1. INTRODUCTION

The development of light-emitting diode (LED) technology has enabled easy and inexpensive ways to create dynamic colored light. As a result, dynamic colored light is nowadays used in several applications, for instance, to enhance the alertness of office workers [1], to create appealing light atmospheres [2–5], and to enhance the immersive experience of displays, such as in the Philips Ambilight TV [6]. In most of these applications, the light has to fulfill (at least) the following two requirements in order to be attractive to observers: the light should change smoothly over time, in luminance and/or chromaticity, and the light should change at the desired rate of change (or speed) [4,7,8]. Several studies have investigated how people perceive smoothness of dynamic light generated with limited temporal resolution [7], subtlety of dynamic light [4], and its attractiveness [2]. However, it is not known yet how to describe the perceived rate of a temporal change in color. For instance, if we want to generate a temporal light transition with a constant perceived rate of change, we need to know what is perceived as an equal amount of change in color per time unit.

Color science has long focused on perceptual differences between colors in the spatial domain, leading to metrics such as CIEDE94 and CIEDE2000 that describe the magnitude of a color difference for spatially separated colors. These metrics are formulated in the perceptually uniform CIELAB color space. Although the uniformity of the CIELAB color space is not perfect (since it depends, among other things, on hue [9]), this color space is considered useful for describing how to make smooth spatial color gradients. Since there is currently no validated model for temporal color perception available, it is most reasonable to use CIELAB to describe temporal color changes as well, and to express the speed of a color transition in terms of $\mathrm{\Delta }{E}_{ab}^{*}/s$. This was done for the first time in 2007 by Sekulovski et al. [7], who measured the maximum color difference between successive colors at which a temporal color transition was still perceived as smooth. When the smoothness threshold was expressed in terms of $\mathrm{\Delta }{E}_{ab}^{*}/s$, a linear relationship was found with the temporal frequency. However, the smoothness threshold was a factor of 10 lower for temporal changes in lightness compared to changes in hue and chroma. This means that the CIELAB color space is quite non-uniform for describing temporal color differences. Therefore, the question remains how to describe the speed of a temporal color transition in a perceptually uniform way.

Existing literature on speed perception cannot be used to answer this question since it manipulates other (for the purpose of our study irrelevant) stimulus characteristics. For example, a few studies have measured the sensitivity to changing luminance for achromatic Ganzfeld stimuli (e.g., [10]). Here, log luminance per min was used as a metric for describing the temporal change in luminance. However, in this study, we are interested in the sensitivity to changing chromaticity. In addition, a large amount of literature exists on motion perception for spatiotemporal stimuli, for which speed can be expressed as degrees per second (where “degrees” refer to the spatial distance in terms of visual angle). However, we want to know the perceived speed of a light transition for a (ideally) homogeneous light stimulus. Since the spatial structure of the stimulus is constant, there is no change in visual angle.

Our long-term goal is to develop a universal metric for describing the perceived rate of a temporal color change. In this paper, we aim to present new data on speed perception using temporal stimuli defined in CIELAB and evaluate how well existing color models, both CIELAB and cone spaces including LMS and Derrington, Krauskopf, and Lennie (DKL) [11] describe the results. Therefore, we conducted a psychophysical experiment in which we measured the perceived speed of temporal linear color transitions in chroma and hue at constant lightness in the CIELAB color space. In order to quantify the perceived magnitude of the speed, several stimuli (with different speeds) were compared to a reference stimulus (with a fixed speed), and the point of subjective equality (PSE) in speed was determined. As expected, none of the models just mentioned were suitable for predicting perceived rate of color change. We propose a straightforward adjustment to these models and evaluate which model is the most promising for further improvement and validation.

