Do common mechanisms of adaptation mediate color discrimination and appearance? Uniform backgrounds

Abstract

Color vision is useful for detecting surface boundaries and identifying objects. Are the signals used to perform these two functions processed by common mechanisms, or has the visual system optimized its processing separately for each task? We measured the effect of mean chromaticity and luminance on color discriminability and on color appearance under well-matched stimulus conditions. In the discrimination experiments, a pedestal spot was presented in one interval and a pedestal + test in a second. Observers indicated which interval contained the test. In the appearance experiments, observers matched the appearance of test spots across a change in background. We analyzed the data using a variant of Fechner's proposal, that the rate of apparent stimulus change is proportional to visual sensitivity. We found that saturating visual response functions together with a model of adaptation that included multiplicative gain control and a subtractive term accounted for data from both tasks. This result suggests that effects of the contexts we studied on color appearance and discriminability are controlled by the same underlying mechanism.

Fig. 1

Two hypothetical response functions. Each function corresponds to a different context (e.g., different chromaticity of background) and plots a mechanism's response as a function of stimulus strength (e.g., test spot contrast). Equality of appearance across the context change is predicted by equality of mechanism response, so that the stimuli indicated by the downward arrows would be predicted to match in appearance. Discrimination thresholds (i.e., test increment required to discriminate between a pedestal presented alone and a pedestal plus the test) are predicted to be inversely proportional to response function slope.

Fig. 2

Intensity response model with expected asymmetric matches and discrimination performance. The x axes in panels A,C,D, and E test stimulus intensity. Panel C shows the response model [Eq. (2)]. The y axis is the magnitude of the response. The two curves in Panel C are the response functions for one mechanism in two adapted states. The gray curve represents expected response in a gray context and the black curve represents expected response in a green context. The difference between the two curves is a difference in the gain-and-subtractive parameters [g and s in Eq. (2)]. Panel B shows the Gaussian response distributions for four test intensities (I₁,I₁+ΔI_1,75,I₂,I₂+ΔI_2,75 where ΔI_i,75 is the incremental intensity that yields 75% correct performance) presented in the green context. The x and y axes are probability and response magnitude, respectively. Panel D shows two psychometric curves for pedestals I₁ and I₂. These curves are the expected discrimination performance derived from the model characterized in panels B and C for the response function adapted to the green context. Panel E shows the increments expected to yield 75% correct (JNDs) as a function of pedestal intensity derived from the response model in B and C. Finally, Panel A shows the expected performance in an asymmetric matching task with the tests presented in the green context and the matches set in the gray context. The height of the shaded rectangle running the width of the x axis represents absolute threshold for a spot presented against a gray background (${\mathrm{JND}}_{\text{gray}}^0$, which is equivalent to the point where the JND_gray curve in Panel E intersects the y axis). The width of the shaded rectangle running the height of the y axis represents absolute threshold for a spot presented against the green background ${\mathrm{JND}}_{\text{green}}^0$. Any test-match pairs in this gray shaded region would be extremely difficult to obtain.

Fig. 3

Spatial and temporal profiles of test spots. The top panel shows the spatial profile of test spots in the discrimination and matching experiments. The bottom panel shows the temporal parameters of a trial in the discrimination experiment. The small white spots indicate frame timing (vertical blanking). The temporal profile in the matching experiment was the same except that only one interval was used.

Fig. 4

JMH's results from discrimination and matching experiments for LM tests and backgrounds that varied in their LM input. The top six panels are discrimination thresholds (JNDs) plotted as a function of pedestal intensity. The three left panels are JNDs for decrements and the three right panels are JNDs for increments presented on, from top to bottom, the Gray+LM, Gray and Gray−LM backgrounds. Error bars are 95% confidence intervals. The bottom panel shows asymmetric matching data for the same set of conditions. The x axis is the test excursion (i.e., the number of isomerizations expected from the test independent of the background) against the Gray+LM (circles) and the Gray−LM (triangles) backgrounds. The y axis is the match excursion from the gray background against which the matches were set. Error bars are standard error of the mean. Dashed and solid lines are results of model fits with parameters selected on the basis of both discrimination and matching data. These are fits for the gain-and-subtractive model of adaptation. Increments and decrements were fit independently but the p,q, and M parameters in Eq. (2) were yoked across adapting conditions. The raw psychometric and matching data underlying the points and model fits shown in this figure and Figs. 4-7 can be obtained at http://color.psych.upenn.edu/supplements/com_uniform/.

