HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 47(1) pp. 17–23 (2019) hjic.mk.uni-pannon.hu DOI: 10.33927/hjic-2019-04 SIMULATION OF COLOR AFTERIMAGES: AN APPROACH TO COMPUTING VIRTUAL COLOR PERCEPTION LŐRINC GARAI *1 AND ANDRÁS HORVÁTH2 1Doctoral School of Multidisciplinary Engineering Sciences (MMTDI), Széchenyi István University, Egyetem tér 1, Győr, 9026, HUNGARY 2Department of Physics and Chemistry, Széchenyi István University, Egyetem tér 1., Győr, 9026, HUNGARY Afterimages are a common and frequent perceptual phenomenon of everyday life. When looking into a high-intensity light source and suddenly turning away from it, a temporary “ghost” of the light source remains visible, for a while. The computer-graphics simulation of afterimages is based on biophysical and mathematical models as published in the literature. A subordinate of afterimages defined in our research is virtual color perception, that is in our interpretation an unusual and intense temporary color perception provoked by a rapid change in the color of the incident light. In research, the modelling of virtual color perception is a field that is by and large untouched. Our publication presents a kinetic model established to characterize the intensity and duration of virtual color perception as a function of rapid changes in the color of the incident light. Keywords: afterimage, rod and cone photoreceptors, photopigment, kinetics 1. INTRODUCTION In our vision, an afterimage is an illusionary image that appears after having been exposed to a prior one. Color afterimages are experienced in everyday life, for exam- ple, when driving at night the headlights of oncoming cars are so bright that when the driver looks away from them, the illusion of bright headlights still remains in perception [1]. When photorealistic images are rendered [1–4], some papers reported simulations of color afterim- ages by combining mathematical models [5–9]. A subordinate of afterimages defined in our research is virtual color perception, a phenomenon that originates from chromatic adaptation in photoreceptors influenced by environmental color interactions, and based on the sensitivity to light and adaptibility of each cone receptor. The physiological background of virtual color per- ception in brief is as follows: human photopic (daylight) color vision is a combined response of type L (long wave- lengths), M (medium wavelengths) and S (short wave- lengths) cone receptors to adequate stimuli of light. The photopigment rhodopsin plays a key role in the process; the equilibrium of its relative concentration is achieved by the opposing processes of rapid cleavage when ex- posed to light and slow resynthesis in darkness [10, 11]. Adaptations of cone receptors to changes in the color of the incident light is time-consuming [12, 13], hence, a *Correspondence: garailorinc@garailorinc.hu rapid change in the color of the incident light facilitates unusual and intense temporary color perception, the so- called virtual color perception. For example, when ex- posed to red light the sensitivity of L cone receptors is low and in this case is accompanied by the high sensitiv- ity of M and S cone receptors. Following a rapid change in color from red to blue in the incident light, the sensi- tivity of S cone receptors remains temporarily high, re- sulting in perception of the color bright blue that trans- forms into common blue after a short period of time dur- ing which the relative concentration of photopigment is equilibrated (restored), i.e. this is the duration of virtual color perception. The purpose of our work is to develop a computa- tional kinetic model capable of simulating and quantify- ing virtual color perception. In our research chromaticity diagrams are used. Note that changes in the xy coordinates [14] are not propor- tional to human color perception. To overcome this dis- tortion, several chromaticity coordinates were defined, for example, CIE u′v′ [15]. The gamut of a device is the complete subset of colors it can produce. Usually, in an RGB (red, green, blue) de- vice, it consists of a color triangle with two-dimensional chromaticity coordinates. A gamut is characteristic of the given display (screen) currently in use, for example, modern RGB LED displays are characterized by wider