Journal of Vision (2022) 22(6):10, 1–15 1 The contribution of luminance and chromatic channels to color assimilation Computer Vision Center and Computer Science Department, Xavier Otazu Universitat Autonoma de Barcelona, Barcelona, Spain Computer Vision Center, Vall d’Hebron Research Institute, and Computer Science Department, Xim Cerda-Company Universitat Autonoma de Barcelona, Barcelona, Spain Color induction is the phenomenon where the physical & Murakami, 2012; Cerda-Company et al., 2018). and the perceived colors of an object differ owing to the This phenomenon appears when the perceived color color distribution and the spatial configuration of the of a target is influenced by the surrounding colors. surrounding objects. Previous works studying this According to the color shift direction, color induction phenomenon on the lsY MacLeod–Boynton color space, can be distinguished into two types: color contrast show that color assimilation is present only when the and color assimilation. The former occurs when the magnocellular pathway (i.e., the Y axis) is activated (i.e., color of the target shifts away from the color of the when there are luminance differences). Concretely, the nearest surrounding object (the inducer). In contrast, authors showed that the effect is mainly induced by the the latter occurs when the color of the target shifts koniocellular pathway (s axis), but not by the toward that of the inducer. For example, when a parvocellular pathway (l axis), suggesting that when gray target is surrounded by a green inducer and it is magnocellular pathway is activated it inhibits the perceived as reddish (the opponent color of green), koniocellular pathway. In the present work, we study whether parvo-, konio-, and magnocellular pathways color contrast is induced. Instead, if the gray target is may influence on each other through the color induction perceived as greenish, color assimilation is induced. effect. Our results show that color assimilation does not The type of induction (contrast or assimilation) mainly depend on a chromatic–chromatic interaction, and that depends on the spatiochromatic properties of the chromatic assimilation is driven by the interaction target and the inducers. Several studies showed that between luminance and chromatic channels (mainly the striped surrounds usually induce color assimilation magno- and the koniocellular pathways). Our results and uniform surrounds usually induce color contrast also show that chromatic induction is greatly decreased (Monnier & Shevell, 2003, 2004; Shevell & Monnier, when all three visual pathways are simultaneously 2005; Otazu et al., 2010). activated, and that chromatic pathways could influence In a recent study, we observed that luminance each other through the magnocellular (luminance) differences are a key factor to induce color assimilation pathway. In addition, we observe that chromatic in the s chromatic axis (Cerda-Company et al., channels can influence the luminance channel, hence 2018). There, we used striped stimuli that lay down inducing a small brightness induction. All these results on either the l or the s chromatic axis of the lsY show that color induction is a highly complex process MacLeod-Boynton color space (MacLeod & Boynton, where interactions between the several visual pathways 1979), which is a commonly used opponent color are yet unknown and should be studied in greater detail. space based on the Smith and Pokorny (1975) cone fundamentals. In this color space, l and s chromatic axes correspond with the red–green (parvocellular pathway, Introduction a.k.a., P pathway) and purple–lime (koniocellular pathway, a.k.a., K pathway) opponent chromatic Color induction is a known phenomenon, exploited channels, respectively, and the Y axis corresponds with by artists for several centuries (Chevreul, 1839; Von the luminance channel (magnocellular pathway, a.k.a., Bezold, 1876), and widely studied by researchers M pathway). We observed that equiluminant stimuli (Ehrenstein, 1941; Van Tuijl, 1975; Monnier & Shevell, (no luminance difference between the test and the 2003, 2004; Gordon & Shapley, 2006; Faul et al., inducers) did not induce color assimilation, or it was 2008; Bimler et al., 2009; Otazu et al., 2010; Kaneko negligible. In addition, we observed that, mainly along Citation: Otazu, X., & Cerda-Company, X. (2022). The contribution of luminance and chromatic channels to color assimilation. Journal of Vision, 22(6):10, 1–15, https://doi.org/10.1167/jov.22.6.10. https://doi.org/10.1167/jov.22.6.10 Received December 3, 2021; published May 31, 2022 ISSN 1534-7362 Copyright 2022 The Authors This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 2 the s chromatic axis, the induced color changed from no To test this hypothesis, we extend our previous induction (or weak contrast) to color assimilation by study (Cerda-Company et al., 2018) using a visual increasing the luminance difference between the target stimuli where both l and s chromatic channels are and the inducer. simultaneously activated. We also study its dependency Several authors suggested that color induction is the on the luminance channel (Y axis), to investigate their result of the neural mechanisms (probably the lateral possible relationship with the luminance–chromatic connections) in the primary visual cortex (Zaidi et al., mutual inhibition mechanism. 