An optimisation study of colour measurements on digitised slides of painted works of art Sophia Sotiropoulou and Yannis Chryssoulakis* Dept of Chemical Engineering, National Technical University of Athens (NTUA), 9 Iroon Polytechniou Str., Zografou Campus, 15780 Athens, Greece *Diagnostic Centre for the Research and Study of Byzantine Hagiography, Holy Convent of the Annunciation, 63071 Ormylia-Chalkidiki, Greece. This paper deals with the problem of the colorimetric fidelity of digitised colour slides of painted works of art. A six-matrix conversion model was derived that permitted the transformation of any RGB device-dependent measurement on digitised colour slides to XYZ CIE 1931 device-independent values. The model was calibrated against a reference colour chart. Eighty-one uniformly-painted colour samples were photographed together with a painting on a 4 × 5 inch colour slide that was digitised using a high resolution scanner. A 3 × 3 transformation matrix, of the corrected R, G and B values and the respective X, Y and Z tristimulus values provided by spectrophotometry, was calculated. The calculated matrix was then applied to a 13th century Byzantine fresco, captured on the same digitised slide, to transform the RGB measurements to XYZ CIE 1931 device-independent values which were then converted into the L*a *b * CIE 1976 colorimetric system. INTRODUCTION Museums and art galleries often face the problem of colorimetric fidelity when digitising colour photographic slides of their exhibits in an effort to create image data banks for specialists and visitors. Colorimetric fidelity in slides can be achieved through appropriate mathematical colour corrections, using, as a reference, colour measurements obtained through spectrophotometry on real colour samples. However, the importance of correct colour reproduction is contrasted by the lack of relevant publications. Martinez and co-authors working on the Vasari project†, concerning a high resolution digital colorimetric imaging of paintings, used a monochrome CCD camera equipped with seven broad-band interference filters that covered the visible spectrum together with an A/D converter [1]. A colour calibration procedure was performed through a Macbeth colorchecker chart of 24 †The VASARI (Visual Arts System for Archiving and Retrieval of Images) project, carried out as part of the European Commission’s ESPRIT II programme, aims to provide a high-resolution digital image capture system in order to record images for conservation research and archival purposes. It replaces conventional photography and has assisted in computer-aided learning in the field of art history. patches. Here, the mean value of the CMC colour difference achieved was ∆ECMC = 2.3. Working in the same area, Vallari and co-authors made a second attempt, retaining the basic process of image capture and colour measurement methodology, and simplifying the equipment by using a colour CCD camera together with a digitising card [2,3]. The mean value of the CMC colour difference ∆ECMC was calculated and found to be 3.2, which, although higher, is close to Martinez’s result. Those colour measurements were for digitised images captured directly from paintings. The photographic slide still remains the most usual and accessible way of reproducing art works. Fortunately, a large part of the world’s heritage of paintings, of which a portion has already been irreversibly destroyed, has been saved in the form of transparencies. However, this method of intermediate representation using colour slides introduces a source of error which, on account of the nature of the dye layers and the construction technique, affects the specifications of the different types of film. Using a reference panel of 14 uniformly-painted patches, Vallari and co-authors attempted measurements of digitised slides using a colour CCD detector coupled to an A/D converter [4]. The results showed that this method could help in the determination of the artists’ colour ‘palette’ and was undoubtedly a promising research tool. However, the mean value of the CMC colour difference, ∆ECMC, between measurements taken on the digitised image and those provided by spectrophotometry, remained significant at about 7. JSDC VOLUME 116 JANUARY 2000 23 In this work, the focus has been on finding a closer relationship between the lighting conditions and the characteristic features of the photographic film being