Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 byguest on 30 September 2021 164 ABSTRACT LEONARDO, Vol. 52, No.2,pp.164–174, 2019 to Unsolved Issues in Art History to UnsolvedIssuesinArt QuantitativeApproach Complementary l a c i n h c e T analysis. As the first step in realizingthis concept, wesought attemptanprocessing astechniques standardize toartwork image motivated biologically with appraisal art traditional painters between Hence,[4–8]. present the study combined authenticating art, of influential andfinding links school its by a painter,classifying a with painting specific a associating including artworks, of identification as a complementary approach for the analysis, evaluation and biologically motivated image processing has been developed methodology to support traditional approaches. Meanwhile, ysis stands in great need of noninvasive analysis and objective straightforwardly generalized [3]. Accordingly, artwork anal results obtained by microanalyses of paint samples cannot be Moreover,artworks. to damageirreparable the of risk their have also methods inherent less,these limitations related to history.increasingproblemsnumberof anart in Neverthe - address to photographyanalysis,pigment infrared and ing, have X-raythussuch as toscientific turnedmethods, imag - art study who Those [2]. limitations many has and praisal, heavily on either historical evidence or highly subjective ap- ity of their contents [1]. Conventional artwork analysis relies lyze manually in a quantitative fashion owing to the complex easily detect. For this reason, works of art are difficult to ana- Artwork contains many features that the unaided eye cannot in manyrespects. showed thatVermeer styles andGerardterBorchhavesimilarartistic proposedashispossiblementors.Theresults with thoseofartists analyzed andcomparedthevisualfeaturesofworksVermeer evidenceforthisquestion,theauthorsquantitatively complementary Who isthemostprobablementortoJohannesVermeer? To provide Institute of Science and Technology, Jeounghoon Kim (artist), School of Humanities & Social Sciences, Korea Advanced Republic of Korea. Email: [email protected]. Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Minseo Kim (artist), Graduate School of Culture Technology, Korea Advanced with thisissue. See www.mitpressjournals.org/toc/leon/52/2 forsupplementalfilesassociated Republic of Korea. Email: [email protected]. M Mentors Probable His and Vermeer of Paintings the in Features Visual of Similarity i n s A r K o e t e l c i

291 Daehak-ro, Yuseong-gu, Daejeon 34141, M I d n a o e J u

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h - - K n o o and Vermeer cosigned a document two days after Vermeer’s Borch ter addition, Inletter. a writing or reading person a of privacy secluded the picturing in especially semblances, re striking show artists two the of matter subject chosen to have influenced Vermeer. The compositional concept and believed is who (1617–1681), Borch ter Gerard is candidate fourth A Bloemaert. Vermeerunder ofstudying the likelihood supports finding This [18,19]. in apprenticeship his of years first four the Utrecht sterdamor spending after Am- in trained Vermeerhave Utrechtmight [17]. in pupils Vermeer’smany of trained relative tantand mother-in-law dis- a was candidate, third the (1566–1651), Bloemaert ham AbraSimilarly,family.Vermeer the with association long Vermeer’sof collection the paintingsofin a to fathertestify Moreover, Bramer’sevidence. drawings vital as regarded is Bramer’swith similarity its andhue, blue distinctive a used Bramer’s between Vermeer’s.connectionand blue Vermeer Vermeer’sas proposingforhim reason subtle the mentoris principal The artist. Delft successful another (1596–1674), Bramer Leonaert is candidate second The time. that at age with the dates of Fabritius’s residence in Delft and Vermeer’s assumption is reasonable. However, this hypothesis conflicts Vermeeroptics.As paintingsFabritius,bythree owned this and perspective in interestcommon their by and style and ported by the similarity of the sup two artistsis in terms hypothesis of subjectsThis [16]. Delft in painter foremost the as Fabritius succeeded Vermeer that indicates (1634–1691) Bon Arnold by poem A pupil. gifted ’s most as recognized (1622–1654), Fabritius Carel is first The [13–15]. documents archival of light Vermeer’s in as mentor posed pro been have artists five present, At attention. critical of The identity of Vermeer’s mentor has attracted a fair amount Un scientific the of reservoir artist’s signature elements. to reveal this mentor of Vermeer, we created and compared a ing remain a mystery owing to lack of evidence [9–12]. Thus, The identity of Vermeer’s mentor andthe nature of histrain - to uncover the mentor to Johannes Jan Vermeer (1632–1675). c ove M I ri ng ng th e Men e doi:10.1162/LEON_a_01401 t o r