1992; Rossi et al., 1996; De Weert & Kruysbergen, 1997; Zaidi, 1999; Shapley & Hawken, 2002; Cao & Shevell, 2005). In this visual area, there exist three types of cells: single- (SO), double- (DO), and non-opponent (NO) Methods neurons (Johnson et al., 2001; Shapley & Hawken, 2002; Johnson et al., 2008; Shapley & Hawken, 2011). SO Apparatus neurons, which are also known as color cells, respond best to low spatial frequencies (ν < 0.5 cycles/◦ ; i.e., low The experiments were conducted in a dark room; pass), and chromatic stimuli (color-sensitive cells). DO that is, all the light in the room was from the neurons, which are also called color-luminance cells, are monitor’s screen, and the walls were black to avoid band pass (0.5 cycles/◦ < ν < 10 cycles/◦ , with the peak interreflections. Stimuli were presented on a calibrated of response at 2 cycles/◦ ) and sensitive to both color 32 LCD Display++ monitor (Cambridge Research and luminance borders. NO neurons, which are also Systems, Ltd.) at 100 Hz, with 1440 × 1080 pixels called luminance cells, are band pass cells and sensitive resolution, and subtending 22.6 × 16.95 visual degrees. to achromatic stimuli. Interestingly, it is suggested that The stimuli was viewed binocularly (subject’s head was DO neurons play a major role in color appearance not constrained) from a distance of approximately 134 (Nunez et al., 2018). cm. We used the Cambridge Research Systems ViSaGe One of the proposed neural mechanisms for color MKII Stimulus Generator, capable of displaying induction is the mutual inhibition (Gordon & Shapley, 14-bit color depth. The monitor was calibrated 2006; Xing et al., 2015; Nunez et al., 2018), where as via the customary software (Cambridge Research luminance contrast (i.e., the luminance difference) is Systems, Ltd.) and the Display++ monitor embedded increased, the color response is decreased by virtue of colorimeter. The subject’s responses were collected connections between luminance and color-sensitive using a Logitec gamepad. cells. That is, NO and DO cells could inhibit DO and SO activity. This mechanism could explain the observed luminance–chromatic interaction in our Stimuli previous study (Cerda-Company et al., 2018), where color assimilation only appeared when there existed All stimuli were implemented in Matlab (The luminance differences. In this previous study, we only MathWorks, Inc., Natick, MA), and the video evaluated the influence of the M pathway on the P and processor was controlled via a Cambridge Research K chromatic pathways separately. At this point, a new System custom-made toolbox. question could arise: Is this mechanism also present As shown in Figure 1, the spatial configuration of between the P and K pathways? An affirmative answer the visual stimuli was the same as in Cerda-Company would imply that, when both chromatic pathways et al. (2018). That is, the test stimulus (presented are activated, the P pathway inhibits the K pathway on the left side of the monitor) was composed of and vice versa. Extending our previous work, in the 11 concentric rings of the same width (15.5 arcmin present study, we explored the possibility that mutual of visual angle), which included the achromatic inhibition occurs between chromatic pathways (i.e., a equal energy white (EEW) test ring (l = 0.66 and chromatic–chromatic K–P interaction), aside from the s = 0.98). Similarly, the luminance of the test ring influence of the M pathway. varied according to the luminance condition: The The hypothesis of the present study is that set of luminance differences between the test and the chromatic pathways influence each other by a mutual inducer rings was Y = [−10, −5, 0, +5, +10], cd/m2 , inhibition–like mechanism. Considering the described being the inducer rings Y = 20 cd/m2 (see details in mutual inhibition mechanism between luminance and Equiluminance measure). Furthermore, the inducer chromatic pathways, therefore, we expect to observe rings (being the first inducer the one adjacent to the color assimilation at equiluminance (when both test ring) had opponent chromaticities, with the EEW chromatic pathways are activated), and the maximum exactly in the middle of both chromatic points. The color assimilation at non-equiluminance (when all chromatic values for l and s axes were the same as in pathways inhibit each other, and the mutual inhibition Cerda-Company et al. (2018) (e.g., l = {0.63, 0.66, 0.69} is maximal). and s = {0.58, 0.98, 1.38}), but we defined four new Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 3 Figure 1. Stimuli design. The first and the second inducers consisted of equiluminant (Y = 20 cd/m2 ) pairs of rings of opposite chromaticities such as RedPurple–GreenLime or PurpleGreen–LimeRed chromaticities. The test ring was always achromatic (l = 0.66 and s = 0.98) and could have five different luminance values (luminance conditions): Y = [10, 15, 20 (equilum.), 25, 30] cd/m2 . Although it is difficult to see in this figure because of their size, 8 black dots of 1 pixel size were drawn around test ring for easier detection: four dots in the inner radius of the ring and four points in the outer radius (at 0°, 90°, 180°, and 270◦ ). Subjects had to match the color of the comparison ring with that of the test ring. Colors in this figure might not be the same as the experiment because they were created for illustrative purposes. Figure extracted from Cerda-Company et al. (2018). Test ring First inducer Second inducer chromatic conditions named as RedPurple–GreenLime, GreenLime–RedPurple, GreenPurple–RedLime, and Condition l s l s l s Notation RedLime–GreenPurple according to their spatial Red–Green 0.66 0.98 0.69 0.98 0.63 0.98 +l Green–Red 0.66 0.98 0.63 0.98 0.69 0.98 −l position in the MacLeod–Boynton color space. Their Purple–Lime 0.66 0.98 0.66 1.38 0.66 0.58 +s l, s are shown in Table 1. We