2. METHODS

The experiment was designed to find the PSE of speed between different color transitions. To do so, a two-interval forced-choice task was used. More particularly, participants were instructed to compare the perceived speed of two temporal color transitions (i.e., a reference stimulus and a comparison stimulus). The transitions varied either in CIELAB chroma or hue direction around a base color point. Five base color points were used, corresponding to the principal Munsell hues 5R (red), 5Y (yellow), 5G (green), 5B (blue), and 5P (purple) [12]. We limited ourselves to two types of stimulus pairs: (1) one stimulus was modulated in the chroma direction and the other stimulus in the hue direction around the same base color point, referred to as $CH$-comparison; (2) the two stimuli were both modulated in the hue direction around two different base color points, referred to as $HH$-comparison. A third possible type of comparison, namely $CC$-comparison (i.e., two stimuli both modulated in the chroma direction around two different base color points), were omitted in this experimental design to limit the experimental time for the subjects, and because higher-amplitude $CC$ stimuli would have resulted in out-of-gamut colors in some conditions. The method of constant stimuli was used to find the PSE of speed with respect to the reference stimulus by fitting a psychometric function through the percentages “the comparison stimulus is faster than the reference stimulus”, averaged over the participants. The experiment used a full-factorial within-subject design with 26 participants.

A. Experimental Setup

The experiment was conducted in a laboratory (see Fig. 1) that is designed to study dynamic color perception and adaptation, dubbed the Dynamic Visual Adaptation (DVA) Lab of the Munsell Color Science Lab of Rochester Institute of Technology. The DVA Lab is a $3.66\mathrm{m}\times 4.27\mathrm{m}\times 2.44\mathrm{m}$ ($\text{length}\times \text{depth}\times \text{height}$) room with a variegated gray carpet and four white walls without a window. All the walls are painted with a matte white paint having an average reflectance of 93%, and the floor has an average reflectance of 7%. One of the long walls consists of three sliding wooden panels 2.4 m wide, which can be opened. The room is equipped with a five-primary (red, green, blue, mint green, white: RGBMW) LED lighting system that can be addressed at 40 Hz to create smooth temporal changes. The lighting system consists of 14 Philips SkyRibbon wall-washing fixtures that are mounted in the ceiling to illuminate the lab’s walls, resulting in a smoothly non-uniform illumination pattern. The uniformity was assessed via spectral measurements at positions spaced 30 cm apart, noted by red dots in Fig. 1; the larger red dot is the location of the brightest region of the wall, where the spectral characterization data used to model the lighting system were measured. Vertically, the point above and the two points below the reference were all above 70% of the reference luminance, and the top and bottom points were 38% and 40% of the reference. Horizontally, the central nine points (the middle 2.8 m of the wall) all measured above 86% of the reference luminance, and the outermost points reached 38%. Chromaticity uniformity is described in Section 2.F below, after the color stimuli are explained. More information about the lab is described elsewhere [13]. We intentionally chose a full room setting instead of the often used 2° or 10° stimuli, since dynamics in general lighting are more realistically represented with a larger field of view; similarly, we allowed participants to look freely around the illuminated wall.

 

Fig. 1. Photograph of the DVA Lab with a neutral white 4000 K light setting. The red dots added to the photo indicate the positions on the wall that were measured; the larger dot shows the location of the characterization measurements.

Download Full Size | PDF

B. Stimuli

The stimuli were periodic temporal color transitions around a base color point in the chroma or hue direction of the CIELAB LCh color space [see Fig. 2(a)]. The color changed every $\mathrm{\Delta }\mathrm{t}$ seconds with a step size $\mathrm{S}$ over a full period of 3 s, which was found in pilot experiments to be both long enough to be visibly changing and short enough to allow many stimulus presentations in a manageable experiment length. The color transition was shown as five full periods of a triangular wave to allow for easier judgements on the speed of the transition. The sharp edges of the triangular wave were smoothed, as indicated by the regions ${\mathrm{R}}^{*}$ in Fig. 2(b). This was done in order to avoid abrupt changes that might influence the perception of speed, as suggested in [7].

 

Fig. 2. (a) Chroma and hue directions in the Ch plane of CIELAB LCh color space. (b) Temporal color transition as a function of time with a speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ or 40 $\mathrm{\Delta }{E}_{ab}^{*}/s$. The regions marked $\mathrm{R}$ have a fixed step size, and hence a fixed speed. The region marked ${\mathrm{R}}^{*}$ is adapted to smooth the abrupt change in color.