used. All corrections have been made based on standard illuminant D50, which is the nearest standard illuminant to the colour temperature of the electronic flashtubes (~5500 K) used as light sources for the slide photography. In addition: – The digitising procedure was simplified using a high resolution scanner – Attention was paid to a large number of experimental points, covering the greater part of the colour space – An extensive study and exhaustive calculations were made in order to determine the limits of the proposed method. Specifically, the procedure was as follows: 1. Xsp, Ysp, Zsp colour measurements were provided by a portable reflectance spectrophotometer (the subscript sp refers to measurements through spectrophotometer) for the standard illuminant D50. Xsp, Ysp, Zsp measurements were normalised to the unit value. 2. A fresco (a wall painting in which watercolours are applied before the plaster surface is completely dry, or still ‘fresh’) and experimental reference colour charts were photographed together on to a 4 × 5 inch (about 10 × 12.5 cm) colour slide which was then digitised with a high resolution scanner. 3. Before any colour measurement was calculated on the digitised image, a colour balance correction was derived from the white colour patch E13, denoted as white reference W, so that Rw = Gw = Bw. The mean values for each colour patch, Rmeas, Gmeas and Bmeas, were obtained using Photoshop software by selecting a ‘D50 simulation model’. A γ-correction factor was applied after the γ-determination procedure for each of the R, G and B colour channels. The R, G, B values after the γ-correction were normalised to the unit. 4. The transformation matrix between XYZ and RGB colour spaces was calculated taking into consideration Xcor, Ycor, Zcor values provided by spectrophotometry, normalised to the unit value and Rcor, Gcor, Bcor values taken on the digitised colour slide after the γ-correction and normalisation to the unit value. The calculation of the transformation matrix, by a leastsquares method (Appendix 1), was performed taking into consideration, separately: (a) The total of the experimental points (b) The points of lightness Y > 10 and those of low and very low lightness value Y < 10 (c) The points inside each of three well-defined separate areas of the chromaticity diagram (points of low lightness value, Y < 10, being excluded (d) The points inside each of six well-defined separate areas of the chromaticity diagram (points of low lightness value, Y < 10, being excluded). 5. In the last case (d), the six matrices yielded were applied to a medieval fresco, The Entry of the Most Holy 24 JSDC VOLUME 116 JANUARY 2000 Mother of God into the Temple, from the Church of the Protaton at Karyes on Mount Athos†. The work was photographed on the same colour slide together with the experimental charts containing the reference colour samples. 6. The credibility of the proposed method was evaluated through a calculation of the ∆ECMC (1:1) colour difference (6) for each colour between the two sets of CIE L*a*b* values: For the first set, XYZ values calculated from the RGB values derived through scanner digitisation, using the transformation matrix each time, were then transformed to CIE L*a*b* values. The second set of CIE L*a*b* values had previously been measured by using a reflectance spectrophotometer. Comparable results were obtained with those of previous attempts. EXPERIMENTAL To implement the proposed methodology, the following equipment and artwork were used: • CM-2022 Minolta portable reflectance spectrophotometer including: pulsed xenon arc lamp, UV radiation cutting filter, an integrating sphere allowing for the measurement of the diffused reflection from the sample’s entire surface, with simultaneous filtration of the specular reflected radiation being cut. Colour measurements were performed in d/8 geometry. The measurement aperture had a diameter of 4 mm and the wavelength pitch was 10 nm in the range 400–700 nm. • Pentium computer (133 MHz/32 Mbytes RAM). • Sony Trinitron Multiscan 17se monitor. • All measurement processes were taken using the following software: Adobe Photoshop 3.0, Microsoft Excel 7.0a and Word 7.0a for Windows 95, Matlab 4.2b for Windows, Microcal Origin 3.5. • Scanmate 5000 Scanview high resolution scanner permitting a scan resolution in the range 50–5000 dpi, colour depth 3 × 12 bits, and an optical density up to 4.0. • Kodak