chose these chromaticities Lime–Purple 0.66 0.98 0.66 0.58 0.66 1.38 −s because, in contrast to Cerda-Company et al. (2018), RedPurple–GreenLime 0.66 0.98 0.69 1.38 0.63 0.58 +l/+s the visual stimuli activate the two chromatic pathways GreenLime–RedPurple 0.66 0.98 0.63 0.58 0.69 1.38 −l/−s GreenPurple–RedLime 0.66 0.98 0.63 1.38 0.69 0.58 −l/+s at the same time, which allows us to measure their RedLime–GreenPurple 0.66 0.98 0.69 0.58 0.63 1.38 +l/−s interaction. Table 1. Summary of the experimental conditions. We detail the chromaticity sets in the MacLeod-Boynton color space. Only the Notation l and s chromatic axes are reported because the luminance of To name the chromatic values we have used the Cao inducers was always Y = 20 cd/m2 and the luminance of the and Shevell (2005) notation, that is, −l for l = 0.63 test ring depended on the luminance condition: and +l for l = 0.69, and not using any symbol for the Y = [−10, −5, 0 (equiluminant), 5, 10. The last column l = 0.66 case. Similarly, we use −s for s = 0.58, +s for indicates the notation of the inducers (see text). For s = 1.38, and no symbol for s = 0.98. The signs refer to convention, when two color names (e.g., red–green) are whether the value of the chromatic condition is bigger indicated, it means that the first (e.g., red) is the name of the ( + ) or smaller ( − ) than the corresponding value of the first inducer, and the second name (e.g., green) is the name of achromatic EEW (l, s) = (0.66, 0.98). the second one. First four conditions (+l, −l, +s, −s) are the To name chromatic conditions, we use the notation ones from Cerda-Company et al. (2018). of the first inducer (see the Notation column in Table 1). For example, GreenPurple–RedLime condition is denoted as −l/+s (because GreenPurple chromaticity is Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 4 denoted by −l/+s), RedLime–GreenPurple condition as Participants +l/−s, and so on. Results from Cerda-Company et al. (2018) lay on the Eleven people recruited from our academic cardinal axes of MacLeod-Boynton color space, that is, community participated in the experiment. Five were they only activated one chromatic channel (e.g., s or l). familiar with color spaces (AC, XO, CS, NS, XC) and Therefore, notation for these points (first four rows in six were not (RP, YR, YX, AM, HP, SD). Nine of them Table 1) is represented by only one letter (e.g., +l for were completely naïve (AC, RP, YR, CS, NS, YX, AM, Red–Green, −l for Green–Red, +s for Purple–Lime, HP, SD), and two of them are the authors of this article and −s for Lime–Purple). In contrast, the results (XO, XC). The age was between 18 and 48 years old. obtained in the present work lie on the diagonal axes Six of them were female (RP, YR, CS, NS, YX, HP) of the chromatic plane. Therefore, for these points, the and five were male (AC, XO, AM, SD, XC). notation is represented by two letters (e.g., +l/+s, +l/−s, All participants had normal or corrected-to-normal −l/+s, −l/−s), because both chromatic channels are vision, and they scored as normals in the Ishiara’s test activated at the same time. (Ishihara, 1972) and the D-15 Farnsworth Dichotomous In addition, to name a particular experimental Test (Farnsworth, 1947). All of them signed the consent point, we have added the value of the luminance form to participate in the experiment, where the aim of condition (Y , the luminance difference between the study was described. The experiment was conducted the test and the first inducer) to the end of the according to the guidelines of the Declaration of previous notation. For example, +l/−s/0 refers to Helsinki, and approved by our university’s ethic the equiluminant (Y = 0 cd/m2 ) point for the commitee (Comissio d’Etica en l’Experimentacio RedLime–GreenPurple condition, and +l/−s/5 refers Animal i Humana CEEAH-4056 de l’Universitat to the Y = 5 cd/m2 point of the same chromatic Autonoma de Barcelona). condition. To have a similar number of participants in both cardinal and diagonal conditions, three completely naïve participants (CS, DC, MF) performed the experiment described in Cerda-Company et al. (2018). Equiluminance measure The total number of participants was increased to 10, and their results were added to the previous ones. These Because the equiluminant point is different for participants had normal or corrected-to-normal vision, every participant, before the experiment we measured they were not familiar with colour spaces, their age was the color values that generated equiluminance. The between 22 and 24 years of age, and two of them were equiluminant-point measure procedure for every female (CS, MF) and one was male (DC). observer lasted 3 hours and was performed through three different days using the minimally distinct border method (MDB) (Boynton & Kaiser, 1968; Kaiser, 1971; Wagner & Boynton, 1972; Boynton, Experimental procedure 1973; Kaiser et al., 1990; Brill, 2014). The stimuli consisted on two semicircular adjacent disks presented After the MDB task to measure the equiluminant in the same apparatus as the experiment. One of the colors, participants performed an asymmetric matching disks was achromatic (l = 0.66 and s = 0.98) and task (Figure 1), where they were instructed to “adjust the other had one of the chromaticities defined in the color of the comparison ring until it was perceived the experiment’s chromatic conditions (i.e., +l/+s, the same as the test ring.” To do this matching, +l/−s, −l/+s, −l/−s) plus an achromatic condition, for participants adjusted independently the chromaticity control. The luminance of the achromatic disk was and the luminance