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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 7 — Aug. 1, 2013
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Brightness perception of unrelated self-luminous colors

Martijn Withouck, Kevin A. G. Smet, Wouter R. Ryckaert, Michael R. Pointer, Geert Deconinck, Jan Koenderink, and Peter Hanselaer  »View Author Affiliations


JOSA A, Vol. 30, Issue 6, pp. 1248-1255 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001248


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Abstract

The perception of brightness of unrelated self-luminous colored stimuli of the same luminance has been investigated. The Helmholtz–Kohlrausch (H-K) effect, i.e., an increase in brightness perception due to an increase in saturation, is clearly observed. This brightness perception is compared with the calculated brightness according to six existing vision models, color appearance models, and models based on the concept of equivalent luminance. Although these models included the H-K effect and half of them were developed to work with unrelated colors, none of the models seemed to be able to fully predict the perceived brightness. A tentative solution to increase the prediction accuracy of the color appearance model CAM97u, developed by Hunt, is presented.

© 2013 Optical Society of America

1. INTRODUCTION

In this study, nine observers have evaluated the brightness of 58 unrelated self-luminous colored stimuli with a luminance of 51cd/m2 and surrounded by a dark background. The spectral radiance of the stimuli has been measured, and observer data of the brightness have been collected. The correlation between the brightness perception of these observers and the brightness calculated according to the models based on the equivalent luminance, the CAM97u model, the ATD01 model, and the CAMFu model has been investigated. Finally, a tentative improvement of the brightness prediction of CAM97u is proposed.

2. VISION MODELS FOR PREDICTING BRIGHTNESS PERCEPTION

The vision models mentioned in the introduction are extensively described below.

A. CAM97u

B. ATD01

The ATD01 model is a color vision model, developed by Guth [17

17. S. L. Guth, “ATD01 model for color appearances, color differences and chromatic adaptation,” Proc. SPIE 4421, 303–3062002). [CrossRef]

], built on the theoretical ideas of Helmholtz, Hering, von Kries, and Mueller. It is developed to predict the brightness, saturation, and hue of unrelated colors and to predict a wide range of vision science data on phenomena, such as chromatic discrimination, absolute thresholds, the Bezold–Brücke hue shift, the Abney effect, heterochromatic brightness matching, light adaptation, and chromatic adaptation [14

14. M. D. Fairchild, Color Appearance Models, 2nd ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).

,22

22. P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001). [CrossRef]

]. In the ATD model, the XYZ tristimulus values are transformed into LMS cone responses. These LMS signals are gain-controlled and undergo a second transformation to yield an achromatic (A) and two chromatic or opponent signals (red–green or T, blue–green or D). These A, T, and D signals go through a compressive nonlinearity and are finally used to calculate the perceptual attributes brightness, hue, and saturation. The brightness QATD is calculated as quadrature sum of the A, T, and D signals:
QATD=(A2+T2+D2)0.5.
(2)
As the achromatic A value approximately corresponds to the luminance Y, this model deals with the H-K effect by adding the chromatic T and D values to the brightness prediction [8

8. S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973). [CrossRef]

].

C. Fu (CAMFu)

Fu investigated the color appearance of unrelated colors under photopic and mesopic levels of adaptation using stimuli displayed on a CRT [18

18. C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012). [CrossRef]

]. Four stimulus sizes (0.5°, 1°, 2°, and 10°) and stimuli with luminance values between 0.1 and 60cd/m2 were used. For brightness evaluation a magnitude scaling method [23

23. M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991). [CrossRef]

] was adopted. Colors appeared more colorful (Hunt effect [15

15. R. W. G. Hunt and M. R. Pointer, Measuring Colour, 4th ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2011).

]) and brighter at higher luminance levels than at lower luminance levels and increasing the stimulus size generally increased both brightness and colorfulness. The data were compared with the predictions of CAM97u and CIECAM02, even though the latter model is in principle not applicable to unrelated colors. An alternative CAM for unrelated colors under photopic and mesopic conditions, in this paper indicated as CAMFu and highly inspired by CIECAM02, was developed. In the CAMFu model, the brightness correlate QCAMFu is given by
QCAMFu=ACAMFu+MCAMFu100,
(3)
with ACAMFu and MCAMFu the achromatic contribution and colorfulness as calculated from the CAMFu model.