Download Full Size | PDF

Each cycle had a fixed number of discrete steps ($\mathrm{N}=120$), and each step was shown for a fixed period $\mathrm{\Delta }\mathrm{t}=0.025$ seconds. Thus, the stimulus lasted for 15 (i.e., $5\times 120\times 0.025$) seconds. 10% (i.e., $\mathrm{p}=0.1$) of this stimulus duration was used for smoothing the abrupt color change. Hence, the stimulus consisted of $\mathrm{N}\times (1-\mathrm{p})$ number of steps with a fixed step size $\mathrm{S}$ and $\mathrm{N}\times \mathrm{p}$ steps with variable step size ${\mathrm{S}}^{*}=\frac{\mathrm{S}}{2^{\mathrm{i}}}(1\le \mathrm{i}\le \mathrm{N}\times \mathrm{p})$. The color transition speed (CTS) is defined as the speed of the linear part of the transition and is calculated as

Each color transition varied around the base color point at a constant speed in either the chroma or hue direction. Five color transition speeds were used: 2.5, 5, 10, 20, and 40 $\mathrm{\Delta }{E}_{ab}^{*}/s$. Since the transitions were described in the CIELAB LCh color space, first the corresponding speeds in terms of chroma and hue were calculated, using

All the stimuli were within the gamut of the system. During the experiment, all the walls were illuminated; however, the seated participants were asked to look at the wall in front of them.

C. Experimental Conditions

In each trial, two color transitions were shown sequentially, in random presentation order: a reference stimulus and a comparison stimulus. In $CH$-comparisons, the reference stimulus was modulated in the hue direction around one of the five base color points at a speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$, whereas the comparison stimulus varied around the same base color point in the chroma direction at one of the five speeds. Hence, there were 25 (i.e., $5\text{hue}\times 5\text{speed}$) $CH$-comparisons. In $HH$-comparisons, both stimuli were modulated in the hue direction. The reference stimulus varied around a hue of 5R (i.e., $h=27°$) at a speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$, and the comparison stimulus varied around one of the five base color points at one of the five speeds. This means that there were also 25 (i.e., $5\text{hue}\times 5\text{speed}$) $HH$-comparisons.

D. Participants

Twenty-six adults (15 males and 11 females) volunteered to participate in the experiment. Their age ranged from 21 to 53 years ($\text{mean}=32.4$, standard $\text{deviation}=10.5$). All participants had normal color vision, as measured with the Ishihara test for color deficiency. Fourteen of them were wearing glasses, and six were wearing contact lenses. Most participants had more-than-average knowledge about color, while three of them had advanced knowledge about color. Ten participants did not have any experience with lighting experiments, while the others had different levels of experience.

E. Procedure

The experiment was approved by the Institutional Review Board at RIT, the Human Subject Research Office. Before the start of the experiment, participants were asked to read and sign an informed consent form, in which they confirmed their voluntary participation.

When participants entered the experimental room, the light was set to a static white light with a correlated color temperature of 4000 K and a wall luminance of $200\mathrm{cd}/{\mathrm{m}}^2$. Participants were instructed to sit on a chair that was positioned at a distance of 1.5 m from the wall in front of them. The average eyesight level was about 1.5 m above the floor. No chin or forehead rest was used since we intended to have a more natural viewing setting. Then the experimenter read the instruction script that consisted of the following parts: welcome words, explanation of the necessity to do an Ishihara test, collection of demographic information, explanation of the stimuli and task, illustration of the voice instructions, and a practice session. The participants were instructed that they were free to make head and eye movements, as long as they looked at the wall in front of them. During the practice session, each observer was asked to compare (1) the speeds of a hue change with 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ at 5R and a chroma change with 40 $\mathrm{\Delta }{E}_{ab}^{*}/s$ at 5R, and (2) the speeds of a hue change with 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ at 5R and a hue change with 2.5 $\mathrm{\Delta }{E}_{ab}^{*}/s$ at 5G. Each comparison was repeated twice. Six computer-generated voice instructions were used: $\mathbf{V}\mathbf{1}$, “First stimulus”; $\mathbf{V}\mathbf{2}$, “Second stimulus”; $\mathbf{V}\mathbf{3}$, “Which stimulus appears faster?”; $\mathbf{V}\mathbf{4}$, “Input recorded”; $\mathbf{V}\mathbf{5}$, “Invalid input, please input again”; $\mathbf{V}\mathbf{6}$, “Congratulations! You finished the experiment, thank you for your participation”.

