Journal of Electronic Imaging 4(4), 360—372 (October 1995).

Colorimetric characterization of a desktop drum

scanner using a spectral model Roy S. Berns M. J. Shyu* Rochester Institute of Technology Center for Imaging Science Munsell Color Science Laboratory 54 Lomb Memorial Drive Rochester, New York 14623-5604 E-mail: [email protected]

Abstract. A desktop drum scanner was colorimetrically characterized to an average CIELAB error of less than unity for Kodak Ektachrome transparencies and Ektacolor paper, and Fuji Photo Film Fuflchrome transparencies and Fujicolor paper. Independent verification on spectrally similar materials yielded an average z Eb error of less than 2. 1. The image formation of each medium was first modeled using either Beer-Bouguer or Kubelka-Munk theories and eigenvector analysis. Scanner digital values were then empirically related to dye concentrations using polynomial step-wise multiplelinear regression. These empirical matrices were required because the scanner's system spectral responsivities had excessively wide bandwidths. From these estimated dye concentrations, either a spectral transmittance or spectral reflectance factor was calculated from an a priori spectral analysis of each medium. The spectral estimates can be used to calculate tristimulus values for any illuminant and obseiver of interest. The methods used in this research are

based on historical methods commonly used in photographic science.

1

Introduction

As early as 1948, colorimetric input to photomechanical

printing was described by Hardy and Wurzburg' and implemented by the Interchemical Corporation and the Radio Corporation of America.2 The basic principle was that the analysis stage, the combination of film and scanner, had spectral

responsivities that were linear transformations of color*Current address: Chinese Culture University, Department of Graphic Communications, Hwa Kang, Yang Ming Shan, Taipei, Taiwan.

Paper 95-006 received Apr.3, 1995; revised manuscript received July 3 1,1995; accepted for publication Aug. 14, 1995. 1995 SPIE and IS&T. 1017-9909/95/$6.OO.

360 /Journal of Electronic Imaging / October 1995 / Vol. 4(4)

matching functions. The synthesis stage, separations and printing, was based on a colorimetric model, namely the Neugebauer equations.3 Because of limitations in achieving a colorimetric analysis stage in both film and the scanner, limitations of the Neugebauer equations because of changes in each primary' s normalized reflectance factor with changes

in dot percentage, and gamut-mapping issues, this colonmetric approach was replaced with higher-order masking equations. Furthermore, for many applications, the original image shifted from the actual scene to its photographic embodiment. Accordingly, transforms were developed for each specific film type. (If an actual scene element needed to be reproduced accurately, the proof would require considerable adjustment. Thus the prepress proof was an integral step in the color-reproduction chain. For the purposes of this article, the photographic image will be considered the original image requiring reproduction.) In modern systems, the higher order masking equations and gamut mapping are implemented as three-dimensional look-up tables with multidimensional linear interpolation. Interest in colorimetnic analysis has renewed with the advent of desktop publishing, direct-digital printing, deviceindependent color, and the contention that colonimetnic descniptions of images as input to desktop publishing and traditional photomechanical printing will improve color accu-

racy and reduce prepress time. Accordingly, four general methods have been described to transform digital-imaging scanners to approximations ofimaging colonimeters. The first method is to design the scanner as a colonimeter. Engeldrum4 provides a historical perspective to this approach as well as current design considerations. Typical of colorimeters, a sin-

gle illuminant and observer combination is selected. Vrhel and Trussel5 have derived filter sets where multiple illuminants are considered. When building a colonimetnic scanner,

Colorimetric characterization of a desktop drum scanner using a spectral model

care must be taken to insure a sufficient number of quantization levels, a large dynamic range, and high signal-to-noise ratios. A colorimetric scanner with noise and quantization properties that are typical of a CCD flat-bed scanner can produce considerable colorimetric error despite spectral responsivities that are linear transformations of CIE colormatching functions.6 The second method is to transform the scanner signal values to colorimetric data using a combination of onedimensional functions or splines for gray balance and tone reproduction, and a 3 X n color-correction matrix, where n often varies from 3 to 64. This method is equivalent to the higher order masking described above. The matrix is derived

or regression methods. Furthermore, this yields spectral image information without building a multichannel scanner. Rodriguez and Stockham'8 and Jung and Tralle'9 were

through the use of multiple-linear regression, where the gray-

tance factor from scanner data for transparent (positive

balanced digital data are the independent variables and the tristimulus values are the dependent variables. The sum-ofsquares tristimulus error tends to be minimized. Hung,6 Kang,7 and Clippeleer8 have implemented this technique. Berns9 found that changing the minimization criterion to LIE or the sum of squares of the cube root of tristimulus values resulted in additional improvement. For all of these regression techniques, performance is very dependent on the modeling target, the spectral responsivities of the scanner, and the noise and quantization properties of the scanner. The third method is to uniformly sample the scanner input space and build a look-up table; through multidimensional

chromes) and opaque (print paper) photographic materials resulting in improved characterization accuracy. This article will describe the theory and historical basis of this fourth

linear interpolation, colorimetric values are estimated. Hung1° and Kasson, Plouffe, and