D. Equivalent Luminance Nayatani (Leq,Nay)

Nayatani proposed two methods that take into account the H-K effect for calculating the equivalent luminance [3

3. Y. Nayatani, “Simple estimation methods for the Helmholtz—Kohlrausch effect,” Color Res. Appl. 22, 385–401 (1997). [CrossRef]

]: the variable-achromatic-color (VAC) and the variable-chromatic-color (VCC) method, given by Eqs. (4) and (5), respectively:
γVAC=Leq,Nay(VAC)L=0.4462[1+{0.1340q(θ)+0.0872KBr(La)}suv(x,y)+0.3086]3,
(4)
γVCC=Leq,Nay(VCC)L=0.4462[1+{0.8660q(θ)+0.0872KBr(La)}suv(x,y)+0.3086]3.
(5)
The presence of the saturation suv(x,y) of the test stimulus indicates inclusion of the H-K effect. The function q(θ) describes the impact of the hue angle θ on the H-K effect. KBr(La) accounts for the increase of the H-K effect when the adapting luminance of chromatic object colors is raised.

In the VAC method, the luminance of the reference achromatic color is changed in order to match the colored stimuli. In the VCC method, the luminance of the colored stimuli is changed in order to match the achromatic reference.

E. Equivalent Luminance CIE (Leq,CIE)

This equation has been based on visual data gathered from several studies [8

8. S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973). [CrossRef]

,13

13. H. Yaguchi and M. Ikeda, “Subadditivity and superadditivity in heterochromatic brightness matching,” Vis. Res. 23, 1711–1718 (1983). [CrossRef]

,24

24. K. Sagawa and K. Takeichi, “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” J. Opt. Soc. Am. A 9, 1240–1246 (1992). [CrossRef]

26

26. D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1298 (1968). [CrossRef]

] and Eq. (6) has been tested by matching experiments [5

5. CIE, Testing of Supplementary Systems of Photometry (CIE Central Bureau, 2001).

]. The supplementary system of photometry as described by Eq. (6) was originally developed based on the 2° quantities, except for the scotopic luminance, but can also be used for a centrally fixed 10° field.

3. EXPERIMENTAL SETUP

In this study, the brightness of unrelated colors was investigated using a specially designed viewing room [see Fig. 1(a)]. The dimensions of the room are 3 m wide by 5 m long by 3.5 m high. The walls, ceiling, and floor were covered with black curtains, gray panels, and a grayish black carpet, respectively. At one wall, a circular tube (diameter 37 cm), containing an RGB LED module and covered by a circular diffuser, was mounted inside the wall [see Fig. 1(b)]. This circular diffuser provided a stimulus of approximately 10° FOV to the observers who were seated on a fixed chair at a distance of 211 cm. The color of the stimulus was changed by controlling the intensity of the RGB LEDs using a DMX digital communication network. For the experiments, 58 colored stimuli with a constant luminance of 51cd/m2 (standard deviation 0.80cd/m2) and a wide chromaticity gamut were carefully selected. This luminance level was chosen in order to ensure photopic viewing conditions without any glare effect. Note that the luminance was calculated using the standard spectral luminous efficiency function V10(λ) for the CIE 10° observer [27

27. CIE, Colorimetry (CIE Central Bureau, 2004).

]. The CIE 1976 u10, v10 chromaticity coordinates of the stimuli, as determined from spectral measurement using a spectroradiometer (MS260i Oriel instruments spectrograph) and suitable calibration, are illustrated in Fig. 2.

Fig. 1. (a) Experimental room and (b) example of a stimulus under dark viewing conditions.
Fig. 2. Chromaticity coordinates of the 58 stimuli plotted in the CIE 1976 u10, v10 chromaticity diagram.

The luminance uniformity of the stimulus area was checked by measurements with a two-dimensional luminance camera (MURATest by Eldim). The luminance of the stimulus was found to gradually decrease (to approximately 20% of the average) from the center to the edge. As the human eye is insensitive to low spatial frequencies [28

28. T. N. Cornsweet, Visual Perception (Academic, 1970).

], observers were not aware of this variation. The background, consisting of a black curtain, provided a 0.01cd/m2 adaptive field extending to 35° around the 10° stimuli.