t o o V e rm ee r ©2019 ISAST - - - - wedding [20]. In view of these facts, it is quite likely that Image Dataset Vermeer was familiar with works by ter Borch, as they might We created an image dataset from various websites offering have been intimate acquaintances. Finally, Rembrandt van documentary records of ownership provided by art muse- Rijn (1606–1669) is also a possible mentor. Vermeer would ums. This process helped minimize the source dependency have felt the impact of Rembrandt, especially his powerful of the images as well as verify that those analyzed were based chiaroscuro and sfumato effects. Vermeer almost certainly on the actual visual content [24]. Second, this study did not studied Rembrandt’s style indirectly [21,22]. Fabritius was a consider painting genre, given the focus on the superficial pupil of Rembrandt and worked in the latter’s studio; as such, components of the painting style of each artist observed their artistic styles in terms of subject, setting and composi- in all their paintings, such as the way of drawing lines (e.g. tion are similar in many cases. Thus, the advisability of this width and orientation), constructing shapes (e.g. drawing study’s method will be validated if the stylistic similarities of face contours) and choosing colors. In a preanalysis step, this two painters can be extracted. study found that the genre does not strongly determine an artist’s idiosyncratic style related to drawing lines or faces and Artistic Styles of Vermeer choosing color. Third, this study classified the artists into two Art historians examine the following factors when visually groups in terms of the number of paintings they produced. assessing Vermeer’s styles. First, sfumato is a drawing style One group comprised Vermeer and Fabritius, who were not without lines or borders, in the manner of depicting smoke prolific artists; we included all their available paintings. The or a plane beyond the focus. Vermeer used blurry lines be- artists in the other group were those who produced many cause he regarded shadow as more significant than elabo- works: Bramer, Bloemaert, Rembrandt and ter Borch. We rated lines for separating different objects. Second, pointillé sorted their paintings based on representative paintings; is a light expression technique in which an artist forms then, we included only paintings that were contemporary points on a polished or metallic surface. Vermeer added with the works of Vermeer. Subsequently, the image dataset new interpretations to the typical pointillé method by us- contained 535 images from six different painters, as shown ing the technique particularly on subjects with unreflecting in Table 1. surfaces, including bread, cloth and baskets. Third, Vermeer Fourth, we collected 266 face images from the entire image used complementary colors to emphasize the effects of light dataset and used them for the radial frequency analysis. As and enhance the vividness of the quality of the materials. In- not all paintings had face images, the analysis depended on deed, Vermeer is known for his pairings of yellow ocher and the number of face images available. We gave special note to cobalt blue. Fourth, Vermeer’s faces in his artworks mean the position of the nose, which influences the formation of to depict mental activities. Many of his paintings portray the face contour. Meanwhile, the range of head orientations women as leitmotif in a domestic context. Apart from these provides reliable discrimination at around 20 degrees [25]. characteristics, light and perspective are among the major Thus, we selected only face images in which the nose did not technical innovations of Vermeer, who is well known for deviate from the face contour. Fifth, for the color analysis, we rendering the effects of light [23]. Meanwhile, his style pro- extracted a total of 1,489 cobalt blue values and 1,177 yellow duced geometrical spaces that evoke a feeling of glimpsing ocher values from the paintings. However, as a number of through a keyhole. The current study deals with three fac- the paintings do not include cobalt blue or yellow ocher, we tors—line, face and color—in the comparative analysis of analyzed each artist with the average value. Sixth, we normal- Vermeer and his possible mentor as regards their common ized each painting to 256 × 256 pixels without changing the artistic styles. aspect ratio. To fit the ratio of each painting, we cropped the

Table 1. Number of images of artworks by Vermeer and the five candidate mentors in the dataset used in three analyses.