have described this

technique in detail. Several patents have also been issued. 1215

These three methods all ignore metamerism and as a consequence are constrained to a single medium, illuminant (in the case of Vrhel and Trussel, several illuminants), and observer. A spectral scanner would alleviate metamerism problems; from a colorimetric perspective, developing such a device would have high priority. However, the engineering hurdles are formidable and, as a consequence, commercial products are as yet unavailable. A similar problem was encountered many years ago by the photographic industry. For certain aspects offilm building spectral data are required, ideally in various locations on an image. This was difficult to obtain because of the large aperture of most spectrophotometers and the slow speed of data collection. From a knowledge of the relationship between the amount of dye in the image area and its corresponding spectrum, one could use a densitometer (preferably narrowband) to measure the dye amounts directly, and through a series of calculations, estimate the spectral values. This is 16 known as the conversion from integral to analytical Computer techniques were described as early as 1970.17 This fourth method can be applied to the present problem, since most scanners have spectral responsivities that peak near the peak absorptivities of typical dyes comprising color film and paper. Scanner digital values are related to dye concentrations that in turn are used to estimate spectral properties. Once the spectral transmittance or reflectance factor is estimated, colorimetric values can be calculated for any or all illuminants and observers of interest. Essentially, this method models the physics of photographic materials and scanners. An analytical model, in general, has the advantage of improved colorimetric accuracy and requires much fewer samples than look-up table

successful in characterizing a drum scanner and positive transparency film using this method. Viggiano and Wang2° were less successful when this technique was applied to a flat-bed scanner and photographic print paper. Quantization, low signal-to-noise ratios, and wideband spectral responsivities were the limiting factors in the latter case. A 1992 patent has been issued for this fourth method.2' A similar approach to Rodriquez and Stockham,'8 Jund

and Tralle,'9 and Viggiano and Wang2' was used in this research to estimate either a spectral transmittance or reflec-

method, our results, and the inherent differences between our method and previous research. Greater details can be found in Ref. 22.

2 Experimental Fourphotographic materials were evaluated: Eastman Kodak Ektachrome and Ektacolor, and Fuji Photo Film Fujichrome and Fujicolor. When available, ANSI 1T8.7 targets23 were used to model each film' s spectral characteristics and relate the scanner signals to dye concentrations. The Ektacolor paper IT8.7/2 target was unavailable at the time ofthis research; the Q6OC target was used in its place. These targets will be referred to as the modeling targets.

Independent targets to test our methodology were produced by exposing 4 X5-in. film, presumably of the same type as the modeling targets, using a Management Graphics Solitaire 8XP digital film recorder followed by processing in the usual manner. The target was a digital 6 X6 X 6 (RGB)

factorial design sampling each material's color gamut. These targets were used to generate the independent yenfication data. The spectral transmittances of the transparent modeling and verification targets were measured using a Photo Re-

search 703A spectroradiometer and a constant-current daylight-filtered tungsten-halogen lamp configured to achieve 0/0 geometry. The central 50% of each color patch was measured. The average of four successive measurements was recorded. The 2-nm data at a half-height bandwidth of 5 nm were averaged to 10-nm intervals at a half-height bandwidth of 10 nm between 390 and 730 nm. The spectral reflectance factor of the opaque modeling and verification

targets was measured using a Gretag 5PM 60 spectrophotometer. This instrument has 45/0 geometry, a circular 3.5-mm aperture, a daylight-filtered tungsten source, and a 10-nm half-height bandwidth. Each target was backed by a black mat material. The average of five successive measurements was recorded from 380 to 730 nm in 10-nm increments. Tnistimulus values were calculated using ASTM tristimulus weights24 for illuminant D50 and the 193 1 2-deg observer. Our metrology and calculation techniques followed the recommendations of the Committee for Graphic Arts Technol-

ogies Standards (CGATS) with the exception of the transmittance measurements 25 CGATS recommends diffuse

Journal of Electronic Imaging! October 1995 / Vol. 4(4)1361

Berns and Shyu

illumination and normal collection d/O (or the reverse). The differences in geometry are negligible. Targets were scanned on a Howtek D4000 drum scanner at 500 dpi. The scanner incorporates a tungsten-halogen lamp, three-filtered photomultiplier detectors, linear and logarithmic amplifiers, 12-bit analog-to-digital converters, and 12bit input and 8-bit output one-dimensional look-up tables. For transparent materials, data were collected at 1 2-bit quan-

factor of a given color patch. The units of concentration can be by weight, volume, or relative to a nominal exposure. The latter method was used. Once R is known, tristimulus values for any illuminant and observer combination can be calculated. It is also possible to use other theories to relate dye concentration and spectral properties of opaque imaging materials.283°

tization depth with a linear photometric response. A C-

5 Estimating Dye Absorptivity Spectra

language interface library available from Howtek was used to develop the necessary driver software. For opaque materials, data were collected at 8-bit linear quantization via an acquire module written by Howtek for Adobe Photoshop. The Ektachrome materials were also scanned at 8-bit linear quantization to evaluate the performance differences between 8- and 12-bit quantization. The central 2500 pixels of each color patch were averaged forming the scanner database. The independent verification targets were scanned on different days from the modeling targets.

Film manufacturers routinely produce single-dye coatings to evaluate the spectral properties ofeach component dye, which are made available through technical literature. For example, Rodriquez and Stockham'8 used the spectral absorptivities

3 Color Formation Theory of Transparent Photographic Media Photographic positive film after processing can be considered, first order, as a transparent medium consisting of dyed gelatin. The three dyes—cyan, magenta, and yellow—are assumed to not scatter light, not fluoresce, and not affect the refractive index of the medium. Following these assumptions, the relationship between the amount of dye in the film and spectral transmittance can be described by the Beer-Bouguer theory26:

T = Txg exp[ —(cD + CmDm + C,Dx)I where c , Cm and c, are the concentrations ;

(1) ,

Dm ' and

are the unit speètral absorptivities of cyan, magenta, and yellow, respectively; Txg 5 the spectral transmittance of the

base; and T is the spectral transmittance of a given color patch. The units of concentration can be by weight, volume,

or relative to a nominal exposure. The latter method was used. Once T is known, tristimulus values for any illuminant and observer combination can be calculated.