of the comparison ring, navigating in set at Y = 20 cd/m2 . Subjects task was “to adjust the the MacLeod–Boynton color space using the gamepad luminance of the colored disk until the border between buttons (Monnier & Shevell, 2003; Cerda-Company the color and the achromatic disks was minimal,” that et al., 2018). They did a first training session to is, when only chromatic but not luminance differences familiarize with the experimental procedure and the were perceived. Ideally, there would be no border apparatus. All the data collected during this training between the two disks (in fact, this should happen for session was removed from the analyses. the control condition), but in other conditions, at least a After the training session, participants did five chromatic border was always perceived. We obtained an sessions during three different days. Each session lasted average (from 8 measures) of the luminance necessary 40 minutes (approximately) and they consisted of to match each of the four colors to the achromatic disk 3 minutes of darkness adaptation and two trials. Each for each subject. These luminance values were used to trial included all possible random combinations of construct the inducer rings of the test stimulus (see left chromatic and luminance conditions (+l/+s, +l/−s, stimulus in Figure 1). −l/+s, −l/−s) × (−10, −5, 0, 5, 10) cd/m2 , totalling 20 Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 5 runs each. In a single day, a participant came to the explained by the interaction of the two chromatic laboratory and spend 90 minutes approximately to do pathways (P and K). This process would help us to 80 runs (two sessions). Between sessions, participants reject or accept our initial hypothesis. were forced to take a 10-minute break. After the 5 To compare distributions against the zero-value, we sessions, the participant finished the 10 trials, totalling used a t test for normally-distributed data, and the 200 runs (matches). Mann–Whitney U test for data that did not follow a normal distribution (functions t.test and wilcox.test from package stats). From these distributions, we Statistical analysis reported the mean value ± the standard deviation for normal-distributed data, or the median and the To measure the strength of color induction, we used interdquartile range (in brackets) for non-normally the color induction metric defined in Cerda-Company distribute data. Furthermore, we also used these tests et al. (2018): to compare two different distributions. From both tests, we reported the p values, the t values from the t test, Cic − Cit and the V − or W − values from the Mann–Whitney Ci = , (1) Cif − Cit U test. The normal distribution was assessed using the Shapiro–Francia test (function sf.test from package where i = [l, s], Cic was the chromaticity of the nortest). comparison ring along the considered color axis, and Cit and Cif were the chromaticities of the test ring and the first inducer ring along the same axis, respectively. This metric allowed us to capture the two color induction effects: negative values (Ci < −JND) Results for color contrast and positive values (Ci > +JND) for color assimilation. The just noticeable difference To have an overview of the results, in Figures 2 and (JND) is the region where no color differences were 3, we show the color induction strength obtained in the perceived. We estimated the JND value from CIELab present study together with the extended results from color space (E = 1) because it is an approximately Cerda-Company et al. (2018) (+l,−l,+s,−s). Each panel perceptually uniform color space, and then transformed represents a single chromatic condition (see Table 1) to the MacLeod–Boynton color space. and, in them, the color induction along the l, the s, All statistical analyses were done in R Core Team and the Y axes is shown (red, purple, and black lines, (2019). Our dependent variable was the color induction respectively). Because some chromatic conditions are strength and, to study its predictors, we fitted Linear defined on the cardinal axes (+l, −l, +s, −s), the color Mixed-Effects Models using the function lmer from induction metric cannot be measured along the other the packages lme4 and lmerTest. Experimental factors axis. Instead, the effect can be measured on both axes such as luminance (ConditionY = [−10, −5, 0, 5, 10]) for the chromatic conditions defined on the diagonals and chromatic conditions (ConditionL = [−l, 0l, +l] (+l/+s, +l/−s, −l/+s, −l/−s). Results in the MacLeod– and ConditionS = [−s, 0s, +s]) were considered as Boynton color space and all individual results for each fixed factors, and the participants and trials were chromatic conditions are shown in Appendixes A and B, considered as random factors. In fact, because each respectively. participant did 10 trials, the factor trial was nested in According to the metric (Equation 1), we can observe participant. that, on one hand, several conditions induced color To avoid model over-parametrization, we compared assimilation (e.g., +s/<0 and −s/>0). On the other the models with and without each factor using the hand, several conditions induced color contrast (e.g., Akaike Information criterion (AIC) and the likelihood −l/<0 and −l/−s/<0). Moreover, because several values ratio test. Significance levels were calculated using the are not above the JND, we can observe conditions Kenward–Roger degrees of freedom approximation where no color induction was induced (e.g., +l/0 and to the F distribution (Kenward & Roger, 1997). +l/−s/0). Furthermore, we used the t test comparisons to identify In agreement with previous studies (Fach & Sharpe, the levels with significant differences, when necessary. 