Vermeer Bramer Bloemaert Fabritius Rembrandt ter Borch Total

Orientation 33 108 139 33 131 91 535 Analysis

Radial Frequency 28 31 44 23 82 58 266 Analysis

Cobalt Blue 435 228 213 58 159 396 1,489 Color Values Analysis Yellow Ocher 152 238 165 47 294 281 1,177 Values

Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History 165

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 background parts when such parts were not important to the Renaissance painter Pietro Perugino (1450–1523) and neo- overall composition. Finally, we converted most of the im- classical French painter Jacques Louis David (1748–1825). The ages from color to grayscale, except those used in the color second control group was Vermeer and his contemporary analysis. artists, including (1629–1684), Jan Havick- szoon Steen (1626–1679), Frans van Mieris (1635–1681), and Control Groups Gabriël Metsu (1629–1667). Using Delft blue analysis, we sought to demonstrate an influential link between Vermeer To evaluate the feasibility of the analysis method, the study and Metsu, who trained concurrently in Utrecht in the early set up control groups considering three factors: first, the re- 1650s [27]. A renowned shade of cobalt blue, Delft blue was lationships of painters known to have had a master−pupil or developed in the city of Delft in the seventeenth century, and intimate relationship; second, the control groups’ helpfulness its use is the most representative characteristic of Vermeer in describing the surroundings of Vermeer in that period; and other artists. Thus, we performed a color analysis with and third, measurability for each analysis (given that all styles them as a credible control group. of paintings cannot be analyzed with one methodology). The study used the studio of Rembrandt, which produced many prominent painters of the period, as the first control group. Orientation Analysis Among Rembrandt’s more notable pupils are Fabritius, Ger- Orientation analysis was based on the fact that visual areas rit Dou (1613–1675), Samuel van Hoogstraten (1627–1678) and V1 and V2 are sensitive not only to specific positions and Nicolaes Maes (1634–1693). However, Rembrandt’s studio of- orientations but also to the spatial frequency of the stimuli. fered a far less rigid apprenticeship than those regulated by These types of profiles can be matched with the Gabor wave- art guilds, and pupils were not forced to adopt Rembrandt’s let, which has been used to simulate configurations of the manner of painting. For example, Dou and Maes developed receptive fields of visual cells in the visual regions of the hu- distinctive styles of their own comparatively early in their man brain [28]. We analyzed and compared the styles of lines career. A number of the artists, meanwhile, accepted their in the artworks of Vermeer and other artists who have been master’s influence and had direct connections among them- suggested as his mentors. selves. Hoogstraten maintained close ties with Fabritius; The Gabor wavelet applies four scales (2, 4, 8 and 16) the two young painters influenced each other and shared a and six orientations (0°, 30°, 60°, 90°, 120° and 150°) to common interest in geometrical perspective [26]. Hence, the yield the Gabor energy, which is defined as the sum of the

analysis took account of the degree of similarity of artistic squared values obtained by convolving Godd (Eq. 1) and Geven style between Rembrandt and his pupils. This study addition- (Eq. 2). It refers to the average value that does not exceed ally tested whether the analytic methodology could identify the standard error (±2 SE). We thus used this value (Eq. 3) an artist who was not a member of Rembrandt’s studio. For to derive the representative value of each artist’s style of this purpose, two artists were included in the analysis: Italian lines (Fig. 1).