4 Color Formation Theory of Opaque Photographic Media Photographic print paper can be considered, first order, as an opaque medium consisting of transparent layers of dyed gelatm in optical contact with an opaque scattering support. The three dyes—cyan, magenta, and yellow—are assumed to not scatter light, not fluoresce, and not affect the refractive index of the medium. The support is assumed to scatter light isotropically and not fluoresce. Following these assumptions, the relationship between the amount of dye in a material with the prior assumed properties and spectral reflectance factor can be described by the Kubelka-Munk theory27:

R = Rxg

exp[ —

2(ck + Cmkm + ckx)I

(2)

km, and where C, Cm, and are the concentrations; are the unit spectral absorptivities of cyan, magenta, and yellow, respectively; Rxg is the maximum spectral reflectance factor of the entire target; and R is the spectral reflectance 362/Journal of Electronic Imaging / October 1995 / Vol. 4(4)

supplied by Kodak for Ektachrome. However, if the metrology between the film manufacturer and the user (i.e., the present research) is not matched, modeling errors will result. Furthermore, if the theoretical models have limited accuracy in practice, the spectral absorptance of an arbitrary concentration of dye may not be scalable by the spectral absorptivity derived from a different arbitrary concentration such as the maximum concentration. Alternatively, eigenvector analysis can be performed to estimate the spectral absorptivity of each dye in a multidye ri3'32 This method has the advantages photographic of characterizing the global spectral properties of each film (more than a single concentration) and eliminating the need for single-dye coatings. For the transparent modeling targets (Ektachrome and Fu-

jichrome), the spectral transmittance of each patch of the 1T8.7/1 was converted to spectral density:

D= —ln(Tx/Txmax)

(3)

The maximum transmittance at each wavelength of the entire

data set was used as an estimate of the base rather than the 1T8.7/1 designated ' 'Dmin' ' patch (lower left-hand corner); we found that at each wavelength the designated Dmin patch did not correspond to the minimum density (maximum transmittance). This is shown in Fig. 1 for Fujichrome as an illustrative example. For the opaque modeling targets, the spectral reflectance factor of each patch of either the 1T8.7/2 (Fujicolor) or Q6OC (Ektacolor) was converted to spectral absorptance:

K = ln(Rx/Rxmax) —2

(4)

Eigenvector analysis was performed using SYSTAT33 (covariance form with equamax rotation) for each data set. Equamax rotation evenly divides the variance among the three eigenvectors. Table 1 lists the cumulative population vanances for the first three eigenvectors of each analysis. Clearly, each colon formation model (Eqs. 1 and 2) describes well the relationship between dye concentration and spectral density or absorptance. The high cumulative variances support the assumption of additivity. There is a trend in these analyses, where the Beer-Bouguer theory has higher accuracy in modeling transparent materials than the Kubelka-Munk theory in modeling opaque materials; the cumulative variances are higher for the transparent materials. One limitation of these eigenvectors is a lack of spectral similarity to real dyes. Although an equamax rotation was

Colorimetric characterization of a desktop drum scanner using a spectral model

0.8

C C

0.6

C C Ia)

0

. 0

C a)

0.2

0

Q 1 CC

.

'1i

'I"i O

C '11

0

N

Wavelength (nm)

Fig. 1 Maximum spectral transmittance of entire target (solid line) and designated Dmin patch (dashed line) for Fuji 1T8.7/1 target.

Table 1 Cumulative percent variance of the first three eigenvectors of each listed modeling target. Material

Percent Variance

Ektachrome

99.958

Fujichrome

99.971

Ektacolor

99.938

Fujicolor

99.936

used, unless the sample set has equal variance among the three dyes, the resulting eigenvectors will exhibit unwanted secondary absorptions as shown in Fig. 2for Fujichrome. We hypothesized that if nonlinear transformations were required to relate dye concentration and digital counts, better perfor-

mance would result if the eigenvectors were rotated to resemble actual dyes. Because we do not have access to singledye coatings and it is nearly impossible to have only a single

developed dye due to interimage effects, three additional sequential eigenvector analyses on the cyan, magenta, and yellow ramps (columns 13, 14, and 15 of each target, respectively) were performed where it was assumed that the first eigenvector of each analysis would represent a single dye. These dyes were used as aim spectra in a primarytransformation rotation, where a spectral least-squares critenon was used between the single-dye approximations and the rotated equamax eigenvectors. Thus the rotated eigenvectors have spectral similarity to real dyes while retaining the advantage of a statistical representation based on each film's entire color gamut. The differences between using the

maximum concentration samples, the first eigenvector of each primary concentration ramp, or the global eigenvectors

for the spectral reconstruction were small and resulted in modeling errors of up to 0.5 LEQ (illuminant D50, 2-deg observer) when comparing the measured modeling data set with its spectral reconstruction estimate. The small lack of spectral fit was expected and is often referred to as ''Beer's law failure. ' ' The theoretical assumptions associated with the

Wavelength (nm) Fig. 2 Fujichrome elgenvectors using Systat equamax rotation.

Beer-Bouguer or Kubelka-Munk theories are not perfectly

met in practice, particularly fluorescence, scattering, and refractive index discontinuities between the media and air. The transparent and opaque eigenvectors of Kodak and Fuji are compared with one another in Figs. 3 and 4. The transparent media show greater similarity than the opaque media. Fujichrome and Ektachrome have similar cyan and yellow dyes, while the magenta dye of Fuji has a peak absorption at a shorter wavelength. The two photographic papers have similar cyan dyes and dissimilar yellow and magenta. The two magenta dyes have very different spectral properties where the Fuji material has a much narrower absorptivity. The Fujicolor yellow absorptivity exhibits magenta and cyan secondary absorptions. This is an artifact of the eigenvector analysis rather than a property of the yellow dye. The first eigenvector of the yellow ramp exhibited secondary absorptions. As a consequence, the rotation also contamed secondary absorptions.