1986; Cerda-Company et al., 2018; Cerda-Company The p values were corrected using the false discovery & Otazu, 2019), we observed that color induction rate (function emmeans from package emmeans). Apart along the two chromatic axes depends on both from the corrected p value (pad j ), from the post hoc the chromatic and luminance conditions. This analysis, we reported the t-ratio also. observation is supported by the best fitted linear As a theoretical interpretation of the analyses, a model: ColorInductionl,s ∼ ConditionL * ConditionS statistically significant interaction between chromatic * ConditionY + (1|Participant). We fit a specific conditions, would imply that the color induction is linear model for each chromatic axis, being the Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 6 Figure 2. Results on the cardinal axis (e.g., +l, −l, +s, −s,) are extended from Cerda-Company et al. (2018), and results on the diagonal axis (e.g., +l/+s, +l/−s, −l/+s, −l/−s) have been obtained in the present study. For the sake of clarity, chromatic conditions (panels) are spatially distributed similarly to their position with respect to the EEW in the chromatic plane of the MacLeod–Boynton color space. Error bars are standard error of means. Y is the luminance condition (the luminance difference between the test and the first inducer), Ci is the color induction metric (positive values mean assimilation and negative values mean contrast). Red and purple lines are results for l and s axes, respectively. The JND values are shown as a coloured area, for example, transparent red for l and transparent purple for s. AICl = −818.40 and AICs = −463.34. The random averaged for each participant and condition. All details factor (participant) explained the 16.8% of the about these models are reported in Appendix C. variability of data that is not explained by the fixed The two fitted models are similar in the sense factors along the l axis, and the 18.0% along the s that both show significant interactions between all axis. Interestingly, we did not include the trials as a chromatic and luminance channels. Indeed, along random factor because the model became singular, that the l axis, we observe a main effect of ConditionL is, this factor made the model more complex, but did (F (1, 265.91) = 33.12, p < .0001) and ConditionY not improve it. Therefore, all the observations were (F (4, 265.76) = 39.56, p < .0001), indicating that Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 7 Figure 3. Brightness induction estimation, that is, luminance difference between the comparison and the test rings (B), for every condition. Error bars are standard error of the means. Positive values B > 0 means that the test ring was perceived brighter than its luminance, and negative values B < 0 indicate that it was perceived darker. For B = 0, the luminance of the test and the comparison rings are equal, that is, no brightness induction. In this figure, we can observe that a chromatic surround induces brightness contrast (i.e., B = 0) in almost all conditions (negative values in the dark conditions Y < 0, and positive in the bright conditions Y > 0). the chromatic induction mainly depends on the Therefore, the chromatic induction along the l axis activation of l and Y channels. Nevertheless, significant depends on the interaction between all channels. interactions exist between l and s, F (2, 265.89) = 18.83, In a similar fashion, a main effect of ConditionL, p < .0001, l and Y , F (4, 265.53) = 8.02, p < .0001, F (2, 238.12) = 12.19, p < .0001, and ConditionY, and s and Y channels, F (8, 265.64) = 2.12, p = .0346. F (4, 266.91) = 17.91, p < .0001, have been observed in Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 8 the chromatic induction along the s axis. In contrast the test stimulus (Figure 1), the surround formed with the previous model, the triple interaction between a luminance uniform annulus, therefore, it is not ConditionL, ConditionS, and ConditionY is also surprising that the test shifted away from the luminance significant, F (8, 266.44) = 6.57, p < .0001. Again, we of the surround (brightness contrast). This can be can conclude that chromatic induction along the s axis observed where the test ring is perceived darker in the depends on the values of the lsY channels. dark conditions (Y = −10: B = −1.49 ± 0.76, The post hoc analysis of the model along the l t[82] = −17.92, p < 2.2e − 16; and Y = −5: axis (red line in Figure 2) shows that, although the B = −1.67 ± 0.83, t[82] = −18.22, p < 2.2e − 16), interaction between ConditionL and ConditionS and brighter in the bright conditions (Y = 10: is significant, color induction effect is similar for B = 0.86[2.25], V = 2925, p = 1.57e − 08). the different s conditions. That is, the effect do Surprisingly, at equiluminance, the test ring is not vary that much from top to bottom rows perceived darker (B < 0) than Y = 20 cd/m2 in left or right columns (e.g., −l/5 vs −l/+s/5: (B = −0.84[2.28], V = 304, p = 7.45e − 10), but t − ratio[274] = −1.49, pad j = .3420; −l/5 vs −l/−s/5: this difference is more enhanced in the diagonal t − ratio[274] = 0.91, pad j = .6150). Exceptions occur (B = −1.66) than in the cardinal conditions in −l/−10 vs −l/+s/−10: t − ratio[276] = −2.51, (B = −0.13, W = 1195, p = 6.14e − 06). pad j = .0205; and +l/ [−10] (+l/ [−10] vs +l/+s/−10: Interestingly, only in +s/0 and −s/0 we do not observe t − ratio[276] = 3.33, pad j = .0023 ; +l/ [−10] vs brightness induction at equiluminance. +l/−s/−10: t − ratio[276] = −3.31, pad