The flow of presenting the stimulus pairs is shown in Fig. 3, and consisted of voice-cued sequential stimuli interspersed with neutral 4000 K lighting that was shown for ten seconds. Research has shown that after ten seconds, chromatic adaptation is approximately 80% complete [15]. This means that participants started from approximately the same adaptation point. Participants were instructed to judge which of the two sequential color transitions appeared to be faster by pressing a button on a keyboard: “1” to indicate the first stimulus appeared faster and “2” to indicate the second stimulus appeared faster. If a participant happened to press a button that was neither “1” nor “2”, the voice instruction $\mathbf{V}\mathbf{5}$ would be played until that participant pressed “1” or “2”. Then $\mathbf{V}\mathbf{4}$ would be played and the program would proceed. Since participants had different levels of knowledge about color, the CIELAB LCh space was briefly explained, and it was pointed out that all the stimuli were only changing in either the chroma or hue direction at a constant luminance level. In addition, we emphasized that all stimuli had the same duration, and that a judgement regarding the speed of the transition could be made based on the slope of the transition. The concept of slope was explained by showing a similar figure to Fig. 2(b). All the stimuli shown during the instruction and practice phase were part of the stimuli of the main experiment. Participants were allowed to ask questions during the instructions and they had the opportunity to repeat the practice session, if needed, before the start of the main experiment. During the practice session and the main experiment, participants wore a baseball cap to prevent them from looking directly into the luminaires mounted in the ceiling.

 

Fig. 3. Illustration of the procedure for presenting one stimulus pair. $\mathbf{V}\mathbf{1}$, $\mathbf{V}\mathbf{2}$, and $\mathbf{V}\mathbf{3}$ are the voice instructions.

Download Full Size | PDF

The main experiment consisted of two sessions. In the first session, participants evaluated all 50 stimulus pairs [i.e., 25 $CH$-comparisons ($5\text{hue}\times 5\text{speed}$) + 25 $HH$-comparisons ($5\text{hue}\times 5\text{speed}$)]. In the second session, only the three intermediate speeds were presented, resulting in 30 comparisons [i.e., 15 $CH$-comparisons ($5\text{hue}\times 3\text{speed}$) + 15 $HH$-comparisons ($5\text{hue}\times 3\text{speed}$)]. As a result, the largest and smallest speeds of the comparison stimulus were presented only once, while the intermediate three speeds were repeated twice per participant. We decided to do this since the lowest and highest speed were visually quite different from the reference speed, and they were basically used (1) to test if participants understood the task by checking whether their responses were close to 100% correct, and (2) to make participants feel more confident about their performance by showing some easier trials. In each session, first all $CH$-comparisons were presented, blocked per base color, and then all $HH$-comparisons were shown. The presentation order of the base colors was based on a balanced Latin square design [16].

The second session was arranged at least half an hour after the first session. For some participants, the sessions took place on different days. All participants watched the demo stimuli and did the practice session again before the start of the second session in order to be sure that they had the same level of understanding. After each session, participants were asked to answer the questions shown in Table 1. They were encouraged to elaborate on their answers, and not simply respond with “yes” or “no”.

Table 1. Questionnaire after Each Session

View Table

F. Verification Measurements

All stimuli were verified (i.e., each step in the temporal color transition was measured) with a Photo Research PR-655 spectroradiometer. The location of the measurement was at 1.7 m above the floor, as indicated by the larger red circle in Fig. 1. Among the 6000 (i.e., $50\times 120$) measured steps, the average deviation from the corresponding intended colors was 2.34 $\mathrm{\Delta }{E}_{ab}^{*}$, with the largest deviation being 4.81 $\mathrm{\Delta }{E}_{ab}^{*}$. From the measurements, the actual transition speeds that were presented to the observers were further calculated, and the results showed that the speeds differed from the intended speeds by 2.17%.

The spatial chromaticity uniformity of the wall was measured at the same spatial locations shown in Fig. 1, and Euclidean $\mathrm{\Delta }{u}^{\prime }{v}^{\prime }$ values from the reference point were computed. Over all five base colors and the neutral white, at all spatial locations (total $6\times 19$ measurements), the median $\mathrm{\Delta }{u}^{\prime }{v}^{\prime }$ from the reference was 0.0010. The maximum difference was 0.0042 for the 5Y base color near the bottom of the wall.