Fig. 1. , Girl with a Pearl Earring, oil on canvas, 44.5 × 39 cm, c. 1665. (Collection Mauritshuis, The Hague.) The Gabor wavelet is applied in image processing to simulate various scales and orientations of visual receptive fields, which aid analysis [40]. The painting is processed using the Gabor wavelet filter. (© Minseo Kim)

166 Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 x 2 y 2 G (x, y) = exp –— + — × Asin(ω x) (Eq. 1) on determining artistic similarity. Scale 2, which represents 0 [( σ 2 x σ 2 y)] s thin lines, does not extract the blended and thicker lines that Vermeer most often used in his paintings. Vermeer’s x 2 y 2 Ge (x, y) = exp –— + — × Acos(ωs x) (Eq. 2) sfumato produced many blurred and blended brushstrokes [( σ 2 x σ 2 y)] because of the transition of contours. Likewise, ter Borch also used a subtractive manner of painting by varying the 2 2 2 E (x, y) = G0 (x, y) + Ge (x, y) (Eq. 3) thickness of the scumbled layer [29,30]. Consequently, their similarity lies in the use of such contours, and the values of For a comparative analysis of the Gabor energy, we used scales 4, 8 and 16 were useful to determine the most valu- multiple comparisons with analysis of variance (ANOVA). able factors for analyzing Vermeer. Further, the relationship As we applied four scales and six orientations, we compared between “Fabritius and Rembrandt” was not a statistically a total of 24 factors (4 scales × 6 orientations) according to significant difference, except for the relationships among Dunnett T3 (equal variances not assumed). the artists. That Rembrandt and Fabritius, who are known to The results showed that among the artists’ relationships, have had a master-pupil relationship, are found here to have only that between “Vermeer and ter Borch” was not a sta- similar artistic styles validates the reliability of the analytic tistically significant difference. In all three cases, Vermeer methods. showed a smaller difference with ter Borch (Table 2). Thus, In the comparison of the Gabor energy in various orien- ter Borch’s artistic style is similar to that of Vermeer. With tations, conducted to reveal other contributing factors to respect to the results of confirmatory factor analyses, scale particular differences among the means, we found orienta- 16 is the most effective factor, whereas scale 2 has little effect tions 30°, 90° and 120° to be practical factors in comparing

Table 2. ANOVA results of Gabor energy values across isolated scales. Data presented as number of factors; bold text means two artists had the closest mean values.

Artists Mean Std. Deviation F (Sig.) Mean Difference (Sig.)

Vermeer (a) 0.230 0.010

Fabritius (b) 0.268 0.011 a < b : −0.038 (0.003)* a < c : −0.216 (0.000)*** Bloemaert (c) 0.446 0.015 Scale 4 310.443(0.000)*** a < d : −0.176 (0.000)*** Bramer (d) 0.233 0.025 a < e : −0.003 (1.000)

ter Borch (e) 0.232 0.019 a < f : −0.069 (0.000)***

Rembrandt (f) 0.299 0.024

Vermeer (a) 0.310 0.011 a < b : −0.046 (0.057) a < c : −0.276 (0.000)*** Fabritius (b) 0.356 0.022 a < d : −0.212 (0.000)***

Bloemaert (c) 0.585 0.020 a < e : 0.015 (0.489) Scale 8 354.124(0.000)*** Bramer (d) 0.522 0.030 b < c : −0.230 (0.000)***

ter Borch (e) 0.295 0.025 b < d : −0.167 (0.000)*** b < e : 0.061 (0.011)** Rembrandt (f) 0.392 0.027 b < f : −0.036 (0.156)

Vermeer (a) 0.565 0.040 a < b : −0.207 (0.035)* a < c : −0.580 (0.000)*** Fabritius (b) 0.772 0.087 a < d : −0.423 (0.000)***

Bloemaert (c) 1.144 0.040 a < e : 0.004 (1.000) Scale 16 295.685(0.000)*** Bramer (d) 0.998 0.064 b < c : −0.372(0.004)**

ter Borch (e) 0.561 0.053 b < d : −0.216 (0.027)* b < e : 0.210 (0.033)* Rembrandt (f) 0.731 0.047 b < f : −0.041 (0.975)

*p <.05, **p <.01, ***p <.001

Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History 167

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 Table 3. ANOVA results of Gabor energy values across isolated orientations. Data presented as number of cases; bold text means two artists had the smallest difference.

Artists Mean Std. Deviation F (Sig.) Mean Difference (Sig.)