j = .0023), where significant differences were observed. Furthermore, we want to stress that, although striped surrounds were used, several chromatic conditions such as −l/<0 Discussion and −l/−s/<0 induced color contrast instead of color assimilation. The use of equiluminant stimuli to study color In contrast, the post hoc analysis of the model induction is not new. In particular, several authors along the s axis reveals that chromatic induction along used them to conclude that the Kirschmann’s Third the s axis (purple lines in Figure 2) depends on the l Law (Kirschmann, 1891) rules the color contrast effect condition. That is, the color induction effects varies from (Gordon & Shapley, 2006; Faul et al., 2008; Xing left to right panels in top and bottom rows, being the et al., 2015). Although in these studies the authors strongest assimilation in +s/−10 (+s/−10 vs −l/+s/−10: presented uniform surrounds, color induction effect t − ratio[277] = −5.36, pad j < .0001; +s/−10 vs has also been measured in equiluminant stimuli with +l/+s/−10: t − ratio[277] = 4.59, pad j < .0001), and striped surrounds (Fach & Sharpe, 1986; Smith et al., −s/10 (−s/10 vs −l/−s/10: t − ratio[277] = −4.45, 2001; Cerda-Company & Otazu, 2019). Several authors pad j = .0001; −s/10 vs +l/−s/10: t − ratio[277] = 4.40, concluded that the spatial frequency of the stripes is a pad j = .0001). Interestingly, in both cases, the strongest key factor to induce color assimilation (Fach & Sharpe, assimilation effect is observed when the l channel is not 1986), and that a transition from color contrast with activated, and the effect is dramatically decreased when color assimilation can be produced by doing the stripes it is. thinner and thinner (Smith et al., 2001). Regarding our initial hypothesis, at equiluminance, In the present work, we have not studied the effect we never observed color assimilation in neither cardinal of the spatial frequency on color assimilation, but we nor diagonal conditions. In fact, in this luminance studied the effect of the activated pathways. The effect condition we always observed no color induction, of luminance on color assimilation has been slightly except for −l/0 where color contrast was induced. studied in striped stimuli (De Weert & Spillmann, 1995; Cao & Shevell, 2005; Cerda-Company et al., 2018), and more studied using the watercolor effect (Pinna, 1987; Brightness induction Pinna et al., 2001; Devinck et al., 2005, 2006; Gerardin et al., 2018). De Weert and Spillmann (1995) studied the As reported in Cerda-Company et al. (2018), cardinal effect of luminance differences (with an equiluminant conditions (+l, −l, +s, −s) not only induced chromatic condition) on a colored background with red and green induction, but they induced a small brightness inducers. They concluded that the color assimilation induction. Let B = Y c − Y t be the luminance depends on the luminance difference (with no color difference between the comparison (Y c ) and the test induction at equiluminance), and that this effect also ring (Y t ). In the present study, a brightness induction depends on the polarity of this luminance difference, effect (Figure 3) is present at those points where B inducing color assimilation when the target was brighter differ from zero. For nonequiluminant conditions, than the inducers. In line with the former observation, a small brightness contrast was observed except for several studies observed a weaker color assimilation Y = 5 (B = 0.1[1.72], V = 1805, p = .4978). In induced by equiluminant inducers, suggesting that color Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 9 assimilation (at least in the Watercolor effect) is the turn, on the K pathway, than vice versa. In that sense, result of a luminance-dependent mechanism (Devinck Cl (Figure 2) has less variation from bottom (−s) to et al., 2005, 2006; Gerardin et al., 2018). Although top (+s) conditions than Cs from left (−l) to right (+l) our stimuli configuration is significantly different, we conditions. also observed no color assimilation at equiluminance, Our interpretation assumes that the site of the effects and that the effect depends on the polarity of the is cortical (Zaidi et al., 1992; Rossi et al., 1996; De luminance difference, with a weak color assimilation Weert & Kruysbergen, 1997; Zaidi, 1999; Shapley & in +l/[>0]. Similar results were observed by Cao and Hawken, 2002; Cao & Shevell, 2005), but the results Shevell (2005). They measured color induction in a in Figure 2 show that color induction is not easy to wide range of chromatic conditions and in two different be explained by low level mechanisms, mainly because luminance conditions (with the target either darker the effect does not only depend on the values of l, s or brighter than the inducers). Our work is similar or Y , but also on a complex combination of them. As to the latter one in the sense that the target is always observed in previous studies, color induction occurs the EEW and we spread the chromaticities of the along the different color axes (i.e., different angles) of inducers around the target in the MacLeod–Boynton the color space, with selective changes for particular colorspace. Specifically, because they did not define an colors: the natural color distributions, and the daylight equiluminant condition, they evaluated the interaction blue–yellow color axis (Webster et al., 2002; Klauke & between two or three pathways. In their study, they Wachtler, 2015). These observations suggest that color observed that the +s and −s conditions are more likely induction could be not only a consequence of