3. RESULTS

A. Calculation of PSEs

First, we checked the reliability of the participant responses. In either $CH$- or $HH$-comparisons, the extreme speeds (i.e., 2.5 and 40 $\mathrm{\Delta }{E}_{ab}^{*}/s$) were visually quite different from the reference speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$. However, in 29 of the 520 cases [i.e., 26 participants × 2 speeds × 2 types of comparisons ($CH$ and $HH$) × 5 hues], participants either reported that the lowest speed was faster than the reference or the highest speed was slower than the reference. In particular, there was one participant with 6 out of 20 likely “incorrect” responses. Therefore, the data of this participant was removed for further analysis.

For each comparison type ($CH$ or $HH$) and base color, the percentage of responses “the comparison stimulus is faster than the reference stimulus” was calculated over all participants and plotted as a function of the speed of the comparison stimulus. This resulted in 10 plots. For $CH$ comparisons the reference was a transition of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction around the same hue as the comparison stimulus. For $HH$ comparisons, the reference was a transition of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction around a (fixed) hue of 5R.

The resulting data were fitted with the psychometric function of Eq. (5), using a generalized linear model (i.e., the glmfit function available from the Statistics Toolbox in MATLAB 2017b):

Figure 4 shows the ten psychometric curves fitted with the data of the 25 participants. In this figure, the speed is plotted on a logarithmic scale to improve the goodness of fit. The output of the logarithmic fit has a root mean square error of 1.68 $\mathrm{\Delta }{E}_{ab}^{*}/s$, compared to the root mean square error of 2.97 $\mathrm{\Delta }{E}_{ab}^{*}/s$ for the linear fit. We used a statistical technique based on Monte Carlo resampling [17] to estimate the variability in the parameters $a$ and $b$ of the psychometric function. To do so, we adopted a non-parametric bootstrap by treating all data points of all participants (for a given condition, i.e., $CH$ or $HH$ comparison and one base color) as if they reflected one underlying distribution. Next, 25 new data points were randomly chosen from this distribution for each of the five speeds and the PSE was calculated. This procedure was repeated 10,000 times, and from these data we calculated the average PSE and its confidence interval as the 2.5th and 97.5th percentile. These data are summarized in Fig. 5.

 

Fig. 4. Proportion of “the comparison stimulus is faster than the reference stimulus” responses against the transition speed of the comparison stimulus for each of the five hues in the $CH$ comparisons (left column) and the $HH$ comparisons (right column). The filled squares represent the raw percentages. The colored area represents the 95% psychometric functions, $m$ with the error bars indicating the bootstrap-based 95% confidence intervals.

Download Full Size | PDF

 

Fig. 5. Bar chart of the 10 PSEs with their 95% CI for (a) $CH$ comparisons and (b) $HH$ comparisons.

Download Full Size | PDF

The straightforward interpretation of the PSE is that, for example, a transition of 18.48 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the chroma direction at 5Y is perceived as fast as a transition of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5Y [Fig. 5(a)]. At the same time, a transition of 6.12 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5Y is perceived as fast as a transition of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5R [Fig. 5(b)]. To describe the data in a more compact way, we use the following notation:

B. Comparison Between 10 PSEs

When the color transitions would be assessed against the same reference stimulus, their PSE could be directly compared. This was, for example the case for the $HH$ comparisons, the PSEs of which could be mutually compared. To relate the PSEs of all color transitions, we expressed them against the same reference stimulus, using the following two assumptions:

Based on these two assumptions, we related the speed of all color transitions to the same reference, being a speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ in the hue direction around 5R. From the notation in Eq. (6), we know that a transition speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5Y was perceived as fast as a transition speed of $(10/6.12)\times 10=16.34\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5R, and as fast as a transition speed of 18.48 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the chroma direction at 5Y. Thus, to compare the transition speed along the chroma direction at 5Y with a transition speed along the hue direction at 5R, we need to divide 18.48 by (10/6.12); as a result, a transition speed of 11.31 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the chroma direction at 5R is assumed to be perceived as fast as a transition speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5R. Similarly, all the PSE values could be related to the same reference stimulus of a transition speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5R, which results in

 

Fig. 6. Length of the arrows in the figure indicates the PSE of the corresponding color transition to make it equally fast as the reference, being a transition speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction around the base color 5R (represented by length “1” in this figure).