Wratten Neutral Density filters set 96. • Two experimental colour charts comprising squareshaped 2 × 2 cm and uniformly-painted colour patches, noted as real colour reference samples. The pigments used in mixtures with an egg vehicle are listed in Annex 1. A large number (81) of colour patches was prepared in order to cover the largest possible area of the colour space. †This is a masterpiece by Manuel Panselinos, a celebrated Byzantine iconographer, who decorated the Protaton before the end of the 13th century. • The fresco The Entry of the Most Holy Mother of God into the Temple by Panselinos, which was photographed together with the experimental charts containing the colour samples of known physicochemical behaviour, using a 4 × 5 inch Kodak Ektachrome EPR 64 ASA daylight, code 6117, colour reversal film and two electronic flashes of ~5500 K. The angle between the normal to the coloured surface and the incident light beam was 45°. Annex 1 Mixtures of pigments used with an egg yolk binder to prepare the colour samples for the experimental charts A12 C12 D10 D12 E10 E12 1B 1C 1D 2D A8 A9 A10 B8 B9 B11 B13 C8 C9 C10 C11 D8 Carmine lake + cadmium red medium + titanium white A12 + titanium white Cadmium red deep + titanium white + caput mortum Madder deep + indigo + titanium white Cadmium red light + cadmium red medium + titanium white C12 + titanium white Cadmium red medium + red lake deep + ultra marine + titanium white 1B + cadmium red medium + titanium white 1C+ cadmium red medium + titanium white Ultra marine + red lake deep + titanium white E13 Chrome yellow Chrome yellow + red lake + cadmium red medium Cadmium red light + cadmium red medium Chrome yellow + yellow ochre Yellow ochre + cadmium red medium Mars brown + cadmium red medium Yellow ochre + caput mortuum Chrome yellow + titanium white Yellow ochre + cadmium red medium + caput mortuum Cadmium red light + cadmium red medium + titanium white Red ochre + cadmium red medium + titanium white Chrome yellow + yellow ochre + titanium white + caput mortuum Chrome yellow + yellow ochre + cadmium red medium + titanium white Warm ochre + carmine lake + titanium white C8 + titanium white Yellow ochre + ochre warm + mars brown + titanium white Mars brown + cadmium red medium + chrome yellow + titanium white Titanium white A7 B7 D6 D7 E7 Cobalt turquoise + chrome yellow + chrome yellow Chrome green + yellow ochre Green earth + yellow ochre + titanium white Chrome green + chrome yellow + titanium white Cobalt green + yellow ochre + titanium white A6 B5 C6 C7 E5 E6 12A 11B 11C 12C 12D E13 Cobalt turquoise + chrome yellow Cobalt turquoise + yellow ochre A6 + titanium white A7 + titanium white Cerulean blue + chrome green + titanium white C6 + titanium white Yellow ochre + turquoise light + turquoise deep Cobalt green + napples yellow + ultra marine + titanium white 11B + napples yellow + titanium white Yellow ochre + turquoise light 12C + yellow ochre + titanium white Titanium white A4 C2 Cerulean blue + cobalt turquoise + titanium white Cobalt blue + cadmium red deep + caput mortum + titanium white A4 + titanium white Cerulean blue + chrome yellow + titanium white Cobalt blue + cerulean blue + caput mortum + titanium white D9 D11 E8 E9 E11 C4 C5 D2 Annex 1 Contd D3 D4 11D Cobalt blue + titanium white Cobalt blue + chrome green + cobalt turquoise + titanium white Cerulean blue + chrome green + titanium white + cobalt blue C2 + titanium white D3 + titanium white C4 + titanium white Ultra marine + red lake deep + titanium white Turquoise light + ultra marine Turquoise light + naples yellow + ultra marine Cobalt green B73 Ultra marine + red lake deep + titanium white Ultra marine +cadmium red medium + titanium white Turquoise light + titanium white + ultra marine+ red lake deep Turquoise light + turquoise deep 8A + turquoise deep Cobalt green + ultra marine + titanium white Cobalt green + carbon black + yellow ochre Ultra marine + cadmium red deep + titanium white Turquoise light + titanium white + ultra marine + red lake deep 6B + 8C+ titanium white 7A + titanium white 8B+7D Cobalt green + turquoise light + titanium white Ultra marine + naples yellow + titanium white Ultra marine + red lake deep + titanium white Turquoise light + titanium white + ultra marine Ultra marine + titanium white Turquoise light + titanium white 8B + titanium white 9C + naples yellow + titanium white Cobalt green + chromium green + titanium white + ultra