low-level to induce color assimilation or no induction than +l processes, but also owing to high-level processes. These and −l conditions, as observed in our results. selective changes are also observed in Figure 2, where +s Regarding our initial hypothesis, we expected to and −s conditions (which could be considered similar observe color assimilation at equiluminance in diagonal to the daylight blue–yellow color axis) are completely conditions (−l/+s/0, +l/+s/0, −l/−s/0 and +l/−s/0), different between each other, and completely different when both chromatic K and P pathways were activated. to the rest. In contrast, both −l/+s and +l/+s conditions Our results do not support the hypothesis, because are similar, but slightly different to −l/−s and +l/−s. the observed color induction is not stronger than the Furthermore, color contrast (C < 0) is mainly JND. Therefore, the influence of chromatic pathways observed in −l condition, which could be approximately between each other is not strong enough to induce related to foliage color. All these selective changes in color assimilation. In fact, color assimilation was only color induction for particular chromatic conditions observed in those conditions where the luminance could suggest that color induction can be affected by M pathway was activated (e.g., Cl > 0 in −l/+s/10 high-level mechanisms. Whether the influence could and +l/−s/10, and Cs > 0 in −l/+s/−10, +s/−10, be through a top–down feedback influence or through +l/+s/10), with the chromatic pathways influencing some neural mechanisms present in higher level areas is each other when it was activated (the results depend on an open question. the interaction between ConditionL, ConditionS, and The results in Figure 3 show that chromatic ConditionY). information in the surround area influences the One possible explanation is that a mutual inhibition– brightness perception of the test ring. That is, chromatic like mechanism does not exist between chromatic variation in the surround can induce brightness pathways. Indeed, one possible interpretation could induction. This finding goes inline with Lotto and be that they indirectly influence each other through Purves (1999), who showed that multicolored chromatic the luminance pathway, that is, a chromatic pathway surrounds generate stronger brightness induction influences the luminance pathway and this one, in than uniform ones. Interestingly, we observed that, at turn, influences the other chromatic pathway. This equiluminance, no brightness induction is induced when can be observed in Cs for +s/−10 (K pathway), the P pathway is not activated (+s and −s conditions). which is dramatically decreased when the P pathway Furthermore, not only the chromatic variability of the was activated (−l/+s/−10 and +l/+s/−10 conditions). inducers influences the brightness induction, but also According to this interpretation, when P pathway the luminance difference between the target and the first was activated (−l/+s/−10 or +l/+s/−10 conditions) it inducer (the Y ). In a previous experiment, Hong and inhibited the M pathway and, as a consequence, the M Shevell (2004) concluded that the luminance context pathway could not inhibit as much the K pathway. In influences the brightness induction on the target region. contrast, in +s/−10, the M pathway could inhibit the K If Y did not affect the brightness induction, we would pathway because the P pathway was not inhibiting it. observe a diagonal distribution in Figure 3, with a In addition, we observed different behaviors for the shift owing to the influence of chromatic variability P and K pathways. Although this observation is not (Lotto & Purves, 1999). Hence, because we observe new (Cao & Shevell, 2005; Cerda-Company et al., 2018; that shifting for the −l and +l conditions, we conclude Cerda-Company & Otazu, 2019), it suggests that the P that the degree of brightness induction depends on pathway has more influence on the M pathway and, in both the chromatic variability of the surround and Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 10 the luminance difference between the target and the surround. Conclusions The brightness induction (B in Figure 3) is different in +s/0 compared with both −l/+s/0 and +l/+s/0, From the results presented here, we can conclude that suggesting that the P pathway (when activated) modifies both luminance and chromatic conditions influence the activity of M pathway. This observation could the color assimilation effect, being the luminance support the possibility that the activation of the P differences a key factor. Indeed, we hypothesized that pathway could influence the M pathway and this, in activating both chromatic pathways (and deactivating turn, could modify the response of the K pathway. the luminance one), we would find color assimilation, But, if the P pathway simply inhibited or enhanced if a mutual inhibition–like mechanism exist between M pathway, we would have observed a change in the the chromatic pathways. Our results do not support slope of the curve. Because we do not observe a slope this hypothesis; therefore, it is unlikely to suggest change but a shifting, we cannot conclude that the P the existence of a mutual inhibition–like mechanism pathway either enhances or inhibits the M pathway between chromatic pathways. Nevertheless, our results (which depends on the signs of both B and Y ). suggest that chromatic pathways influence each other Nonetheless, a clear influence of P over M pathway through the luminance pathway. When all the visual is observed. This influence is a reduction (negative pathways are activated, a