6 Estimating Dye Concentration Before the relationship between scanner digital data and concentration can be modeled, the amount of dye present in each color patch must be determined. Common techniques include dissolving the color patch in an appropriate solvent and using

solvent spectrophotometry and the Beer-Bouguer relationship between absorbance and concentration to estimate the concentration of each patch. Obviously, this is prohibitively time consuming with the large number of color patches to analyze. Status densitometry is a second common technique and 16 the basis for converting from integral to analytical The densitometer' 5 system responsivities are situated at the peak wavelengths of the spectral absorptivities of a representative dye set. The logarithm ofthe integration ofthe linear system responses are assumed to linearly relate to dye concentrations via a 3 X 3 matrix transformation. The matrix is required because of secondary absorptions. However, be-

cause integrating logarithmic data (Beer-Bouguer and Kubelka-Munk theories defining analytical densities) is not Journal of Electronic Imaging /October 1995 1 Vol. 4(4)1363

Berns and Shyu

1.2

that densitometric values linearly relate to dye concentrations. By using a spectral analysis of their scanner to determine its

1.0

spectral responsivities (detector responsivity, optics, and source), measured spectral transmittances ofeach color patch,

0.8

0

0.6

0.4

0.2

0.0

-0.2

400

500

600

700

Wavelength (nm)

Fig. 3 Relative eigenvectors for Fujichrome (thin lines with filled dots) and Ektachrome (thick lines).

and spectral absorptivity data of a given photographic material supplied by the film manufacturer or measured using a single exposure corresponding to the maximum concentration, they implemented an iterative technique that minimized integral density differences between the measured scanner values and estimated scanner values based on a priori knowledge. This corresponds to a densitometric match minimizing the sum-of-squares density error. Because both studies assumed a linear relationship between integral and analytical density and additivity of either the manufacturer-supplied or single-exposure-derived spectral absorptivities, errors resulted that were up to about 4 L\ E or 10 IXE (Refs. 18 and 19). Viggiano and Wang'° used the scalars from the eigenvector analysis as an estimate of the dye concentrations. This corresponds to an analytical density spectral match minimizing the sum-of-squares spectral density error. As previously shown, there is a small amount of model failure (Beer' s law failure) that will translate to colorimetric

error. As a consequence, a tristimulus-matching algo-

1.

rithm3438 was used to estimate dye concentrations rather than

use the eigenvector analysis scalars. This method has the advantage of insuring a visual match for a primary illuminant and observer of interest. The tristimulus matching method as implemented in the present research is described in detail by

Berns,27 who applied this technique to a dye-diffusion thermal-transfer printer. Tristimulus matches were obtained for illuminant D50 and the 193 1 standard observer. Thus, by using these dye-concentration estimates and the global eigenvectors for a given material, one can predict the colon-

0 U)

,0 CU

U)

metric values of each color patch perfectly (0 zE).

CU

U)

400

500

600

700

Wavelength (nm)

Fig. 4 Relative eigenvectors for Fujicolor (thin lines with filled dots) and Kodacolor (thick lines).

equivalent to applying a logarithm on integrated linear data

(densitometry defining integral densities), when density is a function of wavelength, errors result that increase as the bandwidths of the responsivities increase. In our experience, this can translate in modeling errors up to 4 ZE for Status A (Ref. 24) densitometers. This reduction in colorimetric and spectral reconstruction accuracy, due to increases in bandwidth when converting from integral to analytical density, was analyzed in detail by Pringle, McElwain, and Glasgow.34 For this reason, narrowband densitometers with half-height

bandwidths of 10 nm are used in place of Status A or M densitometers.3° However, it is critical that the densitometer' s

peak wavelengths are located close to each dye's maximum spectral absorptivity. Dunne and Stockham,2' Rodriguez and Stockham,'8 and Jung and Tralle'9 used the previously described assumption 364 /Journal of Electronic Imaging I October 1995 I Vol. 4(4)

The tnistimulus-matching algorithm additionally yields a method of quantifying the extent of color formation model failure (Beer' s law failure). Since the concentrations were optimized for illuminant D50, calculating color differences for an illuminant dissimilar to D50 such as illuminant A will quantify the extent of spectral reconstruction errors. This is known as an index of metamenism. As the index of metamenism increases, the spectral reconstruction model error increases. The average and maximum CIELAB color differences for the four films evaluated are listed in Table 2.Similar to the eigenvector results shown in Table 1 , the Beer-Bouguer theory modeled the transparent materials better than the Table 2 Degree of metamerism (Eb, illuminantA, 1931 standard observer) quantifying color-formation-model errors. Film Kodak

Maximum

Average 0.2

0.6

Fuji

0.1

0.4

Fujichrome Kodak

0.2

0.9

0.3

1.3

Ektachrome

Ektacolor

Fuji Fujicolor

Colorimetric characterization of a desktop drum scanner using a spectral model

Kubelka-Munk theory modeled the reflective media. (The unwanted secondary absorptions of the Fujicolor yellow eigenvector do not contribute to these types of errors.) The spectral-reconstruction accuracy of the transparent materials was nearly equal to the limiting precision of the spectral measurements. The opaque materials had greater enor. In hindsight, a surface correction should have been used.27 A final source of contributing error to the index of metamerism was the use of a tristimulus-matching algorithm for samples with less than three dyes present. Because of the uncon-

