased on the Munsell system (Forsyth and Ponce, 2003).In contrast to RGB space, CIELab is a uniform colourspace in the sense that distances between points in thatspace correspond very well to the perceptual differencesof their colour appearances. The CIELab transformationoperates on images defined in XYZ colour space. Theseare obtained by a linear transformation of the RGB values(see, e.g., Wandell, 1995). The coordinates of colours inCIELab space are computed as follows (Forsyth andPonce, 2003):

L� ¼ 116YY n

� �13

� 16

a� ¼ 500XX n

� �13

� YY n

� �13

" #

b� ¼ 200YY n

� �13

� ZZn

� �13

" #ð1Þ

The CIELab transformation requires a so-called whitepoint (Xn,Yn,Zn) as a reference (Forsyth and Ponce,2003). In our study, the white point was extracted fromthe white patch of the reference card. Subsequently, the(a*,b*) coordinates were computed for the red, green, yel-low, and blue patches by averaging the RGB values ofthe corresponding image regions and transforming theminto CIELab coordinates. Fig. 3a displays the (a*,b*) coor-dinates of the four patches for all paintings as points.

Ideally, all points representing reference patches of thesame colour should overlap since the same reference cardwas used for all paintings. However, a considerable scatteris observed, presumably due to different lighting and repro-duction conditions.

Our main interest is in the faithful detection of the well-saturated colours red, green, blue, and yellow. The coordi-nates of the associated points on the (a*,b*) plane reflecttheir appearance in the digital reproductions. Therefore,we take for each painting the coordinates of the four basiccolours, i.e., ða�r ; b

�r Þ; ða�g; b

�gÞ; ða�y ; b

�yÞ, and ða�b; b

�bÞ, as anchor

points for defining the opponent axes. Fig. 3b shows anexample for a single painting. All a* and b* componentsof the colours in the painting are interpreted in terms oftheir distance to the four reference points. To arrive attwo opponent-colour representations of a CIELab-coded

Fig. 3. (a) Projection of the four reference colour patches of all paintings on the a*–b* plane. (b) Four reference colour patches for a single painting. Thelines represent the red–green and yellow–blue axes.

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image I, we transform each pixel triplet (L*,a*,b*) into twovalues Frg and Fby representing the corresponding pixel val-ues in the red–green and yellow–blue representations,respectively. The values are obtained by applying an atten-uation function that enhances colours in the neighbour-hood of the reference colours and that suppressesunsaturated colours (i.e., colours for which (a*,b*) is nearto the white point). The values Frg and Fby are computed as

Fig. 4. Opponency values of the paintings groupe

F rgðL; a�; b�Þ ¼ stepðL=Lmax � hÞ½Gða�r ; b�r ; a�; b�; rattÞ� Gða�g; b�g; a�; b�; rattÞ� ð2aÞ

F byðL; a�; b�Þ ¼ stepðL=Lmax � hÞ½Gða�b; b�b; a�; b�; rattÞ� Gða�y ; b

�y ; a

�; b�; rattÞ� ð2bÞ

with step(x) a step function that returns 1 if x > 0 and 0otherwise, Lmax the maximum luminance value, and h a

d by year of creation for four different scales.

Table 1Results of multiple comparisons methods (Liao, 2002; Tukey–Kramer andScheffe’s methods yielded identical results) for the four scales examined

1885 1886 1887 1888 1889 1890

Scale 1

1885 S S S1886 S S S S1887 S S188818891890

Scale 2

1885 S S1886 S S S1887 S188818891890

Scale 3

18851886 S S1887 S188818891890

Scale 4

18851886 S1887 S188818891890

Each element represents the comparison of the opponency values ofpaintings created in two years represented by the row and column labels.An ‘‘S’’ represents a significant difference (p 6 0.05) between the oppo-nency values.

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threshold value, and G a two-dimensional Gaussian weigh-ing function defined as

GðA;B;a;b;rattÞ¼ exp � a�AA

� �2�r2

att

!exp � b�B

B

� �2

=r2att

!;

with ratt the standard deviation of the attenuation region(ratt = 0.4). Applying these equations to the entire imageyields two opponent-channel images Irg and Iyb, the pixelvalues of which range from �1 to 1.

