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Abstract
Modelling the influence of age on the perception of brightness of visual stimuli is an important topic for indoor and outdoor lighting. As people get older, the transmittance of the ocular media becomes lower, especially in the blue wavelength region. This paper reports on an experimental study aiming to evaluate how the brightness perception of red and blue stimuli is affected by the age of the observer. A matching experiment has been set up in which both young (25 years old on average) and older (70 years old on average) adult observers had to match the brightness of a blue stimulus with the brightness of a red stimulus, both surrounded by a dark background (unrelated stimuli). A significant difference in brightness perception between the two groups of observers was found. In particular, older people report a decrease in brightness perception for the blue stimuli compared to younger people. The results show that the brightness correlate of the colour appearance model CAM18sl (applied with zero luminance background) adequately predicts the matching results of young observers, but failed to predict the results obtained by the older observers. As CAM18sl is built on cone fundamentals which include the transmittance of the ocular media and consider the age of the observer as an input parameter, the authors developed the idea to substitute the cone fundamentals for a young observer by the cone fundamentals for a 70 years old observer. This updated CAM18sl performed very well for the older observer as well, on condition that the transmittance of the ocular media is isolated and kept out of the normalization of the cone fundamentals.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The perception of brightness of visual stimuli is an important topic for both indoor and outdoor lighting as brightness is, next to hue and colourfulness, one of the main absolute perceptual attributes of any visual stimulus. For urban lighting in particular, mainly brightness and contrast of brightness are involved when safety issues such as glare, visibility and the general sense of perceived security are concerned [1,2].
Unlike luminance, which is an objective measure of radiance weighted by the luminous efficiency function of the human eye V(λ), brightness is defined as “the attribute of a visual perception according to which an area appears to emit, or reflect, more or less light” [3]. Although luminance and brightness are highly correlated, the relation between them is rather complicated. In particular, brightness is also influenced by the Helmholtz-Kohlrausch (H-K) effect. The H-K effect is “the change in the brightness of a perceived colour generated by increasing the purity of a colour stimulus while keeping its luminance constant within the range of photopic vision” [3].
The perception of brightness of a visual stimulus has been studied for a long time and a number of predictive models have been proposed [4–8]. In addition to some specific brightness models, brightness is also one of the main outcomes of a more general colour appearance model (CAM) [9–16]. Most of these CAMs are targeting the prediction of object colours illuminated by a test illuminant. The number of CAMs focusing on the perception of light sources, also called self-luminous stimuli, is rather limited. A few of them are only dedicated to unrelated stimuli, self-luminous stimuli in isolation of any other luminous background or surround [9,12,15,16]. One of these, CAM15u, has been extended to the CAM18sl model [10,11] which is a more general applicable model that takes into account the impact of a uniform and neutral background on the perceived brightness. When applying CAM18sl to a zero background luminance, the outputs are highly correlated to the outputs of CAM15u, except for a scaling factor.
The input variables for most of the brightness models and CAMs are classical photometric and colorimetric quantities such as luminance and tristimulus values calculated by the well-known colour matching functions $(\bar{x}$, $\bar{y}$, $\bar{z}$) defined for a 2° or 10° visual field. However, the more recent models, such as CAM15u and CAM18sl, use the absolute spectral radiance of the stimulus as input, which is weighted by the physiologically relevant CIE 2006 cone fundamentals [17], to calculate cone excitations, cone responses and brightness. The classical photometric and colorimetric quantities and most of the reported brightness models have in common that they are mainly targeting young adult observers. As an example, the photopic luminous efficiency function V(λ) was derived with data from mainly young observers of 33 years on average [18]. However other authors have reported age-related changes in luminous efficiency [19–21].
It is estimated that in the next 35 years, the population aged 60 or above will be doubled globally. For the Latin American region in particular, this part of the population will even increase by 140% [22,23]. As people get older, the transmittance of the eye lens becomes lower [24–28], which affects the amount of light that reaches the retina. Extensive numerical age-related data are gathered in CIE 203:2012 [26] and CIE 170-1:2006 [17]. While the overall decrease with age in transmittance appears small within the 380 to 780 nm wavelength range (about 16% for a 70 year old compared to a 25 year old person), it is shown that for the short wavelength range (380 nm to 550 nm), there is a very pronounced decrease in the transmittance of about 40% for a 70 year old person. On the other hand, for long wavelengths (550 nm to 780 nm), the decrease for a 70 year old person is only about 5%.