gamuts compared to old-fashioned cold cathode fluores- mailto:garailorinc@garailorinc.hu 18 GARAI AND HORVÁTH Table 1: Gamut points CCFL RGB LED Gamut point x y x y B 0.2091 0.2218 0.1563 0.0307 B3R1 0.2753 0.2518 0.2837 0.1056 B2R2 0.3415 0.2817 0.4111 0.2181 B1R3 0.4077 0.3115 0.5385 0.3024 R 0.4739 0.3415 0.6658 0.3305 R3G1 0.4420 0.3837 0.5687 0.4236 R2G2 0.4101 0.4239 0.4717 0.5632 R1G3 0.3783 0.4652 0.3746 0.6679 G 0.3464 0.5064 0.2775 0.7028 G3B1 0.3121 0.4353 0.2472 0.5348 G2B2 0.2778 0.3641 0.2169 0.2827 G1B3 0.2434 0.2930 0.1866 0.0937 cent lamp (CCFL) displays that were frequently used about 10 years ago. In our work, gamuts characteristic of CCFL and RGB LED desktop monitors were measured first. Following this, the simulation of virtual color perception obtained by gamut data as a result of a rapid change in the color of the incident light was conducted. Finally, preliminary val- idation tests were run on the aforementioned RGB LED desktop monitor in use [16]. 2. Experimental 2.1 Measurement of the gamuts of the dis- plays used in our experiments and key pa- rameters of our model The spectral power distribution of the red, green and blue primaries of two displays was measured by a spectrora- diometer (a Flame Miniature Spectrometer by Ocean Op- tics, Inc. calibrated 12 strong lines of He, Ne, Ar and H2 flashtubes). One of the displays used was that of an old notebook using a CCFL as a backlight and the other was a more modern one (HP ZR2440w) with a display using RGB LEDs as a backlight. Based on the spectral power distributions measured, the CIE 1931 (x, y) chromaticity coordinates were calculated for all three primaries of both displays, using a Color Matching Function (CMF) of 10° at a resolution of 1 nm between the wavelengths of 360 nm and 830 nm. Intermediate gamut point coordinates were calculated by interpolation. Gamut point numbers in Table 1 and Fig. 1 were further referred to as colors of incident light. In our kinetic model, actual color percep- tion is compiled from the generally known mathematical relations [8, 9, 17] shown below. The actual color perception J of a single (L, M or S) cone receptor can be calculated by the formula J = DEp, (1) where D denotes a conversion constant between the cleavage of rhodopsin and neural impulses and here is Figure 1: Chromaticity diagram of gamut points: an old CCFL display of a notebook (inner gamut) and an HP ZR2440w display (outer gamut) equal to 1. The variable E represents the intensity of in- cident light expressed in trolands (Td). During the cal- culations a maximum luminance of the monitor of 300 cd/m2 was used and a diameter of the pupil of 5 mm as- sumed. Therefore, the maximum retinal illuminance was equal to 5890 Td. The variable p denotes the relative con- centration of photopigment (between 0 and 1). The time differential of p determined from the rate of photopigment synthesis (Qs), spontaneous photopigment cleavage (Qc) and photoinduced cleavage (Qi) is calcu- lated by dp dt = Qs − Qc − Qi. (2) The variables of Eq. 2 are calculated by Qs = 1 τ , (3) Qc = p τ , (4) and Qi = E E0 p τ , (5) where the time constant τ = 99 1/s and E0 = 20, 000 are used [13]. The following differential equation is com- posed from Eqs. 2–5: dp dt = 1 τ − p τ − E E0 p τ . (6) The solution of Eq. 6 yields the actual relative concentra- tion of photopigment: p(t) = 1 b [1 − (1 − p0b)] e−tb/τ, (7) where p0 denotes the initial relative concentration of pho- topigment. Hungarian Journal of Industry and Chemistry BIOPHYSICAL MODEL OF COLOR AFTERIMAGES 19 Finally, the equilibrium with regard to the relative concentration of photopigment pe and percentage of pho- topigment cleaved b are related as follows: pe = 1 b = E0 E + E0 . (8) 2.2 Simulation formula In accordance with CIE 1931 [18, 19], the actual coordi- nates of color perception x(t), y(t) and z(t) are calcu- lated from the color coordinates of incident light xi, yi and zi by equations Eqs. 9–24. In the equations below, variables indexed with L, M and S apply to cone recep- tors L, M and S, respectively. EL = Emultip · M1,1-3 × [xi, yi, zi] (9) EM = Emultip · M2,1-3 × [xi, yi, zi] (10) ES = Emultip · M3,1-3 × [xi, yi, zi] (11) bL = bM = bS = 1 + Emultip E0 (12) Emultip, which is equal to 6, 000, denotes the light inten- sity of