Download Full Size | PDF

C. Questionnaire Analysis

The answers to the questions we asked at the end of Session 1 and 2 are summarized in Fig. 7. 65% of the participants indicated that the experiment was difficult (Question 1). They mentioned various reasons, among which the lack of a fixation point to help them focus, and the fact that it was hard to memorize speeds. Only 15% of the participants indicated explicitly that the color change was most visible in their periphery. Some participants (35%) reported that some color transitions were unsmooth at some hue values. All participants except one mentioned that the cap did not influence their judgement; instead, they reported that the cap indeed helped to stop them from looking at the luminaires in the ceiling. Some participants (31%) reported that Session 2 was more difficult because the speed differences were smaller compared to the stimuli in Session 1.

 

Fig. 7. Overview of the answers given to the questions at the end of Sessions 1 and 2.

Download Full Size | PDF

4. COMPARISON WITH AVAILABLE COLOR MODELS

The results presented in Fig. 5 show that color transitions with the same constant speed in CIELAB are not always perceived as having the same speed. This is no surprise, but it confirms that CIELAB cannot be considered a uniform space to describe the perceived speed of color transitions in the chroma and hue directions. An ideal uniform temporal color model should have equal PSE values independent of the base color and modulation direction of the color transition. A possible way of looking at the uniformity of a color model is to check the standard deviation in PSEs, which is zero in the ideal case.

A. Calculation of Slopes in CIELAB

Despite our assumption that CIELAB would not be temporally uniform, we chose constant-$\mathrm{\Delta }{E}_{ab}^{*}/s$ speeds for this experiment as a starting point. Figure 6 already shows how non-uniform CIELAB is for temporal color transitions, and based on these results we made an attempt to improve CIELAB’s uniformity in this respect. This attempt consisted of including a scaling factor in the mutual weighting of $\mathrm{\Delta }{a}^{*}/s$ and $\mathrm{\Delta }{b}^{*}/s$ in the calculation of $\mathrm{\Delta }{E}_{ab}^{*}/s$ as follows:

 

Fig. 8. Illustration of the segments used for calculating the slope of the $a^{*}$ and $b^{*}$ values of the temporal color transition ($L^{*}$ is constant). ${\text{Slope}}_1$ covers the steps 1–30, while ${\text{Slope}}_2$ and ${\text{Slope}}_3$ cover the steps 31–90 and 91–120, respectively. These segments of steps are shown for the change in $a^{*}$ values.

Download Full Size | PDF

Based on these slopes, we computed the standard deviation of the PSEs for different values of the weighting factor $\alpha$. Figure 9 shows that this standard deviation is minimal for a value of $\alpha =0.404$.

 

Fig. 9. Standard deviation of PSEs as a function of $\alpha$ in Eq. (8). The open circle represents the standard deviation of CIELAB, while the filled circle is the minima found when $\alpha =0.404$.

Download Full Size | PDF

B. Calculation of Slopes in LMS Cone Fundamentals

We designed our dynamic transitions as constant-slope $C^{*}$ and $h$ changes, which do not correspond to constant-slope $L$, $M$, and $S$ changes. To calculate the corresponding L, M, and S cone responses, we used the cone fundamentals of Stockman and Sharpe [18] and the measured spectral data. To minimize the effect of measurement noise, the slopes of $\mathrm{\Delta }L/s$, $\mathrm{\Delta }M/s$, and $\mathrm{\Delta }S/s$ were calculated in a similar way as shown by Eq. (9). Since neutral white light of 4000 K was regularly shown before, during, and after the stimuli in the experiment, it was chosen as the adaptation condition; in reality, we expect that observers’ state of adaptation was influenced by the dynamic stimuli, but we don’t have a way to predict this variation. Thus, the $L$, $M$, and $S$ values at each step were normalized by dividing them by the $L$, $M$, and $S$ values of 4000 K, which is equal to multiplying by 3.28, 4.11, and 11.22, respectively. However, this normalization step does not influence the calculation of slopes.

Using the same concept of minimizing the standard deviation of PSEs, a scaled LMS space with parameters $\alpha$ and $\beta$ could be constructed as follows:

 

Fig. 10. Standard deviation of PSEs as a function of α in Eq. (11). The open circle represents the standard deviation of DKL, while the filled circle is the minima found when $\alpha =0.02$.