Due to the H-K effect [9], saturated stimuli are perceived as much brighter than white stimuli of the same luminance. For blue stimuli in particular, it can be expected that a reduction of the eye transmittance in the short wavelength range due to age might have a severe impact on brightness perception for older observers. However, several studies have shown that some chromatic characteristics of colour appearance at suprathreshold levels remain very stable despite the changes in the transmittance of the lens, the sensitivity losses in the cone receptor mechanisms and the increase in the macular pigment density with ageing [29–33] while others, such as chromatic contrast sensitivity [34], change considerably with age. Therefore, it is believed that some mechanisms compensate for the short-wavelength light loss in the perception of colour [32,33,35,36].
However, losses in eye transmittance imply a reduction in the light reaching the retina and it has been estimated that older people need about a 30% higher illuminance than young people to obtain the same retinal illuminance [33]. Nevertheless, the implementation of the effect of age in colour appearance models for unrelated colours -the brightness correlate in particular- has not been reported in literature.
The scope of this work is to evaluate how the brightness perception is affected by the age of the observer and if these changes can be explained by including the reduced human eye transmittance. A matching experiment has been set up in which both young (25 years old on average) and older (70 years old on average) adult observers had to match the brightness of a blue stimulus with the brightness of a red stimulus, both surrounded by a dark background (unrelated stimuli).
As cone fundamentals consider the age of the observer as input parameter and the CAM18sl model is built upon these cone fundamentals, CAM18sl could be very promising when investigating the effect of age on brightness perception. For both red and blue stimuli, the brightness predicted by CAM18sl is calculated and it is investigated if the reduced eye transmission as incorporated in the cone fundamentals is able to account for the different brightness perception of older observers.
2. CAM18sl
The calculation of brightness for unrelated stimuli (dark background) based on the CAM18sl model involves the following steps [9]:
- 1. Calculation of the normalized cone excitations of the stimulus ($\rho ,\; \gamma ,\; \beta $):$$\rho = {k_\rho }\int\limits_{380}^{780} {{L_{e,\lambda }}(\lambda ){{\overline l }_{10}}(\lambda )d\lambda } ,$$
As the development of the CAM18sl model is based on stimuli with a 10° angular extend, the CIE 2006 10° cone fundamentals (${\bar{l}_{10}},\; {\bar{m}_{10}},\; {\bar{s}_{10}}$) for a 32 years old observer were used. ${L_{e,\lambda }}$ is the spectral radiance of the stimulus and the coefficients ${k_\rho }$, ${k_\gamma }$, ${k_\beta }$ are used for the normalization of ($\rho ,\; \gamma ,\; \beta $). These three constants were chosen such that the cone excitations of spectral equal-energy white (EEW) are identical and nominally equal to the CIE 1964 10° luminance value:
$${k_\rho }\int\limits_{380}^{780} {{{\bar{l}}_{10}}(\lambda )d\lambda } = {k_\gamma }\int\limits_{380}^{780} {{{\bar{m}}_{10}}(\lambda )d\lambda } = {k_\beta }\int\limits_{380}^{780} {{{\bar{s}}_{10}}(\lambda )d\lambda } = 683.6\int\limits_{380}^{780} {{{\bar{y}}_{10}}(\lambda )d\lambda } .$$This yields the values ${k_\rho } = 676.7$, ${k_\gamma } = 794.0$ and ${k_\beta } = 1461.5$.
The next step would be the calculation of Von Kries chromatic adaptation transformation, but this can be dropped for unrelated stimuli.
- 2. Calculation of the compressed and adapted cone responses (${\rho _{c,a}},\; {\gamma _{c,a}},\; {\beta _{c,a}}$):$${\rho _{c,a}} = \frac{{{\rho ^{0.58}}}}{{{\rho ^{0.58}} + {{({291.2 + 71.8\alpha_{wr}^{0.78}} )}^{0.58}}}},$$$${\gamma _{c,a}} = \frac{{{\gamma ^{0.58}}}}{{{\gamma ^{0.58}} + {{({291.2 + 71.8\alpha_{wr}^{0.78}} )}^{0.58}}}},$$$${\beta _{c,a}} = \frac{{{\beta ^{0.58}}}}{{{\beta ^{0.58}} + {{({291.2 + 71.8\alpha_{wr}^{0.78}} )}^{0.58}}}}.$$The adaptive shift is represented by ${\alpha _{wr}}$, which is equal to the cone responses of the uniform background; however, for unrelated stimuli, ${\alpha _{wr}} = 0$.