marine 11A + naples yellow + titanium white C13 D13 2C 3C 4C 3D Cobalt blue + cadmium red deep + titanium white Titanium white + caput mortum Ultra marine + red lake deep + titanium white Ultra marine + cadmium red medium+ titanium white Ultra marine + red lake deep + titanium white 3C + cadmium red medium+ titanium white D5 E2 E3 E4 2A 7A 8A 11A 2B 3B 6B 7B 8B 9B 12B 3C 5C 6C 7C 8C 9C 10C 4D 5D 6D 7D 8D 9D 10D METHODOLOGY OF MEASUREMENTS – DISCUSSION Colour measurements by means of a portable reflectance spectrophotometer Before each series of measurements, the portable reflectance spectrophotometer was calibrated with black and white reference values. Xsp, Ysp, Zsp tristimulus values were provided using a portable reflectance spectrophotometer and derived after integration of the curve of the spectral reflectance versus wave length λ for the standard illuminant D50. Xsp, Ysp, Zsp tristimulus values were normalised to the unit value, using the coordinates of the standard illuminant D50, Xn = 96.4, Yn = 100, Zn = 82.51. The normalised values Xcor, Ycor, Zcor were calculated (Eqn 1) for the 81 colour samples: X sp Ysp Zsp X cor = , Ycor = , Zcor = (1) 96.4 100 82.51 Below, the normalised values Xcor, Ycor, Zcor, calculated from the tristimulus values Xsp, Ysp, Zsp and the respective JSDC VOLUME 116 JANUARY 2000 25 Table 1 Sample Xsp Ysp Zsp Xcor Ycor Zcor xsp ysp A10 E13 23.21 77.50 13.22 80.54 3.46 61.89 0.2408 0.8039 0.1322 0.8054 0.0419 0.7501 0.5819 0.3524 0.3314 0.3662 2.4 1 d f + aR γR 1 log Gmeas 2.0 1.8 log G meas i = − 2.2 1 df + a γG 1 G 2.0 log B meas i = − 2.2 log Bmeas log R meas i = − 2.2 log Rmeas 2.4 2.4 1.8 1 d f + aB γB 1 2.0 1.8 1.6 1.6 1.6 1.4 1.4 0.0 0.4 0.8 1.2 1.6 1.4 0.0 0.4 0.8 1.2 1.6 0.0 0.4 0.8 1.2 1.6 Absorbance Figure 1 Representation of curves for red, green and blue channels chromaticity coordinates for a red colour sample A10 and for the white sample E13, are given (Table 1). Colour measurements on the digitised slide after a scanning procedure The fresco, The Entry of the Most Holy Mother of God into the Temple, and the experimental reference colour charts were all photographed on a 4 × 5 inch colour slide. Special care was given to the uniformity of the lighting conditions and the matching of the colour temperature of the light source with the type of film used. The resulting slide was then digitised with a high-resolution scanner. During the scanning procedure and before any colour measurement, a colour balance correction was performed on the white colour patch E13 – noted as a white reference – so that Rw = Gw = Bw, in order to remove any eventual colour bias related to the characteristic features of the film used or to the following development procedure. The Rmeas, Gmeas and Bmeas mean values for each of the 81 uniformly-painted colour patches were obtained using Photoshop software for the output values of the scanning procedure which was applied selecting a ‘D50 simulation model’. In order to compensate for the non-linear response of the scanner, a γ-correction factor was applied, after the γdetermination procedure, for each of the R, G and B colour channels [2]. Using seven neutral optical density filters of n.d. values: 0.2, 0.5, 0.7, 1, 1.2, 1.5, 1.7; a γ-value was obtained, Each of these filters was digitised. From the slope of the curves (Figure 1). 26 JSDC VOLUME 116 JANUARY 2000 log Rmeas i = − 1 df1 + aR γR for the red channel, log Gmeas i = − 1 df1 + aG γG for the green channel and log Bmeas i = − 1 γB df1 + aB for the blue channel. where df is the optical density of filter fi ; Rmeas i, Gmeas i and Bmeas i are the mean values measured on each filter; γR, γG and γB are the correction factors for every channel and aR, aG and aB are numerical factors. The γR, γG and γB values were calculated by a least-squares method and found to be: γR = 1.95 for the red channel, γG = 1.93 for the green channel, γB = 1.76 for the blue channel. The RGB values, after γ-correction [(Rmeas)γR, (Gmeas)γG, (Bmeas)γB were normalised to the unit value (Rcor, Gcor, Bcor), taking into consideration that (Eqn 2): Rcor = Gcor = Bcor = ( Rmeas )γ R ( Rw )γ R (Gmeas )γ G (Gw )γ G (Bmeas )γ B (Bw )γ B , , (2) Table 2 Sample Rmeas Gmeas Bmeas Rcor Gcor Bcor A10 E13 217 251 50 251 58 251 0.7529 1.0000 0.0444 1.0000 0.0762 1.0000 of colour samples of low and very low lightness, Y < 10 ⇔ L* < 37.8 that yield a mean value of ∆ECMC = 19.5. Two matrices were