chromatic pathway influences shifting) of the absolute value of the brightness. Hence, the luminance one through the mutual inhibition to clarify the real nature of the influence of P on mechanism and, in turn, the latter pathway influences M pathway, a more detailed, future study would be the other chromatic one through the mutual inhibition necessary. mechanism. Furthermore, it seems that the influence of Some properties of visual stimuli used in this study the parvo- on the koniocellular pathway, through the are not comparable with some previous studies. For magnocellular pathway, is stronger than the opposite, example, Shevell and Monnier (2005) showed that and that color assimilation is stronger along the s than chromatic assimilation is maximum for rings of a along the l chromatic axes of the MacLeod–Boynton spatial frequency equal to 3.3 cpd. Because the aim colorspace. of the present study is the comparison of the new In our results, we observed a small brightness diagonal conditions against the existing cardinal ones induction effect that could be explained by the (Cerda-Company et al., 2018), we have used the same chromatic variations of the inducers, but as discussed visual stimuli (∼ 2 cpd). Considering the objective of before, more future work in this direction would be the present study, we need a stimuli that are able to interesting. generate either assimilation or contrast just by changing Keywords: color vision, color assimilation, color the luminance of the test ring and/or the chromaticities induction, psychophysics, mutual inhibition of the inducers. Hence, although a spatial frequency of 3.3 cpd could induce stronger assimilation effect, it is not clear whether it would induce a chromatic contrast effect. Another property is that our stimuli do not have Acknowledgments the same number of inducers at every side of the test ring. Our designed considered four and six inducer The authors thank all the participants for their rings at each side. Because previous studies used four valuable time. rings at each side (Monnier & Shevell, 2003, 2004; Shevell & Monnier, 2005), we consider that the effect of Supported through the research projects: Grant them on the results is negligible. PID2020-115734RB-C21 funded by MCIN/AEI/ As a future work, it would be interesting to study 10.13039/501100011033 and Grant DPI2017-89867-C2- whether the brightness induction effect observed 1-R funded by MCIN/AEI/10.13039/501100011033/ in our results is due to the brightness differences and FEDER Una manera de hacer Europa, by the produced by the equiluminant stimuli or by the Secretaria d’Universitats i Recerca del Departament chromatic variation of the inducers. We know that d’Empresa i Coneixement de la Generalitat de equiluminant stimuli could have brightness differences, Catalunya through 2017-SGR-649, and CERCA and equibrightness stimuli could have luminance Programme/Generalitat de Catalunya. differences. Therefore, conducting similar experiments, but using equibrightness instead of equiluminant Commercial relationships: none. stimuli, could explain the origin of this effect. If Corresponding author: Xavier Otazu. chromatic variation accounts for the brightness Email: xotazu@cvc.uab.cat. induction, both equiluminant and equibrightness Address: Computer Vision Center and Computer stimuli would show brightness induction. In contrast, if Science Department, Edifici O, Campus UAB, brightness (but not luminance) differences accounts for Cerdanyola del Valles (Bellaterra), 08193 Barcelona, this effect, the brightness induction would be negligible. Spain. 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Lateral interactions within color mechanism and spatial frequency selectivity. Vision Research, in simultaneous induced contrast. Vision Research, 45(9), 1147–1154. 32(9), 1695–1707. Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 13 Appendix A: Results in MacLeod–Boynton space Figure 4. Same results as in Figure 2, but shown in the MacLeod–Boynton color space. Error boxes are standard error of means. Achromatic EEW is shown as an asterisk. Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 14 Appendix B: Individual results Figure 5. Individual results on all the defined conditions. Data on cardinal axis (e.g., +l, −l, +s, −s,) are extended from Cerda-Company et al. (2018) (new participants are indicated by thick lines), and results on the diagonal axis (e.g., +l/+s, +l/−s, −l/+s, −l/−s) have been obtained in the present study. Journal of Vision (2022) 22(6):10, 1–15 Otazu & Cerda-Company 15 Appendix C: Statistical models Type III analysis of variance table with Kenward–Roger’s method Color inductionl Mean Sq NumDF DenDF F-value p value signif. ConditionL 0.1160 1 265.91 33.12 2.38e-08 *** ConditionS 0.0013 2 231.47 0.38 .6856 ConditionY 0.1385 4 265.76 39.56 <2.2e-16 *** ConditionL:ConditionS 0.0659 2 265.89 18.83 2.26e-08 *** ConditionL:ConditionY 0.0281 4 265.53 8.02 4.03e-06 *** ConditionS:ConditionY 0.0074 8 265.64 2.12 .0346 * ConditionL:ConditionS:ConditionY 0.0050 8 265.53 1.43 .1827 Color inductions Mean Sq NumDF DenDF F-value p value Signif. ConditionL 0.1347 2 238.12 12.19 9.085e-06 *** ConditionS 0.0243 1 266.42 2.20 .1394 ConditionY 0.1977 4 266.91 17.91 4.847e-13 *** ConditionL:ConditionS 0.0637 2 266.57 5.77 .0035 ** ConditionL:ConditionY 0.0421 8 266.76 3.81 .0003 *** ConditionS:ConditionY 0.2616 4 266.48 23.70 <2.2e-16 *** ConditionL:ConditionS:ConditionY 0.0725 8 266.44 6.57 7.958e-08 *** Signif. codes: 0 ’***’, 0.001 ’**’, 0.01 ’*’, 0.05 ’ ’ Table 2. Statistical details of color induction linear models with mixed effects.