In 2006, the CIE Technical Committee TC-36 established a set of cone fundamentals for the normal observer considering the viewing angle (1° to 10°) and the age (any age above 20 years old) as variables [17]. In order to adapt the CAM18sl model for stimuli with a size of 2°, as is the case for the experiments reported in this paper, the authors suggest to replace the CIE 2006 10° cone fundamentals (${\bar{l}_{10}},\; {\bar{m}_{10}},\; {\bar{s}_{10}}$) in Eqs. 1–3 with the CIE 2006 2° cone fundamentals calculated for a 25 years old observer (${\bar{l}_{25yr}},\; {\bar{m}_{25yr}},\; {\bar{s}_{25yr}}$), being the average age of the young observers in the experiments. The values were generated using the LuxPy package [37].
Next, the coefficients ${k_\rho }$, ${k_\gamma }$, ${k_\beta }$ are recalculated to normalize the cone responses to the CIE 1931 2° luminance: ${k_\rho } = 626.8$, ${k_\gamma } = 768.3$ and ${k_\beta } = 1252.9$. In what follows, references to CAM18sl are to be interpreted in this way.
3. Methods
3.1 Stimuli
A scene consisting of a circular blue and red stimulus with a 0.035 m diameter (stimulus size of 1.3° observed at 1.5 m) and surrounded by a black background were projected on a white board using an 8-bit projector (EPSON VS335W 3LCD WXGA). The separation between the centres of the circles was 0.23 m. In order to maximize the luminance (and brightness) of the stimuli and minimize the luminance of the black background, a black paperboard in which two circles were cut was pasted over the white paperboard; the projected scene image was optimized such that the black background pixels overlapped with the black paperboard and the stimuli pixels overlapped with the circles and hit the white paperboard (Fig. 1).
Fig. 1. (a) The observers were seated in front of a board where the matching scenes were projected at such a distance (1.5 m) that the size of each visual stimulus was 1.3°. (b) Example of a scaled scene presented to observers for the experiment of brightness matching.
The stimuli correspond to the red and blue primaries of the projector and were generated through a script written in MATLAB, specifically using the package of functions called Psychtoolbox-3 [38]. For the blue stimuli, the effect of age is expected to be high, while for the red stimuli only slight age effects are expected.
The spectral radiance of all stimuli were measured using a spectroradiometer (SpectraScan PR-715). The luminance L and the CIE 1976 u’v’ chromaticity coordinates were calculated from these measurements. The luminance uniformity of both stimuli was evaluated by making five spot measurements at different locations (centre and near the edge) within each circle and at three different luminance levels (L = 8.0, 24.2 and 60.3 cd/m2 for the red stimulus; L = 5.5, 11.6 and 25.7 cd/m2 for the blue stimulus) The luminance of both stimuli were found to be constant over the stimulus area with a maximum deviation of 1.9% around the mean.
Five luminance values have been selected for both blue and red reference stimuli (fixed luminance) to be matched with the other stimulus. In selecting these reference stimuli, the following constraints have been taken into account:
- 1. Photopic conditions were targeted. For this reason, the luminance of the reference stimuli in the experiment were selected to be above 5 cd/m2; a stimulus size lower than 2° (1.3°) was used for all stimuli.
- 2. The reference values for both stimuli should be selected in such a way that within the ranges of the projector, a brightness match could be reached for as many reference stimuli as possible, both for young and old observers.
- 3. The step in brightness per digital value should be almost equal for each experiment, no matter which colour has been chosen as the reference stimulus.
Fig. 2. (a) Luminance values produced by the 8-bit projector used in the experiment regarding the digital values from 30 to 255 for the blue and red primary colours of the projector; (b) Brightness values calculated using the CAM18sl brightness model for the digital values of the projector. In both plots, the selected reference values are indicated by stars.
The projector reaches luminance saturation at the digital value of 200 and 210 for the red colour and the blue colour, respectively. Below saturation, these curves represent the gamma curve for the given colour and their luminance values take into account the white balancing. Assuming CAM18sl to be valid, the model is used to allow for more or less equal steps in brightness. This is evidenced in Fig. 2(b) where the corresponding CAM18sl brightness values have been calculated. The CAM18sl brightness values of the red and blue stimuli change more or less linearly with digital value and the brightness values for the red and blue stimuli are very similar between the digital values of 50 and 150. As such, the constraints mentioned above could be fulfilled and digital values of 50, 75, 100, 125 and 150 have been selected.
The spectral radiance and chromaticity values of the 10 reference values are shown in Fig. 3. The luminance and chromaticity values are summarized in Table 1. The peak wavelength of the two stimuli involved in the matching experiment are centred around 450 nm and 600 nm, respectively. Note that the chromaticity values of the stimuli do change quite appreciably with stimulus intensity, but this does not compromise the goal of this investigation.