0.2 -

0.1-

0

U

!:t:

0-0.1-

strained nature of the Allen algorithm that relies on a Newton-

Raphson iteration, nonfeasible solutions resulted in about 10% of the modeling target samples (i.e., negative concentrations). Fortunately, these last two sources of error do not have an effect for D50 characterizations, the most common

-0.2-

tion data was expected as defined by each medium' s color formation model [Eq. (1) or (2)J. Following a natural logarithmic transformation, gray-scale data were evaluated by comparing concentration against the logarithm of the normalized digital counts. For this research, it was assumed that each modeling target's gray scale represented the film's dynamic range and tone scale and had optimal gray balance. Following the logarithmic transformation, small nonlinearities remained that were modeled by stepwise multiple-linear regression (forward selection, a = 0.05), where concentration

c1

Cc

(a)

illuminant for drum scanners. For illuminants other than D50 these errors would probably increase the maximum modeling enors by only 0.5 LE and have a very small effect on the mean performance.

7 Relating Scanner Data to Dye Concentrations A logarithmic relationship between scanner and concentra-

I C — c4

::•

0.2 -

0.1U

.t..

%.• ..

0-

. .%.

-0.1 -

-0.2-

i

—

'-r

Cm (b)

0.2 -

was the dependent variable and first- through fifth-order poly-

nomials of the logarithm of the normalized digital counts were the independent variables. The equations for the twelvebit Ektachrome IT8/7. 1 target were:

d = — 0.27423 + O.85435{ln[dr/(2'2 — 1)]}

0.1U

0-

:s..••

•$.

+ 0.00004{ln[dr/(2'2 —

d — 0.24095 + 0.63416{lfl[dg(2'2 — 1)]} + 0.00007{ln[dg/(2'2 —

-0.1 -

(5)

1)]}

-0.2 -

I

I

,-

d = —0.21947 +0.55854{ln[db/(2'2 — 1)]} + 0.00005{ln[db/(2'2 —

I

I

c.'1

Cy (c)

Fig. 5 Concentration differences between predicted and actual

where dr dg and db are the scanner digital data. The variable

d relates to the cyan dye; d relates to magenta dye; and d relates to yellow dye. The negative offset terms were

(a) cyan, (b) magenta, and (c) yellow dyes from the 3 x 3 model (12bit scan) for Kodak 1T8.711 target.

required because of the negative concentrations predicted by the Allen algorithm. If the scanner' s spectral responsivities are assumed to be narrowband, similar to a spectrophotometer, a 3 X 3 transformation following the tone reproduction characterization will accurately predict dye concentrations. The elements of

the system responsivities of the scanner and instead used

the linear transformation can be directly calculated with a knowledge of the film's spectral properties and the system In our case, we did not have responsivities of the

resulting transformation is given in Eq. (6) and the concentration residual errors are shown in Fig. 5. There are strong nonlinear systematic errors for magenta and yellow dye. Be-

multiple-linear regression to predict the transformation coefficients, where concentrations were the dependent variables and linearized scanner data (d , d , ) were the independent data. This was performed on the Ektachrome target, where

d

all of the color patches were used in the regression. The

Journal of Electronic Imaging/October 1995 / Vol. 4(4) /365

Barns and Shyu

(\ / 1.421 0.540 (Cm J(

0.1 -

\c),/

o __ -0.1

cn r

— c1

(6)

Fig. 6. The residual errors are much smaller than those shown

Cc

0.2 - _______________________

0.1-

in Fig. 5 (resulting from the assumption of linearity). The cyan concentration errors are randomly distributed. Slight curvature remains for the magenta and yellow dyes indicating the candidate model coefficients did not represent the actual nonlinearities present for this film and scanner combination.

Because these modeling errors are close to the scanner's precision and well below visual perception (to be discussed later), alternate higher order models were not evaluated.

0-

cc = — 0.027 + 1 .427d — O.565d +

-0.1 -0.2 -

d

1.4O5/\d

dependent data and the concentrations were the dependent data. Linear, squared, and linear covariance terms were selected as candidate model coefficients based on previous experience.9 For example, the Ektachrome model is given in Eq. (7) and the residual concentration errors are shown in

(a)

C)

1.396 —0.302 J( —0.196

Thus a second nonlinear relationship was expected to account for the wideband spectral properties of the scanner. Stepwise multiple-linear regression (forward selection, a = 0.05) was performed, where the linearized scanner values were the in-

-

-0.2-

\ 0.040

—0.179 —0.036\/d

O.O68d O.O85d d

+ O.O37d2 + 0.05 1d2 — O.OO8d2 I

ri n

I

,-

U

I

Cm

O.O12O.196d,+

I

—O.OO5dd —O.O25dd +O.OO3ddd —O.OO6d2

Cm (b)

0.2

—O.O25d2+O.OO9d2

-

cy= —0.024 —O.045d —O.31Od + 1.49Od

+ O.OO6d d — O.OO2d2 — O.O38d2

0.1L) .'1

.

0-0.1

-

-0.2 -

C-cm I

I

Cy (c)

Fig. 6 Concentration differences between predicted and actual (a) cyan, (b) magenta, and (c) yellow dyes from the 3 x 1 1 model (12-bit scan) for Kodak 1T8.7/1 target.

the scanner's responses were on the order of 50 nm wide at half height and asymmetrical, additivity failure occuned. This is equivalent to the limitation discussed before of converting between integral and analytical densities using Status A densitometers. The linear transformation will work for this scanner only if the dye set has spectral characteristics of block dyes in the spectral region of the scanner's system responsivities. cause

366 IJoumal of Electronic Imaging / October 1995 / Vol. 4(4)

.