the display. The actual relative concentration of photopigment is calculated from the initial relative con- centrations of photopigment p0L, p0M and p0S: pL(t) = 1 bL (1 − (1 − p0Lb))e−tb/τ (13) pM(t) = 1 bM (1 − (1 − p0Mb))e−tb/τ (14) pS(t) = 1 bS (1 − (1 − p0Sb))e−tb/τ (15) For the purposes of iteration in simulations, the initial rel- ative concentration of photopigment p0 was equal to 0.1. From the actual relative concentrations of photopigment Eqs. 13–15, the color perception coordinates are as fol- lows JL(t) = D · pL · EL, (16) JM(t) = D · pM · EM, (17) JS(t) = D · pS · ES, (18) where JL, JM and JS denote the cone receptors of long, medium and short wavelengths, respectively. To obtain more accurate color perception coordinates, tristimulus values were calculated: X(t) = M−11,1-3 × [JL, JM, JS], (19) Y (t) = M−12,1-3 × [JL, JM, JS], (20) Z(t) = M−13,1-3 × [JL, JM, JS], (21) Figure 2: An example of fast color change leading to virtual color perception. Color point yellow shows pri- mary color perception. Color points bright blue show vir- tual color perception as reflected by the tendency to reach equilibrium in photopigment relative concentration. where M denotes a transformation matrix between tris- timulus values X, Y and Z, and the actual color percep- tion J. The actual color perception coordinates x(t), y(t), z(t) are calculated by the following equations: x(t) = X(t) X(t) + Y (t) + Z(t) , (22) y(t) = Y (t) X(t) + Y (t) + Z(t) , (23) z(t) = 1 − x(t) − y(t). (24) In accordance with the CIELUV (1976) chromaticity di- agram, the actual color perception coordinates x(t), y(t) and z(t) are transformed into coordinates u′(t) and v′(t) by an easy-to-compute method [19] : u′(t) = 4x(t) 12y(t) − 2x(t) + 3 , (25) v′(t) = 6y(t) 12y(t) − 2x(t) + 3 . (26) The intensity of the actual virtual color perception is de- termined by ∆c = √ (u′(t) − u′e) 2 + (v′(t) − v′e) 2 , (27) where u′e and v ′ e denote color coordinates at equilibrium following restoration from virtual color perception (see Restoration to the equilibrium in Fig. 2). A summary of variables and parameters is shown in Notations at the end of this paper. 2.3 Simulation To understand the calculations, a graphical approach is shown in Fig. 2. Gamut color point 1 stands for the pri- mary perception of the actual incident light, which is yel- low here. With a rapid change in color from yellow to 47(1) pp. 17–23 (2019) 20 GARAI AND HORVÁTH Table 2: Example of iteration t(s) xi yi u ′(t) v′(t) ∆c 0.0 0.4250 0.56875 – – – 10.0 0.4250 0.56875 0.1893 0.3802 – 20.0 0.4250 0.56875 0.1892 0.3802 – 30.0 0.4250 0.56875 0.1891 0.3802 – 30.1 0.1400 0.05000 0.1748 0.0836 0.02075 30.2 0.1400 0.05000 0.1748 0.0837 0.02066 30.3 0.1400 0.05000 0.1747 0.0838 0.02057 30.4 0.1400 0.05000 0.1747 0.0838 0.02048 30.5 0.1400 0.05000 0.1746 0.0839 0.02039 30.6 0.1400 0.05000 0.1745 0.0840 0.02031 30.7 0.1400 0.05000 0.1745 0.0840 0.02022 30.8 0.1400 0.05000 0.1744 0.0841 0.02013 30.9 0.1400 0.05000 0.1744 0.0842 0.02004 31.0 0.1400 0.05000 0.1743 0.0842 0.01995 31.1 0.1400 0.05000 0.1743 0.0843 0.01987 31.2 0.1400 0.05000 0.1742 0.0844 0.01978 . . . . . . . . . . . . . . . . . . 63.9 0.1400 0.05000 0.1611 0.0991 0.000126 64.0 0.1400 0.05000 0.1611 0.0991 0.000101 64.1 0.1400 0.05000 0.1611 0.0992 0.000092 64.2 0.1400 0.05000 0.1611 0.0992 0.000102 blue, a bright blue color appears in perception that trans- forms into common blue after a short period of time nec- essary for the restoration of the equilibrium in terms of the relative concentration of photopigment, which is the time period required for virtual color perception, namely for the perception of bright blue (Fig. 2). Our kinetic simulation model (Section 2.2) is illus- trated in Table 2. The first five lines in the first four columns show the same values of the color coordinates of incident light xi, yi, zi, against time (0 − 30 seconds). Figure 3: Photopigment relative concentration values in the iteration in Table 2 Over this 30 second-long period, the u′(t) and v′(t) val- ues of color perception are quasi identical. However, af- ter 30 seconds, a rapid change in color of the incident light from red to blue results in virtual color perception, as demonstrated by line 6 and column 5. The values of ∆c in column 7 concern the intensity of virtual color percep- tion. (∆c)max denotes the peak intensity in virtual color perception and the minimum ∆c stands for the duration of virtual color perception (tvirtcol). Actual relative con- centrations of photopigment of cone receptors L, M and S are shown in the diagram in Fig. 3. In terms of simulating virtual color perception, rapid changes in the color of incident light were indicated on CCFL and RGB LED monitors by the assignment of de- fined gamut points to each other (Fig. 1). Altogether, 24 changes in color were simulated. 