Vermeer (a) 0.143 0.046 a < b: −0.055 (0.143)

Fabritius (b) 0.198 0.109 a < c: −0.148 (0.000)*** Bloemaert (c) 0.292 0.114 a < d: −0.114 (0.000)*** Bramer (d) 0.257 0.168 a < e: −0.006 (1.000) ter Borch (e) 0.149 0.126 a < f: −0.043 (0.013)* Orientation 30° 21.424(0.000)***

f < b: −0.012 (1.000) Rembrandt (f) 0.186 0.110 f < c: −0.106 (0.000)***

f < d: −0.071 (0.004)**

f < e: 0.037 (0.304)

Vermeer (a) 0.096 0.029 a < b: −0.035 (0.194)

Fabritius (b) 0.133 0.076 a < c: −0.099 (0.000)*** Bloemaert (c) 0.196 0.075 a < d: −0.075 (0.000)*** Bramer (d) 0.172 0.111 a < e: −0.002 (1.000) ter Borch (e) 0.099 0.083 a < f: −0.028 (0.014)* Orientation 90° 21.685(0.000)***

f < b: −0.007 (1.000) Rembrandt (f) 0.125 0.076 f < c: −0.070 (0.000)***

f < d: −0.047 (0.004)**

f < e: 0.026 (0.239)

Vermeer (a) 0.042 0.012 a < b : −0.013 (0.536)

Fabritius (b) 0.055 0.036 a < c : −0.040 (0.000)*** Bloemaert (c) 0.083 0.031 a < d : −0.033 (0.000)*** Bramer (d) 0.075 0.046 a < e : −0.000 (1.000) ter Borch (e) 0.042 0.032 a < f : −0.014 (0.015)* Orientation 120° 19.784(0.000)***

f < b : 0.000 (1.000) Rembrandt (f) 0.056 0.040 f < c : −0.027 (0.000)***

f < d : −0.019 (0.015)*

f < e : 0.014 (0.058)*

*p <.05, **p <.01, ***p <.001

­Vermeer and other artists (Table 3). In all three cases, “Ver- pose of the control group was to verify the test, particular meer and ter Borch” and “Fabritius and Rembrandt” were differences among the means need not be discussed. In the the only pairs with no statistically significant differences. results, only “Rembrandt and Hoogstraten [t(14) = 0.306]” Orientation 120° was the most efficient factor among the six and “Hoogstraten and Fabritius [t(9) = 0.063]” had no sta- orientations. Thus, we deemed orientation 120° within scale tistically significant differences (Table 4). Meanwhile, Dou 16 the decisive factor for defining artistic similarities between and Maes showed no significant artistic similarity with Rem- Vermeer and other artists. brandt, although both were the latter’s pupils, which may be In the analysis of the control group, we compared aver- attributed to their early departure from Rembrandt’s usual age values using an independent samples t-test. As the pur- way of working. Moreover, artists who were “not a member

168 Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 Table 4. t-test results of the orientation analysis with the control groups. Value pairs with no significant differences are shown in bold.

Rembrandt Hoogstraten Dou Fabritius Maes

Rembrandt 0.306(14) −6.523(23)*** 0.617(17) −7.988(20)***

Hoogstraten −3.518(15)** 0.063(9) −4.101(12)***

Dou 5.729(18)*** −2.020(21)

Fabritius 6.830(15)***

Maes

Rembrandt Hoogstraten Dou Fabritius Maes

David −2.733(19)* −1.474(10) 2.581(19)* −2.458(13)* 3.937(16)***

Perugino −14.750(19)*** −7.306(10)*** −10.573(19)*** −11.212(13)*** −8.402(16)***