3.3. Opponent-colour analysis

MECOCO’s analysis measures opponent-colour transi-tions by convolving both opponent images extracted froma painting with pairs of oriented Gabor filters. The pairs ofGabor filters, Gaboreven and Gaborodd, are defined asfollows:

Gaborevenðx; y; r; a;xÞ ¼ cosð2pxðx sinðaÞ þ y sinðaÞÞÞ

� exp � x2 þ y2

2r2

� �ð3aÞ

Gaboroddðx; y; r; a;xÞ ¼ sinð2pxðx sinðaÞ þ y sinðaÞÞÞ

� exp � x2 þ y2

2r2

� �ð3bÞ

In these equations, x and y are the spatial coordinates, rthe standard deviation of the Gaussian envelope, a the ori-entation of the filter, and x the spatial frequency. Eachopponent image is convolved with odd and even pairs infour orientations (horizontally, vertically, diagonally, andanti-diagonally).

The opponency value for a painting is defined as the sumof the convolutions of the Gabor filter set with the imagesIrg and Iyb divided by the number of pixels in the image. Wevaried the scale of analysis by maintaining a fixed sized fil-ter set and resizing the image by a factor 2�s+1 for scales 2 {1,2,3,4}. In all our experiments we defined the Gaborfilters on a support of 32 · 32 pixels, and employed the fol-lowing parameter values: r = 5, a 2 {0,0.5p,p, 1.5p}, andx = 0.025. For these parameter values, the Gabor profilefalls well within the support (see Fig. 2).

4. Results

The overall results of our analysis are shown in Fig. 4.To establish an increase of complementary colours overtime, we grouped the paintings by their creation year. Eachgraph displays a scatter plot of the opponency values of thepaintings created in the six years encompassing the periodfrom 1885 to 1890. The four graphs show the results of thefour spatial scales analysed. Especially for the finer scales(scales 1 and 2), an increase in opponency values isobserved over the period 1886–1888. These results areobtained with a threshold value of h = 0.7 (i.e., only col-ours with a normalized L value of 0.7 or more were takeninto account). Varying the threshold within the range

[0.6,0.9] did not affect the main pattern of results. A multi-ple comparison test (Liao, 2002) was performed to assessthe statistical significance of the differences between themean opponencies for each year. (Identical results wereobtained for multiple comparisons using Tukey–Kramerand Scheffe’s methods.) Table 1 contains the comparisonresults for the four scales. Each element within a subtablerepresents the comparison of the opponency values ofpaintings created in two years represented by the rowand column labels. An ‘‘S’’ represents a significant differ-ence (p 6 0.05) between the opponency values. A signifi-cant difference in opponent-colour transitions betweenearly and later years is observed at the smallest scalesexamined. The transition agrees well with the increasedusage of complementary colours by Van Gogh (Maffeiand Fiorentini, 1999). These results help us to achieveour second aim of identifying Van Gogh’s painting as accu-rately as possible in time.

5. A verification and a general discussion

The global pattern of our results confirms the generallyacknowledged transition in complementary-colour usage

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by Van Gogh. As stated in the introduction, Van Goghused complementary colours to enhance or emphasize thecontours of the objects in his paintings. To verify whetherlarge opponency values detected by MECOCO’s analysisactually correspond to such enhanced contours, we modu-lated the intensity values of digitized paintings by the con-volution values obtained by the convolution of the Gaborfilter set at scale s with image Irg (red–green opponency) orIyb (yellow–blue opponency). In the modulated images,brightness is proportional to the local opponency value.Fig. 5 shows two typical examples of paintings in whichhigh opponency values detect detailed red–green contours(s = 1, top) and coarse yellow–blue contours (s = 3,bottom).