then calculated with separate consideration being given to the samples of lightness value Y > 10 ⇔ L* > 37.8 and those of lightness value Y < 10 ⇔ L* < 37.8. In this case (Eqns 5 and 6): Below, the normalised values Rcor, Gcor, Bcor, calculated from the measured Rmeas, Gmeas and Bmeas tristimulus values, after the γ-correction for a red colour sample A10 and for the white sample E13, are given (Table 2). Calculation of transformation matrices A 3 × 3 transformation matrix A was initially calculated taking into consideration Rcor, Gcor and Bcor values following colour balance correction, γ-correction and normalisation to the unit value, as well as the normalised tristimulus values Xcor, Ycor and Zcor, which were provided by spectrophotometry for the 81 colour patches of the experimental charts. This matrix A, calculated by a least-squares method (Appendix 1) and referring strictly to the specific type of colour slide and model of scanner used, is considered to be available for any application to Rcor, Gcor and Bcor tristimulus values derived from colour measurements on the digitised slide in order to calculate Xsc, Ysc and Zsc values provided through a scanner (index sc refers to scanner), according to the relations (Eqn 3): R  X   X   X × 96.4  sc 1 1 cor         = × = × Y Y 100 where Y A G sc 1 1  cor         Bcor   Z1   Zsc   Z1 × 82.51         AY>10  0.3601 0.3657 0.0615   =  0.1798 0.6038 0.0314  0.0312 0.1236 0.5662   For colour samples of Y > 10 mean value of ∆ECMC = 4.83, minimum value of ∆ECMC = 0.6 and maximum value of ∆ECMC = 11.6. AY<10  0.349 0.4182  =  0.173 0.8223  0.0666 –0.6252  0.1549  0.0874 0.834  (6) For colour samples of Y < 10 mean value of ∆ECMC = 6.19, minimum value of ∆ECMC = 2.7 and maximum value of ∆ECMC = 10.0. In Eqns 5 and 6 the mean value ∆ECMC is 5.05. A divergence from linearity, a factor of error in the transformation between RGB and XYZ spaces, is believed to result from the unsuccessful colour rendition on the slides. In order to reduce this error, the chromaticity (3) obs: 2o ill: D50 0.8 G 0.6 Y G y Xsc, Ysc and Zsc values, derived from the linear transformation of RGB values measured on the digitised colour slide as well as the respective Xsp, Ysp and Zsp values measured using the portable spectrophotometer for the 81 samples, were then converted to the L*a*b* CIE 1976 colour system. CMC(1:1) colour difference ∆ECMC was calculated [6] taking into consideration the values L*sc, a*sc and b*sc and the respective values L*sp, a*sp and b*sp, considered as referential (Eqn 4):  0.3601 0.3657 0.0615   A =  0.1798 0.6038 0.0314  0.0312 0.1236 0.5662   (5) 0.4 R W 0.2 M (4) Mean value of ∆ECMC = 8.68 for the total of the 81 samples, where minimum value of ∆ECMC = 1.6 and maximum value of ∆ECMC = 29.5. The value of the colour difference ∆ECMC, calculated using the 81 colour patches, was considered to be particularly high. This was due especially to the presence 0.0 B 0.0 0.2 0.4 0.6 0.8 x Figure 2 Distribution of measurements provided by the spectrophotometer (2° observer, illuminant D50); the chromaticity diagram (x,y) CIE 1931, was divided into six separate areas delimited by the points R, Y, G, C, B, M of the spectrum locus, the curves and W(D50) JSDC VOLUME 116 JANUARY 2000 27 Table 3 3 × 3 matrix coefficients and model performance in terms of mean, minimum and maximum values of the difference ∆ECMC Matrix  0.3834 A B =  0.1139   –0.0505 Definition 0.2034 0.4959 0.0039 0.1341 0.1184  0.6447 For samples inside the blue area (CWM) of the chromaticity diagram if Y > 10 mean value of ∆ECMC = 4.09 minimum value of ∆ECMC = 1.0 and maximum value of ∆ECMC = 7.8 0.3271 0.0344  0.4468 A G =  0.0606 0.8334 –0.0845   0.5873  0.1608 –0.0092 For samples inside the green area (YWC) of the chromaticity diagram if Y > 10 mean value of ∆ECMC = 4.58 minimum value of ∆ECMC = 1.3 and maximum value of ∆ECMC = 9.2  0.3378 0.4318 0.0718 A R =  0.1732 0.6455 0.0108    0.0149 0.1166 0.5292 For samples inside the red area (MWY) of the chromaticity diagram if Y > 10 mean value of ∆ECMC = 2.51 minimum value of ∆ECMC = 0.7 and maximum value of ∆ECMC = 5.9 Table 4 3 × 3 matrix coefficients and model performance in terms of mean, minimum and maximum values of the difference ∆ECMC Matrix Definition  0.3067 0.4228 0.1074 AMWR =  0.1622 0.5857 0.0481    0.0369 0.3138 0.3701 For samples inside the MWR area of the chromaticity diagram, if Y > 10 mean value of ∆ECMC = 1.65 