+ 0.01 1dd (7)

These two stages, linearization of the scanner digital data for the gray scale followed by an empirical higher order set of equations, were implemented for all four materials. Separate

optimizations were performed on the Ektachrome target scanned with both 8- and 12-bit quantizations. Estimated concentrations were used along with Eq. ( 1) (transparent materials) and Eq. (2) (opaque materials) to estimate the spectral properties of the various modeling and verification targets. Finally, CIELAB coordinates were calculated between measured and estimated values for illuminant D50 and the 1931 2-deg observer.

8 Results and Discussion Scanning is the first step in the graphic arts color reproduction

chain (assuming the photograph defines the original). As such, errors in scanner colorimetric characterization will be amplified as they are passed along to latter processes. This will occur for both systematic and random errors. Thus it is critical to minimize errors at this first stage. Two goodness criteria were used. First, we used the results of Stokes, Fairchild, and Berns,39'4° where a perceptibility experiment was

performed comparing perturbed images in predefined

CIELAB directions with an original image. Images with average errors less than about 2 LE were indistinguishable

from one another. The average errors should be below 2

Colorimetric characterization of a desktop drum scanner using a spectral model

100

100

1L+

80

20

O,-L(CjL( L(L() 1 0 C'J

0-

0 ) '- L( j L()

C)

(a) Ektachrome 12 bit linear model

L()

L()

L()

C)

(b) Ektachrome 8 bit nonlinear model

1 40

1 50

120 100

1 00

80 60 40 20 0

C1)

C'%j

50 • ri—i i OL(COLtLt)•L() 0 '•-

c'J

0

C)

(c) Ektachrome 12 bit nonlinear model 60 50 40 30 20

II II II III II

i—•i i—.I

OL( 0

-

,—L() cj L(

C)

oJ

III

LOtL() cy)

(d) Fujichrome 12 bit nonlinear model 70 60 50

0 L( L()'- cj L( i)L() . L(

41IIL

(e) Ektacolor 8 bit nonlinear model

(f) Fujicolor S bit nonlinear model

10 0

0

C'J

C)

100

0 LO - Lt 0

csj

L() c L()

c

LO

C')

Fig. 7 Frequency versus color difference (z Eb) of modeling targets.

CIELAB units. Second, gray-scale errors should be small. We used a criterion of simple field tolerances of about 0.5 The errors resulting from the assumption of linearity for scanners with wideband spectral system responsivities can be quantified by comparing the results of estimating concentration from linearized digital data for Ektachrome using a 3 X 3 transformation [Eq. (6)] with a nonlinear transformation [Eq. (7)]. The LAE histograms for these two analyses are shown in Figs. 7(a) and 7(c), respectively, and the summary statistics are given in Table 3. The linear assumption resulted in an average of 1 .0 compared with 0.4 for the non-

linear assumption, both values below our goodness threshold. The maximum errors were 7.0 compared with 1 .0. The large

linear transformation errors occurred for red colors at high concentration, correlating with the magenta and yellow concentration errors shown in Fig. 5.

A number of studies have evaluated the colorimetric effect of quantization depth. As expected, increasing quantization depth reduces colorimetric errors. A separate nonlinear model was optimized for the Ektachrome 8-bit scan. The resulting histogram is shown in Fig. 7(b) and summary statistics are given in Table 3. The decrease in quantization depth about

doubled the average and maximum errors to 0.7 and 1.9

L E , respectively.

Pairwise F tests on the color-difference sample populations were performed to statistically categorize these three models. It was assumed that color differences were normally distributed. Each model was statistically different from one another at an a of 0.05. The 12-bit nonlinear model was superior to the 8-bit nonlinear model (F = 3.38). The 8-bit nonlinear model was superior to the 12-bit linear model (F= 3.31). Therefore, the nonlinear aspect of the model is more important than 12-bit quantization in producing acJournal of Electronic Imaging /October 1995 I Vol. 4(4)1367

Berns and Shyu

Table 3 Summary of colorimetric results.

Ektachrome Ektachrome Ektachrome Fujichrome Ektacolor

Film type

Modeling target

film

film

film

Plus paper paper

Kodak

Kodak

Kodak

Fuji

Kodak

ff8.7/i

FF8.7/i

Quantization depth

fF8.7/i

118.7/1

8

12

12

Fuji fF87/2

Q—60C

12

8

8

Nonlinear Nonlinear Nonlinear Nonlinear Nonlinear

Linear

Digital to concentration model

Fujicolor

film

Avg. AE*ab of modeling target (all colors)

1.0

0.7

0.4

0.4

0.9

0.9

Max. LE*ab of modeling target (all colors)

7.0}

1.9

1.0

1.6

5.2

3.4

Avg. LE*ab of modeling target (neutral

0.7

0.6

0.4

0.4

0.8

0.6

Avg. LE*ab of independent target

0.7

0.7

2.1

8.8

Max. LE*ab of independent target

1.8

1.6

7.3

21.3

colors)

curate colorimetric characterizations. From this analysis, only nonlinear models were optimized for the other media. The colorimetric performance for the four modeling data