Fig. 3. Spectral radiance of the reference stimuli (a) blue and (b) red and their corresponding location in the CIE 1976 u’v’ chromaticity diagram.
Table 1. Luminance and CIE 1976 u’v’ chromaticity coordinates for the reference stimuli
The side-by-side method of brightness adjustment has been applied [39–42] because the method is easy to apply, especially for older observers. Side-by-side visual matching tasks can lead to three potential biases: a positional bias, a bias associated with the application of dimming, and a bias with the direction of dimming. All these biases can be counter-balanced (see below). Nevertheless, eye movements across the sharp edges between the coloured stimuli and dark surrounds might create strong transient responses.
3.2 Experimental procedure
The experiment was conducted in a darkened room. Observers were allowed to move their head and their eyes; the pupil size was not controlled. The observer was seated in front of the board at a distance of 1.5 m in order to have a stimulus size of 1.3° and was allowed to use binocular vision. The task can be described as follows: from a script written in MATLAB, the experimenter sets randomly one of the stimuli to a reference luminance and the observer is asked to adjust the other stimulus (using the ‘up’ or ‘down’ button of the controller) until the observer judges them to have the same brightness. At this condition, the setting is recorded. Then, the observer presses the ‘next’ button to move on to the following brightness matching scene.
In order to get reliable data from the experiment, it is necessary to avoid any source of bias which could occur in a side-by-side brightness matching task [39]. For this reason, each presented scene was counterbalanced: the red and blue stimuli were located in both positions (left-right), the luminance of the starting point of the adjustable stimulus was sometimes lower and sometimes higher than the reference stimulus and the dimming control was used for both the red and the blue stimuli. All these considerations implied 40 trials for each observer (10 reference stimuli, both left and right and using a low and high starting point).
In addition to these trials, 10 of the 40 scenes were presented twice to the observers with the intention to evaluate the intra-observer variability. Another 10 scenes were presented to evaluate the null condition of the experiment: scenes where the observers had to match the same colour, i.e., red-red and blue-blue, five trails each. These 60 scenes have been shown to each observer and all were mixed and randomly presented. There was no time limit to perform the matching task but, on average the observers completed the experiment in approximately 25 minutes. At the beginning of the experiment, 10 additional scenes were presented as training and could include some null condition scenes as well. The training stimuli were also randomly generated and the observers were not aware that the first matchings were discarded in the final result. The training session took about 5 minutes and ensured that the observers were adapted to the experimental conditions.
It is necessary to clarify that when the red stimulus at the highest luminance was the reference (L = 60.75 cd/m2), in 46% of the trials, the older observers required a blue luminance value higher than the capacity of the projector to match the brightness of this red reference stimulus. The unability to reach a match was raised verbally by the observers and the result for this reference value was discarded for both age groups.
3.3 Observers
Prior to the experiment, each observer's colour vision was tested using the Farnsworth-Munsell 100 test and they had to answer a visual health questionnaire in which they were consulted about possible diseases and antecedents that could call into question some characteristics of their visual capacity. Specifically, they were asked if they had cataracts, glaucoma, diabetes, diabetic retinopathy and macular degeneration. All observers were judged to be colour normal. One of the older adults reported having cataracts in the right eye so this participant was not considered for the experiment. Written consent was obtained from each participant prior to the study. All experiments are in accordance with the principles expressed in the Declaration of Helsinki.
Two groups of observers were selected: the first composed of 7 young people (3 women, 4 men) aged between 22 and 28 years (average 25 years); and the second composed of 5 older adults (3 women, 2 men) aged between 66 and 72 years (average 70 years).
For each participant, the intra- and inter-observer variability was evaluated to determine the variance in the responses of the observers. Intra-observer variability characterizes the ability of a single observer to repeat the same match; this was evaluated using the data from the ten repeated matches made by each observer. Inter-observer variability characterizes differences in matches made by different observers; this was evaluated from the variations between the results of an individual observer and the mean value of all observers in each age group.
4. Results
4.1 Data variability
The variability of observers was evaluated with the calculation of the standardized residual sum of squares (STRESS) coefficient [43], as shown in Eq. (13):
where N indicates the number of pairs xi and yi with differences. This coefficient helps to analyse the agreement between two sets of data and can take values between 0 and 100%. If the agreement is perfect, the STRESS will be zero.
xi represents the brightness matched made by the observer averaged over the stimulus i. For the intra-observer variability, yi represents the results of the same scene which was shown twice to the observer. For the inter-observer variability, yi represents the response of the average observer for the stimulus i. The “average observer” result was the arithmetic mean of the results of the individual observers.