minimum value of ∆ECMC = 0.3 and maximum value of ∆ECMC = 5.7  0.3492 0.3993 0.1238 ARWY =  0.1797 0.6191 0.0644    0.0105 0.1019 0.5877 For samples inside the RWY area of the chromaticity diagram, if Y > 10 mean value of ∆ECMC = 2.17 minimum value of ∆ECMC = 0.4 and maximum value of ∆ECMC = 4.9  2.1241 –0.7823 –0.2621 AYWG =  0.9645 0.2326 –0.2221   0.4784  0.4642 –0.1900 For samples inside the YWG area of the chromaticity diagram, if Y > 10 mean value of ∆ECMC = 2.14 minimum value of ∆ECMC = 1.0 and maximum value of ∆ECMC = 3.0 0.1732  0.4294 AGWC =  0.7224 0.7224   0.1648 –0.0319 0.0478 0.0302  0.6090 For samples inside the GWC area of the chromaticity diagram, if Y > 10 mean value of ∆ECMC = 3.90 minimum value of ∆ECMC = 0.6 and maximum value of ∆ECMC = 8.4 0.2206  0.2733 ACWB =  –0.0212 0.5205   –0.0333 –0.0627 0.1612 0.1504  0.6801 For samples inside the CWB area of the chromaticity diagram, if Y > 10 mean value of ∆ECMC = 3.65 minimum value of ∆ECMC = 0.7 and maximum value of ∆ECMC = 8.8 0.3343 –0.0671 0.5392 –0.1379  0.185 0.2607 For samples inside the MWB area of the chromaticity diagram, if Y > 10 mean value of ∆ECMC = 2.93 minimum value of ∆ECMC = 1.7 and maximum value of ∆ECMC = 4.6  0.5765 ABWM =  0.4542   0.3197 diagram was divided into three distinct areas, R, G and B, and three separate matrices were then calculated taking into consideration experimental colour measurement 28 JSDC VOLUME 116 JANUARY 2000 values, which were placed inside each area for lightness value Y > 10 ⇔ L* > 37.8. The three areas of the chromaticity diagram were delimited by the points C(λC = 503 nm), M(λ′M = λG where λG = 546.1 nm) and Y(λY = 579 nm) of the spectrum locus, and the white reference point W(x = 0.3456, y = 0.3585) for standard illuminant D50 (Figure 2), where C, M, Y are the complementary points of R(λ = 700 nm ), G(λ = 546.1 nm) and B(λ = 435.8 nm) respectively for the standard illuminant D50. Table 3 comprises 3 × 3 matrix coefficients and the respective three-matrix model’s performance in terms of mean, minimum and maximum values of the difference ∆ECMC. The mean value of colour difference, resulting from the aforementioned procedure, was reduced to ∆ECMC = 3.73. The considerable decrease of the ∆ECMC mean value invited an attempt to divide the chromaticity diagram (x,y) further into six distinct areas which were delimited by the points R(λ = 700 nm), Y(λ = 579 nm), G(λ = 546.1 nm), C(λ = 503 nm), B(λ = 435.8nm) and M(λ′M = λG) of the spectrum locus, and the white reference point W(x = 0.3456, y = 0.3585) for the standard illuminant D50 (Figure 2). The corresponding six separate matrices were calculated taking into consideration colour measurement values inside each of the six areas for a lightness value Y > 10 ⇔ L* > 37.8. Table 4 comprises 3 × 3 matrix coefficients and the respective six-matrix model’s performance in terms of mean, minimum and maximum values of the difference ∆ECMC. Finally, the mean value of ∆ECMC, calculated inside MWR, RWY, YWG, GWC, CWB and BWM areas, was reduced to 2.74. In order to give an overview of the fluctuation of ∆ECMC in the different colour areas for this last six-matrix model, plots of ∆ECMC versus L*, C* and h are presented in Figure 3. Application of the method to the fresco With all of the above experimental results taken into consideration, it was concluded that the most successful manner of transforming an RGB to an XYZ colour system is by calculating six separate matrices. An application of the proposed methodology was then performed on the fresco, The Entry of the Most Holy Mother of God into the Temple. To determine the reliability of the method, Xsp, Ysp, Zsp colour measurements were made on sixteen colouruniform ‘spot’ areas of the painting, in situ, using the portable reflectance spectrophotometer. The Rmeas, Gmeas, Bmeas colour measurements were also performed on the same ‘spot’ areas of a digitised colour slide of the same representation, which was photographed together with two reference colour charts. The rmeas, gmeas chromaticity coordinates of the sixteen colour-uniform ‘spot’ areas on the fresco were then plotted on a r, g CIE 1931 chromaticity diagram (Figure 4) 8 8 8 6 6 6 4 2 ∆ECMC 10 ∆ECMC 10 ∆ECMC 10 4 2 0 2 0 50 60 L* 70 80 0 20 90 4 40 C* 60 80 0 100 h* 200 300 Figure 3 Plots of ∆ECMC versus L*, C* and h for the six-matrix conversion model 2.5  X   X × 96.4  sc 1     Y Y =  sc   1 × 100   Zsc   Z1 × 82.51     