bases is listed in Table 3. All of the targets were accurately modeled with average errors below 1 L E, well below our goodness criterion of 2 L\ E . Modal values were all below 0.5 ZXE for the transparent targets and below 1for LE the opaque targets. The transparent targets were modeled very well with maximum errors below 2 L . Because the majority of materials scanned with a drum scanner are transparent, these results are very encouraging. Our Ektachrome results were about four times better than those reported by Rodriquez and Stockham'8 (average and maximum slightly below 2 and 4 L\E , respectively) and about eight times better than those reported by Jung and Tralle'9 (average and maximum around 3.3 and 10 respectively) using a similar technique. The improvement was due to using a statistically derived set of dye absorptivities, colorimetric rather than densitometric matching, and the use of a nonlinear rather than a linear matrix to account for the scanner' s wideband spectral system responsivities. The opaque results were of slightly lower performance in comparison with the transparent results. The reduced accuracy was mainly due to the reduced 8-bit quantization depth resulting in greater error in predicting high concentrations. Presumably, these errors can be almost halved by increasing quantization to 1 2 bits per channel as was shown for Ektachrome. The Kubelka-Munk model was less effective in modeling the spectral properties of the opaque materials compared with the Beer-Bouguer model used to predict the spectral properties of the transparent materials. Also, the magenta dyes used in the photographic papers have narrower spectral absorptivities than the dyes used in the transparencies. As a consequence, the wide scanner spectral responsivities are a poorer match to the opaque materials leading to increased errors in predicting concentrations. Nevertheless, as shown in the Fig. 7 histograms, 97% of the errors for Ektacolor and 98% of the errors for Fujicolor are below 2 LE . Thus, this method compares very well with regression methods. For example, Kang7 and Berns,9 using the same Q6OC Ektacolor

E

368 IJournal of Electronic Imaging I October 1995/ Vol. 4(4)

target scanned with 8-bit quantization, achieved average and maximum errors of about 2 and 1 0 z . Clippeleer8 was able to equal our performance by using a 3 X 64 matrix. However, a matrix of this size could not be used for data extrap-

E

olation without adverse results. Furthermore, large higher order transformation equations tend to result in low performance when applied to independent data. A potential limitation with this method is a loss of gray balance. The matrices defined by Eqs. (6) or (7) were not row-element constrained. This will cause the accurate concentration estimates of the neutral scales [used to build the three gray-balance transforms as shown in Eq. (5)] to change. As a consequence, it is important to separately evaluate the colorimetric performance of each model target' s gray scale.

Table 3 lists the average color differences for each target's gray scale. The transparent targets achieved our goodness criterion of 0.5 LE ; the opaque targets slightly exceeded this criterion. Chroma (Ca) versus lightness (L*) vector plots are shown in Fig. 8 for each material' s gray scale. The tail of each vector locates the measured coordinates; the vector head locates the predicted coordinates. Vertical vectors represent accurate tone reproduction; vectors of zero length represent accurate gray balance. Gray balance and tone reproduction are well maintained for Ektachrome [Fig. 8(a)] and Fujichrome [Fig. 8(b)]. In fact, gray balance is improved for Fujichrome as shown by the large vectors pointed in the downward direction, though this result is specific to this particular target. The vectors for the opaque targets are larger than those of the transparent targets, consistent with the colorimetric performance for the entire targets. The two lightest neutrals of the Fujicolor target have particularly large errors in comparison to the other neutrals, 2.3 and 1 .5 LE . (Because the vectors are close to vertical, the vector length is approximately equal to the total color difference.) Fortunately, these errors correspond to an increase in blueness, a preferred attribute for white colors. This result was probably fortuitous. The reason why gray balance was maintained despite the unconstrained nature of the matrices can be attributed to the sampling ofthe 1T8.7/1 and 1T8.7/2 targets. When the sample

Colorimetric characterization of a desktop drum scanner using a spectral model

(a) Ektachrome 12 bit nonlinear model

(b) Fujichrome 12 bit nonlinear model

.

5

4.5

4 3.,

. 2. U

1•

F

3.5 V

—

4 2.5 C-)

-4

—- 4-—- -—

* -*- — — aL

4

—

A

— — — — — — — —

(L

(

o

0 40

0 L* 5

-

3

f-

,. 1..— 0.5

4

I

—

— —

2

1.5

4

1

0.5

02 0 40.

60 70 80 90 100

0 09 11

OCl

7

5

L*

C'

() Fujicolor 8 bit nonlinear model

'3.-$

—

—— — —

—

——

—

---- - - - - -

— —

—

— —

A

A A

20 30 40 50 L*

L*

60

70 80 90 100

Fig. 8 Error vectors for neutral scales of each listed modeling target. Vector tail locates the measured coordinate; vector head locates the predicted coordinate.

colors are plotted in a three-dimensional perspective, it is clear that the sampling is neutral weighted. This is a useful property when using these targets to optimize a global matrix. Figure 8 further reveals that one may not want to use a con-

strained matrix anyway. The vector tails of each target do not have the same C indicating that each target' s gray scale does not have a consistent color balance. For critical grayscale color reproduction, calibrating a scanner with these targets where the gray scale is modeled exactly (which would result from our method with a constrained matrix) could result in unacceptable color reproduction. Given the difficulty in manufacturing these targets, these gray scales are surprisingly

good. It is also worth noting that a target's overall color balance may not be optimal for all applications. For example, 35-mm positive film has a slightly bluish color balance (when quantified with either a scanner, densitometer, or colorimeter) to compensate for incomplete chromatic adaptation that occurs when viewing images projected with a 3200 K tungsten

source. The color appearance of the projected imagery is correctly balanced. If the image is not defined using an appearance model but defined by a more traditional approach,

one should remap the image to remove the slightly bluish color balance. Most of the previously published results have only provided model data results. Polynomial regression using large higher order transformation equations is very susceptible to poor performance in practice, a result of fitting random error in addition to the desired systematic trends and noise amplification. Direct table look-up and interpolation is susceptible to measurement errors and quantization errors if the number of nodes is too small. Thus, independent verification is essential. The independent targets were scanned on a different day following the scanner's internal calibration. Each color' s average digital values were transformed to CIELAB coordinates using the model targets' characterizations. If this technique is robust, the color differences should be similar to the model data with these differences randomly distributed

within the color gamut. The LE histograms for the four independent verification targets are shown in Fig. 9; mean and maximum values are listed in Table 3. The technique was very robust for the transparent targets.