Likewise, STRESS values were calculated to check left-right bias and high-low bias for the starting luminance with xi and yi representing the results of stimulus i matched by the individual observer at the left and right side or for low and high stimulus starting point, respectively.
STRESS coefficient allows statistical inferences using F-tests [43]. The mean STRESS values for the intra-observer assessment, averaged over each observer group, were 16% and 22% for the young and older adults, respectively and no significant difference between the two age groups (F4,6 = 1.96, p = 0.22) was found. As for the inter-observer assessment, the mean values of the STRESS coefficient were 17% for the young people and 22% for the older adults (no significant difference, F4,6 = 1.72, p = 0.26). In general terms, these results are very similar to those mentioned in other studies evaluating brightness matching experiments [9–11,44].
Regarding the left-right position, the mean STRESS coefficient for the young observers was 18%, while for older observers the average coefficient was 21%. Again, no significant difference between the two age groups (F4,6 = 1.41, p = 0.33) was found. As for the starting point of the adjustable stimulus (high-low starting point), the mean STRESS coefficient for the young people was 19% and 26% for the older adults (no significant difference, F4,6 = 1.97, p = 0.22).
Finally, the variability of the observers while matching the brightness of two stimuli with the same colour (null condition variability) was calculated. The results show that the mean STRESS values for the null condition was 10% for the young observers and 11% for the older adults and no significant difference between the two age groups (F4,6 = 1.96, p = 0.35) was found.
All these results show that the variability in both groups is rather similar.
For each fixed reference stimulus, at least four brightness matches were made: two for the right/left positions, two for the high/low starting point of the adjustable stimulus and, in some cases, a repeated scene. These brightness matches were averaged for each observer and then, averaged over all the young and all the older observers respectively.
Previous to this work, a pilot experiment was performed with two circular coloured stimuli (red and blue) with a stimuli size of 2° on a black background but presented on a wide gamut LCD monitor in a darkened room. The experimental procedure was exactly the same as the one described in this work, but the luminance range of the blue stimulus was limited to 12 cd/m2. The observer variability and the results of that experiment were very similar to the results obtained in the main experiment as reported in this paper.
4.2 Results in terms of luminance
Figure 4(a) shows the results of the brightness matching experiment expressed in terms of luminance. The mean data points are grouped by observer age (colour-coded) and the choice of the reference colour (shape-coded). The main diagonal, highlighted with a thin dashed line, represents perfect luminance matching between stimuli. For the young observers, the luminance for the red stimulus is always higher than the luminance of the blue stimuli to achieve a brightness match. This is in line with earlier observations indicating that a saturated blue light will be perceived brighter than a saturated red light with the same luminance [45]. For the older observers, interestingly, the results fall rather close to the 45° dashed line which indicates that a brightness match is almost identical to a luminance match. The choice of the reference colour seems not to play an important role. Note that both colours are quite saturated, and the H-K effect is ‘active’ for both colours.
Fig. 4. Results of the brightness matching carried out by the young (green) and the older (black) observers in terms of luminance. The thin dashed line represents perfect luminance match. (a) Reference stimuli type is codified through shapes: circles for blue and triangles for red reference stimuli. Each error bar represents one standard error above and one standard error below the mean. (b) The lines are fitted to the data points grouped by age; the data corresponding to both references are pooled. The grey shade area represents the 95% confidence interval. See Data File 1 for underlying values [46].
To quantify and examine the differences across the observer’s groups, linear regression models to the data were fitted (Fig. 4(b)). The lines were fitted to the data points grouped by age; the mean data corresponding to both references are pooled. The model fit was a linear model on a grouped data with interactions. The model fit output shows that the intercept does not differ significantly from 0 (t = 0.025; p = 0.98), which is expected. The slopes of the lines for each group are 0.86 (older observers, R2 = 0.84) and 0.42 (young observers, R2 = 0.96), which is equivalent to say that the young observers need only about half of the luminance of the blue stimuli required by older observers to match the red stimulus.