2.0 G 1.5 (9) G 1.0 C(λ = 493 nm) X  R  1 cor     Y A = × G RWY  1  cor   Z1   Bcor      Y(λ = 570 nm) 0.5 W where R 0.0 B –1.0 0 M (10) 1.0 R Figure 4 CIE 1931 r, g chromaticity diagram of the RGB measurements taken on predetermined points of the fresco represented on the digitised colour slide; in situ colour measurements were performed on the same locations in order to determine the area of the chromaticity diagram in which were located (Eqns 7 and 8): rmeas = Rmeas Rmeas + Gmeas + Bmeas (7) and g meas = Gmeas Rmeas + Gmeas + Bmeas (8) From the (r, g) CIE (1931) chromaticity diagram given in Figure 4, it was observed that the measurement points belonged to the RWY colour area which is delimited by the points R(1, 0), W(0.33, 0.33) and Y(0.5, 0.5). Consequently, the ARWY matrix was applied respectively in order to transform colour measurements from an RGB to an XYZ colour system. From Rmeas, Gmeas, Bmeas measurements on the sixteen ‘spot’ areas of the digitised slide, Rcor, Gcor and Bcor values were calculated and an ARWY matrix was applied in order to calculate Xsc, Ysc and Zsc values: and ARWY  0.3492 0.3993 0.1238   =  0.1797 0.6191 0.0644  0.0105 0.1019 0.5877   (11) Xsc, Ysc and Zsc values of the sixteen ‘spot’ areas of the colour measurements, calculated after the application of the proposed methodology (using the six-matrix conversion model) and the respective Xsp, Ysp and Zsp values provided by reflectance spectrophotometry, were then converted into the L*a*b* CIE 1976 colour system. Taking into account the L*sc, a*sc and b*sc values and the respective L*sp, a*sp and b*sp values, noted as reference values, a CMC colour difference ∆ECMC was evaluated. Table 5 summarises in detail the differences ∆L*, ∆Cab*, ∆Hab*, ∆ECMC and the lightness L*, chroma C* and h values in the L*a*b* CIE 1976 colour system, related to the sixteen ‘spot’ areas of colour measurements, and the absolute mean values of these differences. From Table 5 it is obvious that the mean value of ∆ΕCMC is considerably increased compared with that of the experimental reference colours. This is mainly due to the values of the differences ∆L* and ∆C*, while the ∆H* value remained relatively low. The sizeable error observed in the lightness value L* could ultimately be explained by the very low values of lightness measured on the fresco compared with those measured on the reference patches of the colour charts. JSDC VOLUME 116 JANUARY 2000 29 Table 5 L*, Cab*, hab*, ∆ECMC colour differences and lightness L*, chroma C * and hue h values in L*a*b* CIE 1976 colour system, related to the 16 spot areas of colour measurements on the fresco represented on digitised slide 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Abs. mean value L*sp Cab* h ∆L* ∆Cab* ∆Hab* ∆ECMC 39.21 38.11 40.56 43.06 42.04 47.98 44.20 45.51 54.63 51.88 42.41 51.64 44.30 38.48 51.48 39.78 27.39 19.06 12.19 11.45 12.04 20.10 20.29 32.95 13.96 13.03 12.78 33.48 6.32 30.64 28.61 10.69 44 47 46 43 49 77 76 68 74 93 108 70 80 53 57 100 9.395 10.346 5.896 –1.724 –4.659 –0.025 –0.835 –5.270 –7.303 –8.312 –3.220 –5.664 –4.771 0.176 –7.052 8.481 –0.430 –3.710 –2.174 –2.345 –4.681 –6.738 –5.711 –10.149 –7.531 –4.058 –1.091 –8.674 –1.555 –9.674 –6.820 0.648 2.217 2.557 4.312 1.925 1.893 0.059 0.701 3.895 2.832 0.417 2.713 2.811 2.920 0.027 4.885 2.855 10.310 12.091 10.255 4.252 6.952 4.076 3.598 7.727 8.999 8.084 4.284 6.928 6.283 4.762 9.002 9.393 5.196 4.749 2.314 7.312 Table 6 Comparison of methods and results from previous work in the same field. The mean, min and max value of CMC colour difference ∆ECMC is given in each case Min ∆ECMC Max ∆ECMC 7.1 1.7 31.8 8.68 5.05 3.73 2.74 1.6 0.6 0.7 0.3 29.5 11.6 9.2 8.8 Author Experimental ∆ECMC Martinez [1] B+W CCD sensor 7 broad-band interference filters A/D converter Macbeth colour chart of 24 patches 2.3 3CCD camera A/D converter 14 reference colour patches 3.2 Slides 3CCD camera A/D converter 14 reference colour patches Slides scanner 81 reference colour patches • one transformation matrix • two transformation matrices • three transformation matrices • six transformation matrices Vallari and co-authors [2,3] Vallari and co-authors [4] Present work In the example under consideration, all of the wall painting’s colours are restricted to a single area of the chromaticity diagram (RWY). It is essential that the methodology be applied also to other samples of pictorial art whose palette covers