2.4 Validation of the simulation Our kinetic model was validated by a test that consisted of 20 subjects involving an in-house piece of software run in a Python environment. Accordingly, a homogeneous solid colored circle is displayed on a homogeneous back- ground of a different color for 30 seconds (Fig. 4), then the circle disappears (Fig. 5) and the intensity and dura- tion of virtual color perception is determined by the key inputs of the user. Further details concerning the test are found below: • First, the test subject looked at a white screen for 30 seconds. Figure 4: Second screen of validation test. Figure 5: Third screen of validation test: circle removed. Hungarian Journal of Industry and Chemistry BIOPHYSICAL MODEL OF COLOR AFTERIMAGES 21 Table 3: Comparison of virtual color perception intensity in model situations and in validation test results Ranking in model Ranking category Ranking in validation test results ID Rank ID Median of ranking Corre- lation R → G 1 High B → G 1.00 No G2B2 → R 2 B2R2 → G 2.00 Yes G1B3 → R 3 R → G 3.00 Yes B2R2 → G 4 B → R2G2 4.00 No R → G2B2 5 Medium R → G2B2 4.00 Yes R2G2 → B 6 Low G1B3 → R 4.50 No G → B2R2 7 G2B2 → R 5.00 No B → G 8 G → B2R2 5.00 Yes B → R2G2 9 R2G2 → B 7.00 Yes Matching percentage between model and validation test results: 56% Table 4: Comparison of virtual color perception time pe- riod in model situations and in validation test results Ranking in model Ranking category Ranking in validation test results ID Rank ID Median of ranking Corre- lation R → G2B2 1 High B → G 1.00 No R → G 2 G1B3 → R 2.00 No G → B2R2 3 B → R2G2 3.00 No B2R2 → G 4 R → G2B2 4.00 Yes R2G2 → B 5 Medium G2B2 → R 4.00 No G2B2 → R 6 Low G → B2R2 4.50 No B → R2G2 7 B2R2 → G 5.00 No G1B3 → R 8 R → G 5.00 No B → G 9 R2G2 → B 7.00 No Matching percentage between model and validation test results: 11% • Second, the eyes of the subject were fixed on a circle at the center of the subsequent colored image (Fig. 4) for 30 seconds. According to our definition, the color of the central circle represents the first gamut point, while the color of the background represents the second gamut point. Altogether, 9 assignments of gamut points have been validated so far. • Third, the central circle suddenly disappeared (Fig. 5) and the subject responded according to the inten- sity and duration of virtual color perception experi- enced. • The intensity of virtual color perception was rated on a four-grade scale, where zero stands for the ab- sence of virtual color perception and 4 denotes its highest intensity. The duration of virtual color per- ception was indicated by the subject pressing a key as the perception faded away. First, the assignments of gamut points for each test subject were ranked according to the intensity (Table 3) and duration (Table 4) of virtual color perception in- duced. Then, the median of the rank order with regard to the intensity and duration of virtual color perception was calculated. Table 5: Intensity and time period of virtual color percep- tion related to gamut points assignments (∆c)max tvirtcol(s) Color point 1 Color point 2 CCFL RGB LED CCFL RGB LED B R3G1 0.00792 0.01212 30.9 24.5 B R2G2 0.00553 0.00513 36.3 27.5 B R1G3 0.00339 0.00197 41.9 16.0 R3G1 B 0.00794 0.01210 33.5 29.5 R2G2 B 0.00852 0.01367 34.9 32.2 R1G3 B 0.00953 0.01523 37.2 34.6 G3B1 R 0.00931 0.02381 27.1 29.3 G2B2 R 0.00958 0.02187 27.5 27.6 G1B3 R 0.00994 0.01989 28.1 25.8 R G3B1 0.00920 0.02298 46.9 44.2 R G2B2 0.00821 0.01686 51.2 52.8 R G1B3 0.00735 0.01260 50.2 38.2 G B3R1 0.00807 0.01789 48.2 41.1 G B2R2 0.00648 0.01362 45.8 42.2 G B1R3 0.00693 0.01722 30.5 31.0 B3R1 G 0.00324 0.01337 25.0 27.8 B2R2 G 0.00524 0.01799 33.7 33.7 B1R3 G 0.00749 0.02256 41.4 38.7 B R 0.01036 0.01786 28.8 23.8 R B 