*p <.05, **p <.01, ***p <.001

of Rembrandt’s studio” were distinguished by the analysis dians (Eq. 4, γ0 is the radius of the circle, A is the amplitude method, thus confirming its reliability. As further proof, we of the sinusoidal modulation, ω is radial frequency and θ de- found a statistically significant difference between David and termines the phase of the modulation). Any closed complex Perugino (Table 4). pattern, such as a face, could be composed of combinations of different RF components. Radial Frequency Analysis (Eq. 4) The human visual system has a special sensitivity to radial γ(θ) = γ0 (1 + Asin (ωθ + θ)) frequency patterns in the visual area V4; radial frequency in- formation plays a critical role in combining complex patterns However, higher orders of 5 to 15 RF components do not of face [31]. Accordingly, this study analyzed and compared generally influence the overall results. This analysis thus ex- the idiosyncratic characteristics of faces in the artists’ paint- tracted and compared 1 to 4 RF components from each artist’s ings in terms of the distribution of radial frequency (RF) face painting, and we regarded the average value that did not components (Fig. 2). exceed the standard error (±2 SE) as representative of the face The RF is defined by the number of sinusoidal cycles for painting style of each artist. deforming the radius of one full circle at polar angles in ra- “ter Borch and Vermeer” and “Bramer and Vermeer” were not statistically significant differ- ences, unlike the other pair relationships. In particular, the RF 4 component offered crucial information on the common factors between “Vermeer and ter Borch [0.002 (1.000)]” and “Vermeer and Bramer [−0.017 (1.000)]” (Table 5). The results indicate that ter Borch and Bramer have artistic styles similar to Vermeer’s, and the results of “ter Borch and Bramer” are obvious consider- ing the similarity between them. This result corresponds with the orientation analysis results and lends weight to the study’s hy- pothesis that ter Borch might have been Vermeer’s mentor. Further, “Fabritius and

Fig. 2. (a) Formation of a composite face from Johannes Vermeer, A Young Woman Seated at a Virginal, oil on canvas, 51.5 × 45.5 cm, c. 1670–1672. (Courtesy of The National Gallery, London.) (b) Distribution of radial frequencies extracted from the painting. The painting is processed using the radial frequency distribution. (© Minseo Kim)

Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History 169

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 Table 5. ANOVA results for the RF components of the works of Vermeer compared with those of other artists. Bold text represents two artists with the closest mean values.

Artists Mean Std. Deviation F (Sig.) Mean Difference (Sig.)

Vermeer (a) 0.034 0.000

Fabritius (b) 0.028 0.001

Bloemaert (c) 0.030 0.001 RF component 1 20.607(0.000)*** b < f: −0.001 (0.549) Bramer (d) 0.035 0.002

ter Borch (e) 0.028 0.001

Rembrandt (f) 0.030 0.000

Vermeer (a) 0.254 0.011

Fabritius (b) 0.249 0.024

Bloemaert (c) 0.208 0.005 RF component 2 17.015(0.000)*** Bramer (d) 0.217 0.015

ter Borch (e) 0.260 0.009

Rembrandt (f) 0.250 0.005

Vermeer (a) 0.159 0.007

Fabritius (b) 0.134 0.017

Bloemaert (c) 0.167 0.007 RF component 3 9.062(0.000)*** Bramer (d) 0.143 0.011

ter Borch (e) 0.160 0.003

Rembrandt (f) 0.154 0.003

Vermeer (a) 0.068 0.009 a > b : 0.040 (0.003)** Fabritius (b) 0.028 0.001 a > c : 0.023 (0.035)* Bloemaert (c) 0.045 0.009 RF component 4 35.174(0.000)*** a < d : −0.017 (0.116) Bramer (d) 0.086 0.009 a > e : 0.002 (1.000) ter Borch (e) 0.070 0.008 a > f : 0.023 (0.020)* Rembrandt (f) 0.045 0.004