a broader colour range. Table 6 summarises the essential experimental tools and the respective results of the present work in comparison with those of previous attempts in the same field. The mean value of the CMC colour difference ∆ΕCMC is given in each case. 30 JSDC VOLUME 116 JANUARY 2000 CONCLUSIONS The most important reasons for the divergence between colour measurements derived from spectrophotometry and those performed on digitised colour images captured directly from paintings or colour slides, have been reported by Vallari and co-authors [2,3]: (a) The integrating sphere of the reflectance spectrophotometer reduces specular reflectance, a situation impossible to avoid fully when capturing the photographic image (b) Colour coordinates obtained by the spectrophotometer are calculated taking into consideration the spectral radiant power of the standard illuminant D50 that remains an approximation of the electronic flashes (5000–5500 K) used when capturing the photographic image (c) The sensitivity of a typical colour slide to each of the primary stimuli of electromagnetic radiation differs considerably from that of the human eye. Moreover, the response to red, green, and blue radiation by the slide doesn’t correspond precisely with that of the human eye. However, the calculation of colour coordinates is based on the colour matching functions of the human eye after the standard observer CIE 1931 (2°). (d) Errors introduced by the digitising procedure. transparency films to derive models that incorporate the variety of slide media available. These models must take into consideration the colour divergence of each type of slide, evaluated through the reference colour samples reported, and also allow for a corresponding colourcorrecting restoration. The authors are continuing this work by investigating the automatic correction of digitised images, against reference colour samples, by computer software. The problem that needs to be addressed is the discontinuity in the transition between the areas of the chromaticity diagram foreseen by the six-matrix model, especially for colours of neutral hue. REFERENCES 1. 2. In the present work, the mean value of the CMC colour difference ∆ΕCMC was found to be lower than that suggested by Vallari with respect to colour measurements on slides of painted works of art. Consequently, the simplification of the digitising procedure performed on high quality 4 × 5 inch colour slides, taken under controlled lighting conditions, together with the appropriate mathematical processing, undoubtedly contributes to a better understanding of the problem of colorimetric fidelity on digitised colour slides. This confirmation permits the application of the proposed methodology for the following purposes: 1. Colour palette determination of paintings 2. Determination of any kind of modification in colour due to pollutants, retouching or unsuccessful restoration attempts in paintings. 3. 4. 5. 6. 7. K Martinez, J Cupitt and D Saunders, SPIE Cameras, Scanners and Image Acquisition Systems, 1901 (1993) 25. M Vallari, Y Chryssoulakis and J M Chassery, Mes. Sci. Technol., 5 (1994) 1078. M Vallari, Y Chryssoulakis and J M Chassery, J.S.D.C., 113 (1997) 237. M Vallari, Y Chryssoulakis and J M Chassery, Col. Res. Appl., submitted. G Wyszecki, W Gunter and W S Stiles, Colour science: concepts and methods, 2nd Edn, (New York: John Wiley, 1982). F J J Clarke, R McDonald and B Rigg, J.S.D.C., 100 (1984) 281. J L Goldberg, Matrix theory with applications (New York: McGrawHill, 1991). Appendix 1 Calculation of the matrix The results of these experiments stimulate further research, focusing efforts on a better simulation of the transformation between RGB and XYZ spaces, and taking into account the divergence from the linearity introduced with colour reproduction on slides. It is important to note here that this study has been confined to focusing on the correction and the structuring of the process at hand. The next step is to assess the reproducibility of the method with different types of The general solution of the linear transformation X = AR, where A is a 3 × 3 matrix, X and R are 3 × 1 matrices, after the least squares method, is: X=A×R X × R T = A × (R × R T) X × R T × (R × R T) = A × (R × R T) × (R × R T) A = X × R T × (R × R T)–1 where R T is the transpose of the matrix R and (R × R T)–1 is the inverse of the matrix R × R T JSDC VOLUME 116 JANUARY 2000 31