Figure 1.
Brightness and Darkness Induction
Viewed from left to right, the grey disks appear to vary from dark to bright, even though they share the same luminance value. This induction effect arises because the background luminance varies along a gradient, leading to a change in the polarity and magnitude of contrasts formed against the disks. Brightness refers to the perceived luminance, or grey shade, of the disk when the luminance of the disk is greater than that of the background. Conversely, darkness is defined as the perceived luminance of the disk when the luminance of the disk is less than that of the background. The conventional way of thinking about this perceptual effect is that darkness is simply the negative of brightness, meaning that all the grey shades above are contained in a 1-D continuum, like real numbers along a number line.
Figure 2.
Stimuli Used in the Experiments
We are interested in the question of how to describe, for example, the achromatic color percept of a ring surrounded by a dark disk inducing brightness and a white background inducing darkness. Previous work, summarized in the main text, suggests that achromatic color space is composed of two or more dimensions. Here we argue that the achromatic colors of the above rings are described by separate brightness and darkness dimensions.
(A) Experiment One. Stimuli composed of a background brighter than both the reference (left side) and matching (right side) rings. A horizontal luminance gradient was rendered along the midline of the background such that the contrast formed by disk and background was different on the two sides (the gradient did not extend to the rings). Note that the contrast formed by the ring and disk on the reference side was of the opposite polarity to the contrast formed by the ring and background.
(B) Similar to (A) except that the background was darker than the rings, whereas the disks were brighter than the ring. In each stimulus, the background and central disk induced brightness or darkness into the rings by means of simultaneous contrast.
(C,D) Experiment Two. The polarity relationships reversed between successive presentations of reference and matching displays. See text for details of the experiments.
Figure 3.
Possibility of Match Plotted against the Contrast Difference between Reference and Matching Displays
Average data from six subjects (error bars indicate standard errors of the mean). With bright backgrounds (left side), subjects adjusted the luminance of the matching ring to be either much higher (yellow data points in white region) or much lower (blue data points in white region) than the luminance of the reference ring (always at 30 cd/m2). The dotted grey lines denote perfect darkness matches, indicating that subjects weighted darkness more heavily than brightness in this situation. With dark backgrounds (right side), subjects set the matching luminance close to the reference luminance (red and green data points in white region). In both cases, however, subjects rated matches as progressively less possible as the contrast difference between reference and matching sides of the displays increased (data points joined by continuous lines in grey region). This implies that brightness and darkness constitute dimensions of achromatic color space. We modeled this 2-D space by estimating brightness and darkness weighting factors from the luminance data (model fits are the continuous lines in the white region) and then predicting the possibility ratings from the fitted weights (dotted lines in the grey region). The model predictions agree reasonably well with the data. Symbols representing the stimuli are included to assist understanding of the data and should not be considered as realistic representations.
Figure 4.
Brightness and Darkness as Perceptual Dimensions
(A–D) Achromatic color space consisting of brightness and darkness dimensions. For each luminance value of the matching ring, we plot the corresponding grey shade as a point in the 2-D grey space. Horizontal dotted lines denote perfect darkness matches. Dotted colored lines represent the gamut of grey shades available in the single dimension of luminance space along which subjects can physically adjust the matching ring. Solid grey lines are the approximate vector projections of the grey shade associated with the reference ring onto all matching displays. The intersections of these projection lines with the lines-of-adjustment roughly indicate the grey shades that subjects would set if they were minimizing the vector between reference and matching rings. Subjects did not appear, however, to minimize this vector. This is particularly evident with brighter backgrounds (A,C), where subjects placed far more weight on matching the darkness component than the brightness component. The different scales for brightness and darkness in (A) and (C) provide further evidence that subjects weighted darkness more heavily than brightness.
Figure 5.
Model Predictions for the Reversed-Polarity Experiment (Experiment Two)
The model predicts that subjects will rate ring pairs as identical only when the grey shades associated with reference (colored disks) and matching (black squares) coincide in grey space (A,C). Otherwise, the model predicts that perfect matches will not be possible (B,D). The black square in (D) does not coincide exactly with the position of a yellow disk, although it is very close.
Figure 6.
Results of the Reversed-Polarity Experiment (Experiment Two)
Average data from six subjects (error bars indicate standard errors of the mean). The model correctly predicts the data curves associated with the two control conditions (A,C). The data curves for the reversed-polarity conditions are consistent with the predicted skewness (B,D), and to a lesser degree with the amount of mismatch.
Figure 7.
Redness and Greenness as Perceptual Dimensions
(A) Stimulus conditions giving rise to mixed color percepts composed of complementary local and edge-induced colors.
(B) The x- and y-axes correspond to the CIE-designated redness and greenness of the reference and matching displays, respectively. The matching (or adjustable) disk is matchable to the reference disk when the reference disk is green (the red matching background adding greenness to the matching disk) or more red than the matching background (the red matching background subtracting redness from the matching disk. No match can be made, however, when the disk is less red than the matching background. We claim that this is because the matching background adds greenness to the matching disk, which remains separate from the local redness. As there is no corresponding color induced from the grey reference background into the reference disk, only a partial color match is possible. Data adapted from [18].