*p <.05, **p <.01, ***p <.001

Rembrandt [0.549 (−0.001)]” showed similar artistic styles Rembrandt’s studio,” and they showed a statistically signifi- in terms of the RF 1 component. Although the RF 2 and RF 3 cant difference between them. These results further bolster components were not informative in this analysis, the results the reliability of this analysis method. also showed tendencies similar to those of the RF 1 and RF 4 components. In the case of the RF 3 component, for example, Color Analysis the mean difference between “Vermeer and ter Borch” was We performed color analysis according to the process of the smaller compared with that of the other artists. As such, the color-specific neurons of visual area V4. Individual neurons RF 1 and RF 4 components contribute to the overall results in the visual system respond to “opponent colors,” which are and provide further support for the study’s hypothesis. red−green and yellow−blue [32,33]. Therefore, the present Table 6 shows the independent samples’ t-test results of the analysis compared cobalt blue and yellow ocher in the art- control group for the RF components. No statistically signifi- works of Vermeer and of other artists. For exact compara- cant differences were seen for “Rembrandt and Hoogstraten tive analysis, we performed image normalization because raw [t(19) = −1.090],” and “Hoogstraten and Fabritius [t(13) = color value is connected to a particular feature of an image 0.242].” Again, David and Perugino were not “members of given its source. Through three steps, the RGB-coded­image

170 Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 Table 6. t-test results of the radial frequency analysis with the control groups. Value pairs with no significant differences are shown in bold.

Rembrandt Hoogstraten Dou Fabritius Maes

Rembrandt −1.090(19) −10.677(24)*** −0.684(22) −11.925(21)***

Hoogstraten −6.022(15)*** 0.242(13) −6.923(12)***

Dou 6.120(18)*** −2.369(17)*

Fabritius −6.901(15)***

Maes

Rembrandt Hoogstraten Dou Fabritius Maes

David −4.307(19)*** −2.073(10) 3.117(15)** −2.250(13)* 4.404(12)***

Perugino −15.330(13)*** −10.001(14)*** −7.220(19)*** −10.574(17)*** −4.357(16)***

*p <.05, **p <.01, ***p <.001

dataset was transformed into the CIE L*a*b color space for- with the other artists. Their similarity was also clear in the mat, which corresponds with the perceptual differences of luminance results, which showed only had a slight differ- their appearances. The study judged the relevant color of each ence (Fig. 3b). Vermeer’s extraordinary blue is believed to artist by calculating the average value that did not exceed the be similar to Bramer’s, as in Vanitas [34]. However, in the standard error (±2 SE). current result, Vermeer’s coloring technique shows more af- To distinguish the characteristic colors of artists’ works finity with ter Borch’s. Hence, future research should recon- quantitatively, we analyzed colors in terms of complementary sider long-held opinions to reach a fuller understanding of color differences based on Euclidean distance (ΔE), which the problem. has been used in simulating configurations of opponent cod- As for the control group of Vermeer and his contemporary ing information processing in research on human color per- artists, the analysis showed that “Metsu and Vermeer” used ception (Eq. 5). Euclidean distance is generally regarded as perceptually equal colors of cobalt blue [ΔE = −0.8511] com- equal in terms of color within ΔE = 0.5–1.2, and the analysis parable to Vermeer’s similarity with ter Borch (Table 7). As is judged by this criterion. cobalt blue was extremely expensive at that time, most art- ists used it sparingly, hoping to derive maximum effect from 2 2 2 n 2 ΔE = √(q1p1) + (q2p2) +...+ (qnpn) = √∑i=I (pi  qi) its distinctive intense color. By contrast, Vermeer combined (Eq. 5) cobalt blue with green to produce a distinctive greenish blue color. Seen in this context, the finding from the similarity The analysis found that “ter Borch and Vermeer” used per- in blue use strongly suggests Vermeer and Metsu’s closeness ceptually equal colors [ΔE = 0.5276]. As shown in Fig. 3(a), and reconfirms the conclusion that ter Borch is more likely Vermeer showed a smaller distance from ter Borch compared to be Vermeer’s mentor.

a b

Fig. 3. Scatter plots of Vermeer and his candidate mentors based on Euclidean distance regarded as equal in terms of color within ΔE= 0.5–1.2. Vermeer shows the smallest distance from ter Borch in both cases. (© Minseo Kim)

Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History 171

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 TABle 7. t-test results of the color analysis between Vermeer and five of his contemporary artists.