Despite these clear results, the validity of MECOCO’sanalysis depends critically on two factors: (1) the biologicalplausibility of the opponent-space representation and theGabor filtering, and (2) the quality of the data set. Weare confident that the analysis is biologically plausiblealthough further improvements may be obtained by deriv-ing the opponent-colour space and Gabor filters automat-ically from the images using statistical techniques based onindependent component analysis and principal componentanalysis (cf. Lee et al., 2002). We are also confident aboutthe quality of the Van Gogh data set since we were able to

Fig. 5. (Top) The detail of the painting ‘‘Bridge in the Rain’’, Paris 1887 (Frectangle indicates the area that is shown on the right as a red–green opponency(Bottom) The painting ‘‘Wheatfield with Crows’’, Auvers-sur-Oise 1890 (F 779)painting on the left, yields a high yellow–blue opponency value (s = 3) in the yethe references in colour in this figure legend, the reader is referred to the web

map the colours of the paintings in the painting-specificcolour space spanned by the four reference cards. Ofcourse, we owe much gratitude to the Van Gogh museum.

In summary, we employed opponent-colour analysis todetect complementary-colour transitions in Van Gogh’spaintings. In what follows, we discuss related work in con-tent-based image retrieval and in image analysis. In con-tent-based image retrieval, colour represents an importantcue for retrieving images. For the domain of the visual arts,special colour representations have been proposed to facil-itate the retrieval of paintings containing specified combi-nations of colours. A notable example is a representationdue to Itten (1961) in which hues are arranged on the sur-face of a chromatic sphere, the so-called Itten sphere(Colombo et al., 1999). Perceptual contrasting colours haveopposite coordinates on the sphere. Itten’s generalisationof the colour circle offers the advantage that it includessemantic interpretations of colour contrasts that can sup-port queries such as ‘‘find all paintings contain warm col-ours’’. In addition, it can be incorporated into artanalysis systems to detect and characterise semantic oremotional characteristics in paintings.

In image analysis, colour contrasts and opponent-col-ours have been investigated by several researchers. A largenumber of studies have been performed on the automatic

372), shown on the left, contains a clear red–green transition. The white-modulated image (s = 1) in which intensity is proportional to opponency.. The yellow–blue transitions between the wheat and the sky in the originalllow–blue opponency-modulated image on the right. (For interpretation ofversion of this article.)

I. Berezhnoy et al. / Pattern Recognition Letters 28 (2007) 703–709 709

analysis and classification of colour textures (see, e.g.,Postma et al., 1998). In the present context, the combina-tion of spatial and chromatic features is of particular rele-vance. Jain and Healey (1998) proposed a multiscale Gaborrepresentation including unichrome and opponent features.Our multiscale opponent-colour representation is similar tothat of Jain and Healey (1998). The main two difference arethat (1) our colour representation is defined relative to thepainting-specific colour cards, and (2) our representationemphasizes saturated colours (by means of Eq. (2)).

The use of Gabor filters in our representation is moti-vated by biological insights. Single and multiscale Gaborfilters are widely used in image analysis and especially tex-ture analysis. Still, it may very well be the case that alterna-tive representations such as co-occurrence matrices or thelocal binary pattern approach (Maenpaa, 2003) yield simi-lar or even better results. This is left for future study.

6. Conclusion and future work

MECOCO’s analysis of the usage of complementarycolours by Van Gogh is mainly dependent on the colour-reproduction quality of the digital images. However, sincethe projections of the detected complementary-colour con-tours fully correspond to the contours of objects in thepainting, we are confident that our analysis is fairly reli-able. Therefore, we may answer the problem statement asfollows. MECOCO clearly succeeds in establishing anincrease of complementary-colour usage by Van Gogh overhis most productive period. Moreover, the opponency val-ues of individual paintings provide a hint to identify thetime in which a painting by Van Gogh has been made.As is well known, the ordering of Van Gogh’s work hasbeen a challenge for many art experts over the years (Huls-ker, 1996). Based on these results, we foresee an increasinguse of AI techniques in the domain of visual arts to supportart experts in their analysis of paintings. In our future workwe will expand our investigations by covering the followingfour features: colour, texture, shape, and composition ofVan Gogh’s paintings. In addition, alternative colour-tex-ture representation schemes will be explored.

Acknowledgements

This research is carried out within the NetherlandsOrganization for Scientific Research (NWO) ToKeN pro-ject Authentic (Grant 634.000.015). We gratefully acknowl-edge Louis van Tilborgh and Ella Hendriks of the VanGogh Museum for providing us with the colour-calibrated

ektachromes of Van Gogh’s paintings. The authors wish toexpress their gratitude to two anonymous referees for thecomments which helped us to improve the paper.

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