4.3 Results in terms of brightness using the CAM18sl model
Figure 5 shows the means of the CAM18sl brightness values of the matches as calculated from the spectral radiance of the stimuli. A significant difference in the perception of brightness between the two age groups is observed. For the young observers, the brightness values of the matching stimuli almost fall on the 45° dashed line which means that the CAM18sl model predicts fairly well the brightness matching of young observers. The root-mean-square errors (RMSEs) between the reference values and their corresponding brightness matching values are 0.05 for blue as reference, 0.09 for red as reference and 0.07 for the pooled data. CAM18sl seems to take into account the impact of luminance and the H-K effect properly. These results do support the validity of CAM15u and CAM18sl, at least when dark backgrounds are involved.
Fig. 5. Results of the brightness matching carried out by the observers in terms of brightness using the CAM18sl model for young (green) and older (black) observers. (a) Reference stimuli type is codified through shapes: circles (blue) and triangles (red). Each error bar represents one standard error above and one standard error below the mean. (b) The lines are fitted to the data points grouped by age; the data corresponding to both references are pooled. The grey shade area represents the 95% confidence interval. See Data File 2 for underlying values [47].
However, for older observers, CAM18sl does not perform as well. The RMSE values are 0.39 for blue as reference, 0.48 for red as reference and 0.43 for all values, which is considerable larger than for younger observers. For matching stimuli, CAM18sl systematically predicts a brightness for the blue stimuli which seems to be too high.
Again, linear regression models were fitted to the data grouped by age but without considering the choice of reference (Fig. 5(b)). The model fit was again a linear model on a grouped data with interactions. In this case, the slopes of the lines for each group are 1.2 (older observers, R2 = 0.84) and 0.99 (young observers, R2 = 0.99) respectively while the intercepts are different.
In summary, the results presented in Fig. 4 and Fig. 5 point to the fact that older adults require the radiance of the blue stimuli to be higher than for the young observers in order to achieve a match with a red stimulus; older observers indeed seem to have a lower perception of brightness for blue light compared to young people.
5. Adapting CAM18sl
The results of the experiments have shown that CAM18sl predicted quite good the brightness matching of the stimuli for the young observers (Fig. 5). This result was expected since CAM18sl was developed with observers of 26 years old on average. For the older observers, CAM18sl does not perform very well: a reduced brightness perception in the blue wavelength range is obvious from the experimental data.
CAM18sl makes use of the cone fundamentals (Eqs. 1–3), which include three physiological processes [17]: (1) the transmittance of the lens and other ocular media; (2) the transmittance of the macular pigment and (3) the absorptance in the photo pigments of the cones. The transmittance of the macular pigment and the absorbance of the pigments are modelled as a function of wavelength with the field size as a model parameter. It is assumed that both factors do not depend on age. On the contrary, the transmittance (or optical density) of the lens and other ocular media is modelled as a function of wavelength with the age of the observer as a parameter. The spectral transmittance of the lens and other ocular media with reference to CIE 2006 is shown in Fig. 6. The spectral transmittance is not uniform regarding the wavelength along the visible spectrum; the eye lens shows a higher absorption in the short-wavelength region while at longer wavelengths the absorption is very low. Furthermore, the spectral transmittance drops with age but the effect is much higher for the short wavelengths; in the wavelength range 380 nm to 550 nm a reduction of more than 40% has been reported; in the range 550 nm to 780 nm the reduction is less than 6%. Note that the maximum transmittance reaches 100%, pointing to a normalization of the physical data.
Fig. 6. Variation of spectral transmittance of the human eye with wavelength and age (based on CIE 170-1:2006 [17]).
In order to adapt the CAM18sl model for the vision of adults of 70 years old, it seems logic to substitute the 2° CIE 2006 cone fundamentals for young observers as used in Eqs. 1–3, with the cone fundamentals for a 2° field of view and a 70 years old observer (${\bar{l}_{70yr}},\; {\bar{m}_{70yr}},\; {\bar{s}_{70yr}}$). The same values for k are used (${k_\rho } = 626.8,\; {k_\gamma } = 768.3,\; {k_\beta } = 1252.9$) but this issue will be discussed in more detail below. The impact of this change on the brightness results for the older observers is shown in Fig. 7.
Fig. 7. Brightness matching results of the older observers based on two approaches: using 2006 LMS cone fundamentals for a 25 years old person (as in Fig. 5, in black) and using 2006 LMS cone fundamentals for a 70 years old person (in purple).
There is no improvement and even the RMSE increases from 0.43 to 0.45 (red and blue reference pooled data). The cone fundamentals for a 25 years old and a 70 years old observer are shown in Fig. 8. As the transmittance of the ocular media as shown in Fig. 6 is included in the calculation of the cone fundamentals, one would expect an important decrease of the short wavelength cone fundamental values for older observers compared to young observers. However, cone fundamentals are always normalized towards a maximum value of 1, irrespective of the age or the field of view. This normalization is counterbalancing the reduced transmittance in the blue wavelength range for older observers; consequently, the impact of age on the cone fundamentals is only expressed as a small spectral shift towards larger wavelengths (as indicated in Fig. 8). However, when absolute correlates such as brightness is involved, normalization of cone fundamentals might not be the best approach.