vermeer Metsu Maes de Hooch Mieris Steen

Vermeer −0.8511 5.3945 −3.0154 1.9274 2.7419

Metsu 6.2456 −2.1643 2.7785 3.5930

Maes 8.4099 3.4671 2.6526

de Hooch 4.9428 5.7573

Mieris 0.8145

Steen

fig. 4. Genealogy of Dutch painters associated with Vermeer. In this genealogy, two main streams are categorized, and solid lines especially indicate the artistic fl ow from ter Borch to Vermeer. (© Minseo Kim)

172 Kim and Kim, Complementary Quantitative Approach to Unsolved Issues in Art History

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/leon_a_01401 by guest on 30 September 2021 Results a group, and they are directly connected within an influential This study aimed to complement existing art historical views grouping. The other is ter Borch’s particular . on the identity of Vermeer’s mentor. First, we analyzed art- The paintings of ter Borch strongly influenced Metsu, Steen ists’ signature elements quantitatively, and the converging re- and de Hooch as well as Vermeer [36,37]. In the process, sults of three analyses show that the most influential possible Metsu seems to have played a central role in converging mentor of Vermeer is ter Borch. In fact, many studies have two artistic streams. The early works by Metsu tended to be pursued a number of comparisons between the two artists. executed in the manner of Dou. At the same time, Metsu As ter Borch painted his genre scenes primarily for an Am- also responded to the thematic and stylistic innovations of sterdam market, his paintings were familiar to many Amster- Vermeer, ter Borch and de Hooch. Thus, Metsu, as an in- dam artists. Vermeer may have recognized the practicality of spirational colleague, was in the middle of Vermeer’s mo- studying the artistic sense of ter Borch, and in 1653, he was mentous change. In addition, ter Borch would have walked introduced to ter Borch by Bramer [35]. Ultimately, the find- in step with Vermeer and Metsu as mediator and mentor. ings support art historical records by showing that Vermeer Ultimately, Vermeer’s style was a synthesis of qualities found and ter Borch have similar artistic styles in many respects. in a considerable number of other artists. He digested each Second, the analyses fully considered the art historical of these influences fully before going on to study the next context to avoid hasty conclusions on the relationship be- development in the modern art of his time [38]. Although tween Vermeer and ter Borch; technical similarity does not several questions associated with Vermeer’s missing links always ensure a master−pupil relationship. In the sixteenth merit discussion, this study will help shed light not only on and seventeenth centuries artists underwent apprenticeship how Vermeer matured as an artist but also how he represents for official approval as artists and for joining guilds. Through the Delft school. apprenticeship, pupils acquired skills such as coloring and subtle painting effects from their masters, and their masters’ Discussion styles tended to be reflected in their pictures. Training under The proposed image analysis method is an empirical base a mentor was thus a significant factor in a mentee’s artistic to be used to complement traditional approaches. This new development. In this context, the present results suggest that approach neither invalidates nor replaces the existing ap- Vermeer might have learned painting skills through appren- proaches to persisting historical gaps and challenges in art ticeship with ter Borch. studies. In other words, this method, when tightly linked to Finally, this study attempted to provide a key to many of known contextual and art historical knowledge, may con- the puzzles of Vermeer’s artistic environment. Including the tinue to shed light on a range of problems in the history of results of the control group, the authors constructed a gene- art [39]. Nevertheless, the significance of this study is its alogy of Dutch painters associated with Vermeer. Figure 4 provision of scientific and quantitative support for the art shows two major flows marking the growth of Vermeer as a historical investigation on the identity of Vermeer’s mentor, mature artist. One is the main stream of Rembrandt and his who remains unnamed owing to lack of objective evidence. pupils Dou, Fabritius, Hoogstraten and Maes, whose chiar- The interdisciplinary approach adopted here will be able oscuro and Caravaggesque techniques inspired Vermeer. to contribute to a systematic analysis of artworks and to Bramer and Rembrandt were connected; they painted each a strengthening of future attempts at solving mysteries in other’s portraits. Thus, Rembrandt’s studio and Bramer form art studies.

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