Fig 1.
Assimilation and contrast in action (in the style of [17] Fig 1).
Up, left. Simultaneous contrast: the small patches on the left and the right are identical, but they tend to appear darker inside the yellow surround, lighter inside the dark surround. Up, right. Chromatic assimilation: the same grayish background tends to be blue or green depending on the color and spatial frequency of the grid covering it. Down. Synergy of both phenomena: the two central rings are identical, but are perceived as pink or orange when surrounded by concentric annuli with a purple/lime or lime/purple pattern.
Fig 2.
Color matching measures the influence of context over color perception.
The green color ctest is tested against a yellow surround in the test image Jtest. The observer changes the comparison color ccomp inside Jcomp until a match occurs at cmatch between the two central patches. Color induction is measured as the obtained shift.
Fig 3.
A typical color matching experiment.
Upper row, left to right. For each of the three pairs of (gray, yellow) large squares, the central patches have identical colors. Their HSL coordinates are (120°, 55%, 46%), (120°, 85%, 71%), (60°, 57%, 56%), respectively. The HSL color space is extensively used in computer graphics and defined in [21]. Lower row, left to right. One of the authors (A.S.) has modified the HSL coordinates of the left central patch, in order to obtain perceptually equal patches (as much as possible). This is called matching. We can see how far the “perceived” HSL are from reality: (138°, 55%, 39%), (140°, 41%, 59%), (66°, 29%, 54%). The reader probably does not perceive the two patches as perceptually equal, because matching is subject-dependent.
Table 1.
Mathematical notations.
Fig 4.
f and g functions, displayed on a 1D axis for illustration purpose.
The influence of c′ and r′ over c and r, respectively, depends on their position relative to (c, −c) and r. In color space, it is positive when c′ is closer to c, negative when it is closer to −c; in physical space, it is positive when r′ is an adjacent neighbor of r, and negative when it is a remote one.
Table 2.
Sign of the connectivity kernel ω.
Fig 5.
Using fixed Yellow test and Gray comparison surrounds (symbolized as squares in the figure) similarly to Fig 3, we obtain a vector field of shifts (ctest, cmatch) in the HSL space (symbolized as spheres and arrows). There is clearly a “yellow pushes towards blue” phenomenon, where contrast wins.
Fig 6.
Connectivity kernel in 3D physical and color space.
Left. W1 defined with r0 = 0 and c0 = 1. Right. W2 defined with r0 = 0 and c0 = .5. The color bar extends between −1 and 1, going from dark green (negative values, strong inhibition) to dark orange (positive values, strong excitation). We provide an interactive 3D animation of the connectivity kernels ω(r0, c0, ⋅, ⋅) for all values of in S1 File. For varying r0, the kernel is just spatially translated along r0. However, for varying c0, the positive and negative gaussian kernels in f follow c0 and −c0, collide when c0 goes through zero, then exchange of position when |c0| grows again.
Fig 7.
Cortical input and color sensations in 3D physical and color space.
Left. Cortical input H. Right. Color sensations a∞. In both subfigures, the color bar extends between 0 and 1, and is set so that small variations are easily seen. We provide an interactive 3D animation of the evolving activities a(⋅, ⋅, t) along the iterations of the fixed point algorithm in S2 File. The convergence is quite fast and 15 iterations are sufficient.
Fig 8.
Dynamics of the color neural field Eq (3).
The neural activities are plotted after a. one, b. two, c. thirty iterations, and convergence is reached after fifteen iterations. The red curve indicates the activity of hypercolumn r0 corresponding to the test stripe. Other blue curves correspond to spatial points ri located on surrounding stripes. Notice that only four and not eight different curves are seen, because of the axial symmetry artificially introduced to facilitate numerical computations, as explained in S2 Appendix. A video of the dynamics is provided in S1 Video.
Fig 9.
Our tuned model predicts color shifts from [18].
Left. Observer ‘MC’. Right. Observer ‘AZ’. Red dots indicate experimental data, while blue crosses stand for predicted matching comparison colors. The data has been averaged over three sets of experiments, as detailed in the original article. The ordinate corresponds to the color shift, expressed in coordinates with c = s − 1 . The abscissa i = 0, …, 7 refers to the test pattern: p/p, l/l, p/w, l/w, w/p, w/l, p/l, l/p, where p stands for purple, l for lime, w for white.
Fig 10.
Comparing color sensations for real and predicted matching color.
Left. Color sensations ,
and
. Right. Functions f and g for the regressed parameter value q = qMC. Right, up. Heatmaps for g and f. Right, down. Corresponding side views.
Fig 11.
Color matching is a projection.
Blue and green curves are as in Fig 10 and correspond to and
. After regression, the green one should be the nearest to the blue one with respect to the
norm, among all the curves
generated by the family of comparison images
(shown in gray).
Fig 12.
Our tuned model is able to reproduce nonlinear data from [17] Fig 3.
The blue and orange curves correspond to our predicted shifts along the tested chromaticity given by the absicssa. The data above and below the zero line correspond to a fixed purple/lime or lime/purple pattern, respectively. Red crosses indicate the means of shifts across four subjects for seven tested values, and stand as groundtruth (refer to [17] for details).
Fig 13.
Our model reproduces nonlinearity even when tuned to other data.
We use the parameter value qAZ corresponding to Fig 9 (right) while emulating the experiments of Fig 12.
Fig 14.
The color neural field model reproduces nonlinear shifts in the chromatic disk.
Left. 36 pairs of experimental data points (test and matching colors) in the HSL chromatic disk at constant luminance, resulting from averaging the shifts (refer to Data section and Fig 5). Right. Predicted results.