Fig. 8. 2° cone fundamentals for ages 25 years and 70 years calculated with LuxPy [37] based on CIE 171-1:2006 [17].
One option could be to keep the variation of the transmittance of the ocular media with age out of the normalization of the cone fundamentals. To this extend, the calculation of cone excitations for older observers is calculated as follows:
Fig. 9. Spectral transmittance of the ocular media for a 70 years old person relative to a 25 years old person as applied in Eqs. 14–16. This curve has been calculated according to CIE 170-1:2006 which is based in the model of Pokorny et.al. [28].
At this stage, one also needs to reconsider the determination of the k-constants (${k_\rho },{k_\gamma },{k_\beta }$) as described in clause 2. EEW is known to be approximately perceived as ‘neutral’ for young observers [11,48]. As a consequence, the red-green and yellow-blue colour difference channels defined in Eqs. (9) and 10 should become zero, which is achieved when the cone excitations are equal to each other for EEW. The additional constraint to make the cone excitations equal to the luminance is less stringent and determines only the absolute magnitude.
In calculating the k-values occurring in Eqs. 14–16, there are 2 options. Either the cone excitations for EEW are renormalized, expressing that EEW is still perceived ‘neutral’ for older people, or the normalization for young observers is retained (${k_\rho } = 626.8$, ${k_\gamma } = 768.3$ and ${k_\beta } = 1252.9$), resulting in a non-neutral perception of EEW for older people. Applying option 1 will however again counterbalance the reduced short wavelength cone response, in a similar way as has been the case when renormalizing the cone fundamentals to a maximum of 1. As it was mentioned before, this approach cannot explain the experimental results. For this reason, option 2 in which the k-values will be kept identical to the values for a 25 years old observer is chosen. As a consequence, CAM18sl will result in a non-neutral perception of EEW for older observers.
The result of applying CAM18sl in the way described above is illustrated in Fig. 10. The result seems to be much more consistent with the experimental data and the brightness matching results for the older observers fall very close to the dashed line representing equal brightness (RMSE of 0.15, red and blue reference pooled data). The slope of the line fitted for the older observer’s data is 1.03 (R2 = 0.85). This result confirms that the brightness prediction of CAM18sl performs much better for older observers if renormalization of cone fundamentals and of cone excitations is omitted.
Fig. 10. (a) Results of the brightness matching experiment for the older observers (in black) after the CAM18sl model has been affected by the eye’s spectral transmittance for 70 years old age (Eqs. 14–16). The results for young observers are shown in green (as in Fig. 5). (b) The lines are fitted to the data points grouped by age; the data corresponding to both references are pooled. The linear models fitted to the data show that both lines for the age groups of observers fall very close to the main diagonal (thin dashed line) that represents perfect brightness matching between stimuli.
6. Discussion
As stated before, omission of renormalization for older observers induces shifts in the CAM18sl colourfulness. For an EEW stimulus of a luminance of 100 cd/m2, the colourfulness is calculated to be 88 instead of zero; for comparison, the colourfulness of the saturated blue and the red stimuli of the same luminance are calculated to be 218 and 259, respectively. This suggests that older observers would not observe EEW as neutral white any more, which is in contradiction with other publications reporting no significant change in the perception of the white point as a function of age [29,33,49]. CAM18sl, as applied in this paper, might offer a solution for brightness, but not for colourfulness. Indeed, according to [29], the changes in cone sensitivity might be compensated by post-receptoral and cortical adaptation processes, which are not included in CAM18sl. These cortical adaptive processes will affect the CAM18sl calculation steps, in particular Eqs. 9 and 10. However, implementing these processes into CAM18sl calls for a new set of experiments and corresponding data analysis. It might also be possible that the absence of any neutral stimulus in the experimental scenes considered in this paper (unrelated saturated colours) might hamper these post-receptor adaptation processes.
Although not included explicitly in colour appearance models, it might be interesting to consider the impact of pupil size. It is known that the pupil response is wavelength dependent, being larger for blue stimuli than for red stimuli [50]. Pupil size is also known to decrease as a function of age [51–56]. For these reasons, effects of pupil size should be integrated in the next generation of colour appearance models.