4. EVALUATION OF BRIGHTNESS

In the psychophysical experiment, observers were asked to evaluate the perceived brightness of the stimuli using a magnitude estimation method. With this method, a numerical and scalable result for the perceptual attribute under test, in this case brightness, can be obtained directly [21

21. CIE, A Colour Appearance Model for Colour Management Systems: CIECAM02 (CIE Central Bureau, 2004).

,29

29. F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011). [CrossRef]

31

31. W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).

]. The experiment started by showing a reference achromatic stimulus with chromaticity close to that of illuminant D65 (u10, v10=0.1979, 0.4695) and a luminance equal to that of the colored test stimuli, i.e., 51cd/m2. The color difference ΔEuv between the reference stimulus and the illuminant D65 was 0.00234. To keep the colored stimuli unrelated, the presentation of a reference stimulus shown in temporal juxtaposition with the test stimulus, possibly inducing small memory errors, was preferred to a reference stimulus presented at the same time in adjacent spatial locations. To this reference a fixed brightness value of 50 was attributed. After 5 s, the colored test stimulus was presented for 15 s. Just after switching to the reference again, the observers were asked to rate the brightness of the stimulus relative to the reference achromatic stimulus. Pilot experiments had shown that it is easier to rate the brightness immediately after the colored stimulus has disappeared. Furthermore, by showing the reference stimulus after each stimulus presentation, any errors induced due to memory effects were minimized. Total darkness never occurred in order to reduce the potential for temporary blindness and afterimages. Before the experiment, the observers adapted to the dark viewing conditions for at least 5 min. The following instructions were given to each observer:

You will see 58 test stimuli. First a reference stimulus will be shown for 5 s. Each test stimulus is then presented for 15 s. Between each of these 58 test stimuli, a reference stimulus will be shown for 5 s. Give a value to the brightness of the test stimulus immediately after the disappearing of this test stimulus and in comparison with the reference. The reference has a brightness value of 50. A value of zero represents a dark stimulus without any brightness. There is no upper limit to the value of brightness.

To become familiar with the magnitude estimation method, a straightforward exercise was completed in which observers were asked to rate the length of a line in comparison with a line of length 100. A similar method is described in the ASTM International standard test method for unipolar magnitude estimation of sensory attributes [32

32. ASTM International, ASTM Standard E1697-05(2012)e1, “Standard Test Method for Unipolar Magnitude Estimation of Sensory Attributes” (ASTM International, 2012).

]. In addition, a set of training stimuli, with the same hue and luminance as in the experiments, was also presented to the observers, allowing them to be aware of the brightness range and to become familiar with brightness rating technique. The duration of this training session was about 45 min, while the experiment took about 25 min. A small break was taken between the training and the experiment in order to reduce the influence of fatigue.

Nine observers, five female and four male, with ages ranging between 23 and 30 years (average 27) participated in the experiments. All had normal color vision according to the Ishihara 24 plate Test for Color Blindness and were naïve with respect to the purpose of the experiment. To avoid irreproducibility in the luminous flux and chromaticity of the LEDs induced by thermal conditions, the 58 stimuli were presented in an identical sequence to all observers. The same sequence was also used for the optical measurements. The training session contained the same set of stimuli but in a different order.

5. RESULTS

A. Inter-observer Agreement

The agreement between any two sets of data can be analyzed using the coefficient of variation (CV) [Eq. (7)] [33

33. P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007). [CrossRef]

]. For a perfect agreement between two sets of data, the CV should be equal to zero. Inter-observer agreement was assessed by calculating the CV values between each individual observer’s results and the geometric mean of all the observers:
CV=1001ni=1n(Qgeom,ifQobs,i)2Q¯geom2withf=i=1nQgeom,iQobs,ii=1nQobs,i2.
(7)
Qobs,i represents the individual observer brightness of stimulus i, Qgeom,i the geometric mean of Qobs,i for all the observers, Q¯geom the arithmetic mean of Qgeom,i for all stimuli, n the number of evaluated stimuli, and f the factor adjusting the Qgeom,i and Qobs,i values to the same scale.

Table 1. Evaluation of Inter-observer Agreement by Calculation of the Coefficient of Variation (CV)

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B. Brightness Perception

The values of the geometric mean of the observers’ brightness Qgeom,i (further referred to as Qgeom) for each of the 58 test stimuli of equal luminance (51cd/m2) are given in Table 2, together with the CIE 1976 u10, v10 hue-angle (huv,10) and the saturation (suv,10) of each stimuli, calculated using Eqs. (8) and (9) [27

27. CIE, Colorimetry (CIE Central Bureau, 2004).

]:
huv,10=arctan[v10vn,10u10un,10],
(8)
suv,10=13[(u10un,10)2+(v10vn,10)2]12,
(9)
where u10, v10 and un,10, vn,10 are the CIE 1976 chromaticity coordinates for the CIE 10° observer of the colored stimulus and the reference achromatic stimulus, respectively. Eleven series with more or less constant hue can be identified. Saturation values range from 0 to 3.61 (red stimulus).