Download Full Size | PDF

5. DISCUSSION

A. Optimization of Color Spaces

Our results demonstrate that more uniformity can be achieved by improving available color spaces. Specifically, the CIELAB-based improvement suggests that $\mathrm{\Delta }{b}^{*}/s$ contributes less to speed perception than $\mathrm{\Delta }{a}^{*}/s$, but the resulting reduction in the standard deviation of the PSEs is very small. The improved DKL-based space suggests that $\mathrm{\Delta }(S-(L+M)/s$ hardly contributes to speed perception compared to $\mathrm{\Delta }(L-M)/s$. In this way, the standard deviation in PSEs is reduced by almost a factor of 6. It is important to notice that the small weight ($\alpha =0.02$) for the $S-(L+M)$ channel may suggest that the $L-M$ channel dominates the speed perception of chromatic change. Although there is no literature for the direct comparison with our results, several papers indicated the “weak” contribution of the $S-(L+M)$ channel in speed perception. For example, Dougherty et al. [19] proposed an equation that combines the luminance, red–green, and blue–yellow opponent mechanisms to describe the mechanism of moving color responses. They assigned the largest weight to the luminance channel $(L+M)$, followed by the weight in the red–green $(L-M)$ channel and then the blue–yellow ($S-(L+M)$) channel. Nguyen-Tri and Faubert [20] performed a speed-matching experiment using drifting chromatic gratings. They found that the $S-(L+M)$ post-receptoral mechanism does not appear to contribute significantly to determining the perceived speed of chromatic motion. McKeefry and Burton [21], however, did not agree with the opinion that S-cone signals are not as effective in signaling stimulus motion. Their results suggest that the perception of speed is based on $L-M$ and $S-(L+M)$ cone opponent processing.

Figure 11 shows the bar charts of the 10 PSEs in the four spaces: CIELAB and improved CIELAB [Fig. 11(a)], DKL and improved DKL [Fig. 11(b)]. It is not intuitively meaningful to compare these two metrics, as they are of different magnitude. The fact that the optimized DKL space has reduced the standard deviation of PSEs to a larger extent than optimized CIELAB might indicate that DKL is more promising to work with in future. However, that this space implies that the S-(L+M) responses can be largely neglected for speed perception of color transitions remains worrisome. It might as well be too simplistic to just target the minimum of the standard deviation of PSEs to improve the uniformity of a color space for temporal transitions. Hence, to gain more insight into how to build a color space with global uniformity for speed perception of temporal color transitions, more data collection and more extensive modeling are needed.

 

Fig. 11. Bar charts of the 10 PSEs expressed in different color spaces: (a) CIELAB and improved CIELAB; (b) DKL and improved DKL.

Download Full Size | PDF

B. Limitations and Future Work

Our stimuli temporally varied in $C^{*}$ and $h$, keeping the luminance constant. For the design of these stimuli, we kept the luminance constant for an averaged observer. It is, however, generally known that luminance perception varies over individuals, and consequently, our stimuli might not have been fully isoluminant for all our participants. Nonetheless, we estimate the effect of individually tuned isoluminance to be small for this particular experiment. First of all, various researchers have found that adults are more sensitive to chromatic than luminance contrast for temporal frequencies below 4–5 Hz [22]. In this experiment specifically, the frequency of the temporal transition was about 0.33 Hz, and at this frequency the data of [22] indicate that adults are at least four times more sensitive to chromatic change than to luminance change. Second, if we simulate possible variations in the $L+M$ channel of our stimuli using the CIE 2006 Physiological Observer (CIEPO06) [23], we found that these variations have a slope close to zero, and at least five times smaller than the slope in any of the chromatic channels [i.e., either $L-M$ or $S-(L+M)$]. Still, in our next experiments to extend our data, we will evaluate the effect of including individual isoluminance in the design of our stimuli.

In the current experimental design, lightness changes were not included. Since our long-term goal is to develop a temporal uniform color space, comparing the perceived speed of lightness change with chromaticity change is important. In addition, as mentioned before we omitted the $CC$-comparisons in this study, but they clearly are relevant to extend the set of stimuli for the modeling or to validate the improved color space for temporal color transitions. In the future, lightness changes and more chroma levels will also be included in the experimental design.