Average and maximum errors are still below the 2 Z E Journal of Electronic Imaging/October 1995 I VoL 4(4)1369

Berns and Shyu

1 20 1 00

80 60 40 20

0 . . I P1—I I I I I I I I I I I I I I I U, OL(—L( L(rL( i- C%4L( 0 c'J C)

0

(a) Ektachrome 12 bit nonlinear model

(b) Fujichrome 12 bit nonlinear model 200

30 25 20 15 10 5 0

1 50 1 00

50 0 L( ,—L( cj L() )L() 'J. 'C) 0

L( U,

C'J

(c) Ektacolor 8 bit nonlinear model

0

II II

11

OLC-L( 0

IIII

1tt1 f)LOj-LOU, ; CsJL9 ('1

':i-

(d) Fujicolor 8 bit nonlinear model

Fig. 9 Frequency versus color difference (z Eb) of independent verification targets. (Note that the

5 LEb bin represents values 'Eb.)

goodness criterion. Because the verification targets have a more uniform sampling in CIELAB than the 1T8.7/1 targets, this is an excellent result. We expect the average errors to be larger because of this sampling difference as well as the independent nature of the target. The errors are reasonably random as shown in Fig. 10 for Ektachrome, where color difference is plotted against lightness (L*), chroma (Ca), and hue (hab) of each color patch. There is a slight trend where color differences increase with chroma. Fujichrome had a similar result. The Ektacolor paper resulted in an average CIELAB error of 2. 1, just beyond the limit of the 2.0 goodness criterion. Concentrations were predicted with greater residual error than the modeling data. The prior explanation of the reason for reduced performance of opaque materials in comparison with transparent materials also explains these results. Clearly, the errors are magnified when evaluating independent data. However, these results are a realistic indication of how this method will perform in practice.

The independent Fujicolor target resulted in very poor predictions; the average and maximum errors were 8.8 and 21.3 L\E. This was a surprising result because for the other independent targets, the decrease in performance compared with the modeling target was, at most, a factor of two. In a post hoc analysis, it was found that the independent target had different dye characteristics than the 1T8.7/2 target. As a result, the spectral reconstruction was in error. Apparently, the Fujicolor paper we used to produce the independent target

was different from the paper used to produce the 1T8.7/2 370 /Journal of Electronic Imaging I October 1995 I Vol. 4(4)

target. This points out a limitation of this method. It is critical

that the material requiring scanning and colorimetric characterization have the same spectral properties used to build the spectral model. We expect that the Fujicolor results would be similar to the Ektacolor results if repeated using the correct

paper.

9 Conclusions There is a tendency to use statistics as a colorimetric char-

acterization tool without regard to the physics of the imaging

system. Regression techniques79 fall into this category as well as methods based on linear models of reflectance factor data (for example, Ref. 41). Given that photographic media are comprised of cyan, magenta, and yellow dyes, three eigenvectors, correctly defined, should describe the spectral properties of the media. Therefore, a three-channel input de-

vice should, in theory, be able to record information that relates to the three eigenvectors. Understanding the physics enables one to correctly identify the function of either transmittance or reflectance factor where a linear model is ex-

pected to apply. In this research, the Beer-Bouguer and Kubelka-Munk theories were used to transform the fundamental spectral transmittance and reflectance factor measurements to spectral density and absorptance, respectively. As quantified using an index of metamerism, each set of three eigenvectors reconstructed each photographic medium very

closely. This level of accuracy cannot be achieved using a linear model of either transmittance or reflectance factor un-

Colorimetric characterization of a desktop drum scanner using a spectral model

2

1.5.0

,. . ,, ... . •ss: : .',

"1

.

..

*

0.5-

'

::• , •. .

S

.

::

S• •,••% ,• •.1

00

•

I

40

20

60

80

L* (a)

2-

10 nm would be optimal. Because the scanner used in this research had much wider bandwidths, it was known a priori that a nonlinear matrix was necessary despite the linearization stage based on the modeling targets' gray scales. Thus, applying the technique of converting from integral to analytical density for photographic media to the problem of scanner colorimetric characterization yielded excellent results for transparency materials and very acceptable results for reflective materials. The key issues include characterizing the spectral absorptivity properties of the film, narrowband scanner responsivities, and insuring the image requiring characterization has the same spectral absorptivity characteristics as the model data. This method has the advantage of easily characterizing the scanner for any illuminant and observer of interest, minimizing problems of metamerism. Its one limitation is that the film type must be known and have been previously characterized.

Acknowledgments 1.5

This research was kindly supported by Dupont Printing and

Publishing Division and Howtek. -C

*

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372/Journal of Electronic Imaging / October 1995 / Vol. 4(4)

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Roy S. Berns: Biography and photograph appear with the paper "Cathode-ray-tube to reflection-print matching under mixed chromatic adaptation using RLAB" in this issue.

M. J. Shyu received a BS in engineering science from Cheng-Kung University and an MS in computer science from Colorado State University. He then worked for AT&T as a comuter programmer for telecommunications for five years. He returned to academia and earned an MS in color science from Rochester Institute of Technology. This

article was based on his thesis research. He is now a part of the faculty in the Department of Graphic Communication, Chinese Culture University in Taiwan.