Table 2. Values of the Geometric Mean of the Observer Brightness (Qgeom), CIE 1976 u10, v10 Saturation (suv,10), and CIE 1976 u10, v10 Hue-Angle (huv,10) of All the 58 Stimuli Ordered by Hue

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It is clear that for each hue series, there is generally an increase in perceived brightness with saturation. A plot of Qgeom for each stimulus versus the saturation suv,10 is given in Fig. 3. As each stimulus has the same luminance, Fig. 3 clearly illustrates the H-K effect. The figure suggests a possible difference in the size of the H-K effect for different colors (larger for red and blue, lower for yellow). Therefore the dependency of the perceived brightness on the 11 hue series has been investigated using a one-way ANOVA. With Qgeom as dependent variable and the 11 hue series as factor, the analysis showed that the observed brightness is not significantly different for the eleven hues, F(10,43)=1.347, p=0.237. Even though prior studies of the H-K effect showed a tendency to be larger for reds and blues than for yellow [6

6. G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982), p. 410.

], the current experimental data was insufficient to support this with statistical significance.

Fig. 3. Average observer brightness (Qgeom) with SE error bars, calculated for each individual stimulus from all observer answers, plotted against the CIE 1976 u10, v10saturation (suv,10) of the stimuli with the yellow, green, blue, and red stimuli highlighted.

C. Model Performance

The ability to predict the observer data for brightness has been investigated for each of the previously described models. Before comparing their performances, some clarifications about the input values required by the models are discussed. Because of the 10° field-of-view (FOV) of the test stimuli, the 10° photometric quantities have been calculated, although not all models were developed for this FOV.

For CAM97u, the equi-energy stimulus SE was used for the conditioning field and the adapting field. The luminance of the conditioning field Lc and the adapting field La was taken as L2/3/200 [19

19. R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998), pp. 239–246.

]. The scotopic luminance of the stimuli Ls was calculated using the spectral luminous efficiency function for scotopic vision V(λ) and the scotopic luminance of the conditioning field Lc,s and the adapting field La,s was taken as 2.26(Ls/2.26)2/3/200 [19

19. R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998), pp. 239–246.

].

For CAMFu, the experimental reference stimulus was taken as the reference white. The tristimulus values of the stimuli X, Y, Z and of the reference white Xw, Yw, Zw were normalized such that Y=Yw=100. The luminance of the reference white Lw and the adapting field La were, respectively, set to Lref and 1/5Lref. The scotopic luminance of the stimuli Ls was calculated using the spectral luminous efficiency function for scotopic vision V(λ).

For each of the six models described in the second section, the averaged visual brightness as assessed by the observers, Qgeom, has been plotted against the calculated brightness, Q, on Fig. 4. The blue, green, red, and yellow stimuli have been highlighted. To assess the amount of variation in brightness perception that is explained by each model, the coefficient of determination (R2) of the regression between the observed and calculated brightness has been calculated. A R2 close to 1 suggests a good prediction by the model [34

34. A. Field, Discovering Statistics Using SPSS, 3rd ed. (SAGE, 2009).

]. Although a linear relation between the observed and the calculated brightness is expected, the Spearman correlation coefficient [34

34. A. Field, Discovering Statistics Using SPSS, 3rd ed. (SAGE, 2009).

] has also been calculated. The Spearman correlation coefficient is a rank order metric (not sensitive to the potential nonlinearity of the relation between observed and calculated values of Q), having a value between 1 (perfect negative correlation) and +1 (perfect positive correlation). Table 3 summarizes the statistical results for each model.

Table 3. Overview of the Correlation between the Average Brightness Data of the Observers and the Predictions of the Vision Models Together with the One-Way ANOVA of the 11 Hue Series

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Fig. 4. Average observer brightness (Qgeom) with SE error bars plotted against the brightness predictions of (a) CAM97u, (b) ATD01, and (c) CAMFu and the predictions of the equivalent luminance of Nayatani [VAC (d) and VCC (e)], and (f) CIE. The blue, green, red, and yellow stimuli are highlighted.

From Table 3, it is clear that none of the described models perform well. Although the two best models, LEq,CIE(R2=0.730) and LEq,Nay(VAC)(R2=0.718), included the H-K effect explicitly, they were not developed for unrelated colors, which could explain their lack of predictive strength for the constant luminance stimuli. Remarkably the VAC model of Nayatani’s equivalent luminance, where the achromatic color is changed to match the colored stimuli, performs better than the VCC model (R2=0.598), although it should be less applicable to the method used in this experiment, with a constant achromatic stimulus.