Since the task of comparing multiple pairs of sequential color transitions is quite time-consuming, the number of repetitions per participants had to be limited and we were not able to fit a psychometric function per participant. In contrast, the responses were averaged over participants to fit one psychometric function for each hue in the $CH$ comparisons and each hue in the $HH$ comparisons. We already know that fitting a psychophysical curve across observers may introduce between-observer noise. Thus, if time would allow, an ideal case would be fitting a psychometric function per observer. This would require a more efficient psychophysical method or a reduction in the number of experimental conditions, where the latter is undesirable as well.

We intentionally chose for full room setting instead of the often-used 2° or 10° stimuli because temporal dynamics in artificial lighting are more realistically represented with a room-size field of view. At the same time, this choice introduces uncertainty about the direction of the observer’s gaze and the effects of peripheral vision. For the observers sitting at the predefined position, our stimuli resulted in a 101° horizontal and roughly 77° vertical visual angle. Research has shown that both spatial vision [24] and temporal vision [25] vary across this eccentricity, but our data does not allow a comparison of temporal color perception in central or peripheral vision. However, in lighting applications, central and peripheral vision will always mix, so a generally suitable temporal color space is needed. Creating models that take eccentricity into account would require new data in the future.

We chose to use a wall illumination of 4000 K as an intermediate light in an attempt to continuously reset the participants’ state of adaptation. Still, participants constantly adapted during the experiment to the varying light environment they were immersed in. This may have affected the experimental results, though most probably in a systematic way. This surely impacts the modeling, since color spaces assume adaption to a fixed illuminant. Due to the lack of a good model for temporal chromatic adaptation (which would change $L$, $M$, and $S$ reference over time), the calculation of the cone responses to model speed perception can be further improved.

Finally, it should be noted that we might have accumulated error in our calculations to compare the perceived speed of various color transitions with one fixed reference. The accumulated error can be best estimated from the first row of the result summary in Eq. (7). In our experiment, we directly measured that the transition speed along the chroma direction at 5R needed to be 7.76 $\mathrm{\Delta }{E}_{ab}^{*}/s$ in order to be perceived as fast as a transition speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5R. Using the calculation towards the same reference stimulus, we estimate a transition speed of 8.73 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the chroma direction at 5R to be perceived as fast as a transition speed of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$ along the hue direction at 5R. The deviation results from the fact that the $HH$ comparison with both the comparison and reference stimulus at 5R yielded a PSE of 11.25 instead of 10 $\mathrm{\Delta }{E}_{ab}^{*}/s$. It’s worth pointing out that $\mathrm{\Delta }{a}^{*}/s$ and $\mathrm{\Delta }{b}^{*}/s$ are linear for $C^{*}$ transitions, but sinusoidal for $h$ transitions, which also has a drawback in the calculation of the slopes according to Fig. 8.

Based on the just-mentioned limitations, we see multiple options for further research. Perception of dynamic color has many dimensions, such as three dimensions to define a base point in a color space, three dimensions of the modulation direction, and the related periodicity and waveform. In the future, more base colors (hues) and modulation directions (not only cardinal directions) will be needed to more accurately model a temporally uniform color space. Instead of defining the related stimuli in CIELAB, we see added value in defining them directly in cone-contrast space. In addition, there are more ways of generating the shape of the stimuli. Rather than giving all stimuli a fixed time period and changing the speed by changing the amplitude of the chroma or hue, one could keep the chroma or hue amplitude constant and change the speed by changing the time interval. The disadvantage of this choice, though, may be that observers use the additional time cue to judge the perceived speed of the color transition. Finally, it could be advantageous to use different JNDs instead of PSEs to distinguish perceived speeds, so they can be further used to build the temporal sensitivity function.

6. CONCLUSIONS

In this study, the perceived speed of periodic color transitions in chroma and hue was measured, starting from the five principal Munsell hues. The results indicate that available color spaces are not able to predict our speed perception. It is not so surprising that CIELAB is not perceptually uniform for temporal color transitions, as it was designed for describing spatial color differences. Color spaces built on cone responses were also insufficiently accurate to predict uniform speed perception of color transitions. Simple modifications of these spaces improve the uniformity in speed perception, but we foresee more extensive experimentation to build a more accurate model.