In 2012, the CIE Technical Committee 6–15 compiled spectral data from the literature regarding human eye transmission and absorption, published in the report ‘A Computerized Approach to Transmission and Absorption Characteristics of the Human Eye’ in which an equation to calculate the spectral non-normalized total optical density (and total transmittance) of the human eye as a function of age and wavelength is proposed [26], based on earlier work from van de Kraats and van Norren [57]. Figure 11 shows the spectral transmittance curves for different ages calculated based on CIE 203:2012.
Fig. 11. Variation of spectral transmittance of the human eye with wavelength and age (based on CIE 203:2012) [26].
In Fig. 12, the transmittance ratio as used in Eqs. 14–16 based on CIE 2006 is compared to the ratio based on the total transmittance values from CIE 2012.
Fig. 12. Eye’s spectral transmittances for a 70 years old relative to a 25 years old observer, based on CIE 170-1:2006 and CIE 203:2012.
The curves are very similar and using a transmittance ratio based on the CIE 2012 data lead to only minor differences in CAM18sl brightness. Note that the ratio converges to 1.0 for CIE 2006 but to 0.97 for CIE 2012. This difference is not irrelevant, as it determines the numerical values of the cone excitations once the k-factors are fixed for a young observer. Also in absolute terms, both transmittance data are quite different: while the CIE 2006 transmittance data all converge to a 100% transmittance from 660 nm onwards (Fig. 6), the CIE 2012 data don’t (Fig. 11). Note that the spectral transmittance values in CIE 2012 do include the transmittance of the cornea, aqueous and vitreous humours, explicitly. The international community would certainly benefit from the availability of one unique and widely accepted data set. However, the low difference found in the performance of the brightness model when using each of the data sets does not allow any judgement or recommendation.
7. Conclusions
This paper reports on an experimental study aiming to evaluate how the brightness perception of red and blue stimuli is affected by the age of the observer.
The results show a significant difference in brightness perception between the age groups. They were evaluated directly in terms of the brightness correlate as predicted by the colour appearance model CAM18sl for self-luminous stimuli and applied for a zero luminance background. CAM18sl, developed with young observers, uses the absolute spectral radiance of the stimulus as input, which is weighted by the physiological based cone fundamentals to calculate cone excitations. The results show that CAM18sl adequately predicts the brightness perception of young observers, which confirm the validity of the model. It is interesting to mention that, despite developed for self-luminous stimuli, the model seems also to perform well for stimuli originating from reflection on a white screen.
However, CAM18sl could not explain the older observers’ brightness matching results. In comparison with the young observers, older observers needed a significant higher level of intensity from the blue stimuli in order to match the red stimuli. This means that old observers perceived the blue stimuli as less bright than the young observers. This difference in brightness perception could be most probably attributed to the well-known changes in lens transmittance with ageing.
Two approaches were followed with the objective to update the CAM18sl model (for unrelated stimuli) to be valid for all age groups. As the CAM18sl model is based on cone fundamentals which include the transmittance of the ocular media and consider the age of the observer as an input parameter, an obvious step is to substitute the original cone fundamentals by the cone fundamentals for 70 years old observer. However, as the change in cone fundamentals only shows to be a slight shift in wavelength due to the inherent normalization procedure, the results for older adults did not improve. A second approach, in which the transmittance of the ocular media is isolated from the cone fundamentals for both young and old observers and avoiding any renormalization, was more successful: the updated CAM18sl performed very well and could predict the brightness experiments for both young and old observers. This shows that the recent models using absolute spectral radiance and cone fundamentals can offer a solid framework to incorporate age-dependent effects on brightness.
When absolute correlates such as brightness are involved, normalization of cone fundamentals might not be the best approach. However, omitting the renormalization has another consequence: according to CAM18sl, the colourfulness of EEW, set to zero for young observers, will not be zero for older observers anymore. This suggests that the older observers would experience a shift in the neutral white point, which seems not to be in line with literature. This contradiction might be explained by considering post-receptoral and cortical adaptation processes, which are however not included in CAM18sl. This needs to be investigated further.
Funding
KU Leuven (Contract 000000129288); Universidad Nacional de Tucumán (PIUNT E627); Consejo Nacional de Investigaciones Científicas y Técnicas (ILAV P-UE 0114).
Acknowledgments
O. Preciado thanks to the Coimbra Group of Universities and KU Leuven for the support through the Scholarship Programme for Young Professors and Researchers from Latin American Universities. K. Smet wants to thank Internal Funds KU Leuven.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are available in Data File 1 and Data File 2, Ref. [46,47].
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