While the one-way ANOVA showed that there was not a significant difference between Qgeom for the 11 hue series, the same analysis with LEq,CIE, LEq,Nay(VAC) and LEq,Nay(VCC) as dependent variables (Table 3) indicated that there is a difference between the brightness predicted by these models for the 11 hues. In fact, the models predicted a difference between the brightness for these hues while this was not observed by the observers.

The one-way ANOVA with the brightness prediction of the other models—CAM97u, ATD01, and CAMFu—also showed a difference between the predicted brightness for the 11 hue series. Although these have been developed for unrelated colors and include the H-K effect, the results from the ANOVA, the low values of the Spearman correlation coefficient, and the low coefficient of determination (Table 3) indicate that they are unable to predict the experimental brightness data (with a luminance of 51cd/m2). The brightness prediction of CAM97u [Eq. (1)] and CAMFu [Eq. (3)] both consist of a summation of an achromatic signal, which is nearly constant (all stimuli have equal luminance), and a contribution of the colorfulness factor M, which takes into account the H-K effect. The failure of these two models to predict the perceived brightness for the self-luminous stimuli in this study might be attributed to a poor implementation of this colorfulness factor. In fact, the correlation between M and Qgeom can be used to investigate the implementation of the H-K effect.

The correlation between MCAMFu and Qgeom(R2=0.483and Spearmanr=0.607) indicates that the H-K effect is poorly predicted. This failure of CAMFu might be attributed to the use of a colorfulness factor MCAMFu based on the CIECAM02 model [21

21. CIE, A Colour Appearance Model for Colour Management Systems: CIECAM02 (CIE Central Bureau, 2004).

], which was not developed to handle unrelated colors.

Fig. 5. Average observer brightness (Qgeom) with SE error bars plotted against the colorfulness predictions of CAM97u. The blue, green, red, and yellow stimuli are highlighted.

The H-K effect can thus be predicted by MCAM97u while the achromatic factor ACAM97u is nearly constant for all 58 stimuli and QCAM97u does not correlate with the observed brightness. This suggests that the performance of CAM97u could be considerably improved just by increasing the contribution of this colorfulness. In fact, increasing the contribution of the colorfulness in Eq. (1) will also increase the correlation between Qgeom and QCAM97u. However, because ACAM97u and MCAM97u are not totally independent and the magnitude of the increased colorfulness contribution should be determined, additional visual data at different luminance levels are required in order to propose a better model.

6. CONCLUSIONS

In a psychophysical experiment the brightness perception of unrelated self-luminous colored stimuli with a constant luminance was investigated. The ability of six vision models to predict the observed brightness was evaluated using the coefficient of determination, the Spearman correlation coefficient, and an ANOVA analysis. Although the models included the H-K effect and half of them were developed to work with unrelated colors, none of the models seemed to be fully able to predict the perceived brightness. The expected linear relationship between the observed and predicted brightness was not achieved.

However, the brightness prediction of CAM97u and CAMFu both consist of a summation of an achromatic signal, which is nearly constant (all stimuli have equal luminance), and a contribution of the colorfulness factor M, to take the H-K effect into account. The failure of these two models to predict the perceived brightness for the self-luminous stimuli in this study might thus be attributed to a poor implementation or an underestimation of this colorfulness factor. The former is most likely the case for the Fu model as the correlation between the observed brightness and its predicted colorfulness is rather low and the model is based on CIECAM02, which is unable to handle unrelated colors. However, CAM97u, specifically designed for unrelated colors, showed a good correlation between its colorfulness factor and the observed brightness suggesting that an increase of the contribution of the colorfulness factor in the calculation of the brightness might lead to a better model. In order to determine the exact magnitude and possible luminance dependence of this increased colorfulness contribution, further research at different luminance levels will be performed.

ACKNOWLEDGMENTS

The authors would like to thank the Research Council of the KU Leuven for supporting this research project (STIM-OT/11/056).

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OCIS Codes
(330.1690) Vision, color, and visual optics : Color
(330.5020) Vision, color, and visual optics : Perception psychology
(330.5510) Vision, color, and visual optics : Psychophysics

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: December 19, 2012
Revised Manuscript: April 16, 2013
Manuscript Accepted: April 30, 2013
Published: May 28, 2013

Virtual Issues
Vol. 8, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Martijn Withouck, Kevin A. G. Smet, Wouter R. Ryckaert, Michael R. Pointer, Geert Deconinck, Jan Koenderink, and Peter Hanselaer, "Brightness perception of unrelated self-luminous colors," J. Opt. Soc. Am. A 30, 1248-1255 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-30-6-1248


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References

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