Fig. 5

QRS's results from discrimination and matching experiments for LM tests and adapting fields that varied in their LM input. Results are plotted in the same format as Fig. 4.

Fig. 6

JMH's results from discrimination and matching experiments for S-cone tests and adapting fields that varied in their S-cone input. Results are plotted in the same format as Fig. 4 except that values correspond to expected S-cone isomerizations.

Fig. 7

QRS's results from discrimination and matching experiments for S-cone tests and adapting fields that varied in their S-cone input. Results are plotted in the same format as Figs. 4-6.

Fig. 8

Error trade-off analysis for JMH's −LM test data in the Gray and Gray+LM adapting condtions. Central panel are results of the error trade-off analysis described in the text for the gain-and-subtractive model of adaptation. The x axis is the normalized negative log likelihood (−LL) of model parameters given the full complement of discrimination data from the Gray and Gray+LM adapting conditions (we plot the negative log likelihood so small values correspond to better fits, consistent with the sum-of-squared error metric used as a criterion for the matching data). The y axis is the normalized least-squared error (LSE) of model fits for the matching data in the same adapting conditions. The two left panels show the data that underlie the analysis presented in the central panel and are replotted from Fig. 4. The two right panels show the same data. The model fits in the two left panels are fits where model parameters were determined exclusively by the discrimination data. The gray star in the central error trade-off panel is the −LL, LSE combination corresponding to these fits. The model fits in the two right panels are fits where model parameters were determined exclusively by the matching data. The gray diamond in the central error trade-off panel is the −LL, LSE combination corresponding to these fits. The filled gray circles in the central panel are −LL, LSE combinations where both data sets were used to determine the model parameters. Each gray circle represents a −LL, LSE combination for a specific combination of weights to the matching and discrimination error. Higher points in the graph are from fits where more weight was given to maximize the likelihood of the parameters given the discrimination data than to minimize the sum-of-squared error for the model parameters given the matching data. Similarly, the more rightward points are from fits where more weight was given to minimize the sum-of-squared error for the model parameters given the matching data than to maximizing the likelihood of the parameters given the discrimination data.

Fig. 9

Error trade-off analysis for LM tests and adapting fields that varied only in their LM component. The top two panels are, from left to right, JMH's results from +LM tests on Gray and Gray−LM adapting fields and −LM tests on Gray and Gray+LM adapting fields. The bottom two panels are from the same conditions for QRS. Plotting conventions are the same as those for the central panel in Fig. 8. We have included results of the error trade-off analysis for the gain-only (open white symbols) model as well as the gain-and-subtractive (gray symbols) model.

Fig. 10

Same as Fig. 8 except for S-cone tests and adapting fields that varied only in their S-cone component.

Fig. 11

JMH's JND ratios for the split field versus uniform field conditions for LM increments presented against Gray and Gray−LM backgrounds. The x axis is isomerizations of the pedestal (same as lower right and middle right panels in Fig. 4). The y axis is the JND ratio for discrimination data collected on a uniform and split field. Open circles are JND ratios from the Gray adapting field and filled gray circles are ratios from the Gray−LM adapting field. Error bars are 95% confidence intervals determined by a bootstrap analysis.

Fig. 12

JMH's detection and matching results for LM-cone tests presented on adapting fields that varied only in their S component and S-cone tests presented on adapting fields that varied only in their LM component. The top two panels are detection thresholds plotted as a function of background intensity. The bottom two panels are results of the asymmetric matching task. The two left panels are results from LM-cone tests presented on backgrounds that varied only in the S-cone components. The two right panels are results from S-cone tests presented on backgrounds that varied only in their LM-cone component. The x axis in the top left panel is the expected number of S-cone isomerizations from the background light for the same area and temporal interval as the test stimuli, and the y axis is the expected number of isomerizations for an LM-cone test. Similarly, the x axis in the top right panel represents background LM-cone isomerizations and the y axis S-cone test isomerizations. Data points in these top two panels are the 75% thresholds determined by fitting the detection data with a cumulative normal. The x axis in the bottom left panel is the expected number of isomerizations for fixed LM-cone tests presented on either the Gray+S, Gray, or Gray−S adapting fields. The y axis is S-cone isomerizations for JMH's match settings against the gray background. Filled squares are from the symmetric matching conditions (where both the fixed test and adjustable match were presented on the Gray background). Open circles and filled diamonds are conditions where the fixed tests were presented against the Gray+LM and Gray−LM conditions, respectively. Error bars are standard errors of the mean. The convention for the bottom right panel is the same as for the bottom left panel except that the axes correspond to the expected isomerizations of S-cone tests.