0.00788 0.01053 33.3 26.6 R G 0.00980 0.02707 48.2 43.1 G R 0.00915 0.02571 26.7 30.8 G B 0.01084 0.01677 40.1 37.0 B G 0.00234 0.00868 17.8 20.5 Since the number of test subjects was limited, the re- sults could not be divided according to their age and gen- der. Further tests are needed to ensue virtual color per- ception with regard to gender and age. 3. Results and Discussion In Table 5, the maximum (∆c)max for the CCFL and RGB LED displays were identified during the rapid change in the color of incident light from gamut point G to B (from green to blue) and R to G (from red to green), respectively. When compared to the CCFL display, the RGB LED display appears to yield higher (∆c)max values with the exception of rapid changes in the color of the incident light from gamut point B to R2G2 (from blue to orange). With regard to our results, the duration of virtual color perception seems to be platform-free, i.e. tvirtcol dis- played on both the CCFL and RGB LED monitors was identical. However, rapid changes in the color of the in- cident light from gamut point B to R1G3 (from blue to yellowish green) was an exception with regard to the val- ues of tvirtcol. As is shown in Table 5, tvirtcol computed on the CCFL display has doubled in value compared to that computed on the RGB LED display. The kinetic simulation results so far point to the like- lihood of the appearance of virtual color perception on all 47(1) pp. 17–23 (2019) 22 GARAI AND HORVÁTH display platforms. As for our preliminary tests performed on 20 test sub- jects so far as well as the parameters (∆c)max and tvirtcol, a correlation between model situations (simulations) and the results of a validation test cannot be confirmed at present. Further tests, statistical evaluations and the in- troduction of additional parameters are also necessary to achieve more accurate conclusions. 4. Conclusion Photopic human color vision is a combined response to the stimulation from light of red, green and blue cone re- ceptors. Cone receptors adapt individually to the actual color of the incident light. Since the adaptation of cone receptors is time-consuming, virtual color perception can be achieved in the meantime by rapid changes in the color of the incident light. Our kinetic model developed for individual cone re- ceptors is based on mathematical correlations that simu- late the intensity and duration of virtual color perception which result from rapid changes in color. According to our model, virtual color perception can result from both CCFL and RGB displays. Our preliminary validations are yet to confirm a cor- relation between model situations (simulations) and the results of a validation test. Some refinements to the simu- lation by the introduction of additional parameters as well as further validation tests with regard to the gender and age of participants are indispensable to reach more accu- rate conclusions. Acknowledgement This research would not have been possible without the participation of volunteers from Széchenyi István Univer- sity as test subjects. Notations Symbol Meaning Unit J in actual color perception: JL = red cone receptors specific for long wavelength JM = green cone receptors specific for medium wavelength JS = blue cone receptors specific for short wavelength dimensionless p relative photopigment concentration dimensionless (range:0 . . . 1) D conversion constant between rhodopsin cleavage and neural impulses dimensionless (value: 1) E incident light intensity troland Qs Synthesis of photopigment dimensionless Qc Spontaneous cleavage of photopigment dimensionless Qi Light induced cleavage of photopigment dimensionless τ time constant in rhodopsin synthesis seconds Symbol Meaning Unit p0 photopigment initial relative concentration dimensionless p(t) photopigment relative concentration at t time after p0 dimensionless b percentage of photopigment cleaved dimensionless M transformation matrix of tristimulus values XYZ and the actual color perception J dimensionless REFERENCES [1] Mikamo, M.; Slomp, M.; Raytchev, B.; Tamaki, T.; Kaneda, K.: Perceptually inspired afterimage synthe- sis, Computers & Graphics, 2013 37(4), 247–255 DOI: 10.1016/j.cag.2013.02.008 [2] Gutierrez, D.; Anson, O.; Munoz, A.; Seron, F. 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