Slow updating of the achromatic point after a change in illumination

Abstract

For a color constant observer, the color appearance of a surface is independent of the spectral composition of the light illuminating it. We ask how rapidly color appearance judgments are updated following a change in illumination. We obtained repeated binary color classifications for a set of stimuli defined by their reflectance functions and rendered under either sunlight or skylight. We used these classifications to derive boundaries in color space that identify the observer's achromatic point. In steady-state conditions of illumination, the achromatic point lay close to the illuminant chromaticity. In our experiment, the illuminant changed abruptly every 21 s (at the onset of every 10th trial), allowing us to track changes in the achromatic point that were caused by the cycle of illuminant changes. In one condition, the test reflectance was embedded in a spatial pattern of reflectance samples under consistent illumination. The achromatic point migrated across color space between the chromaticities of the steady-state achromatic points. This update took several trials rather than being immediate. To identify the factors that governed perceptual updating of appearance judgments, we used two further conditions, one in which the test reflectance was presented in isolation and one in which the surrounding reflectances were rendered under an inconsistent and unchanging illumination. Achromatic settings were not well predicted by the information available from scenes at a single time point. Instead, the achromatic points showed a strong dependence on the history of chromatic samples. The strength of this dependence differed between observers and was modulated by the spatial context.

Figure 1

Examples of stimuli. The left panel shows background and test under sunlight (“global”), the middle panel shows the test under sunlight and the background unilluminated (the simulated illuminant was a zero-energy-spectrum, “isolated”) and the right panel shows the test under skylight and background under Illuminant C (“inconsistent”). Note that variations in display and printing processes make it impossible to exactly reproduce here the colours presented under experimental conditions.

Figure 2

Features of the sequences of trials in the three experimental conditions. The background colour wash and test illuminant letter indicates the simulated illumination on the test patch: sunlight (A) or skylight (B). The number with each illuminant letter indicates the number of trials since the test patch illumination changed, which happened every 10^th trial. The three conditions are matched in the sequence of illumination on the test patch, but differ in the illumination of the background region. This was (i) the same as the test patch in the global condition, (ii) black in the isolated condition, and (iii) Illuminant C in the inconsistent condition. The stimulus examples in this figure have been cropped so that the test patch is clear.

Figure 3

Coloured crosses represent the material chromaticities (under skylight in the top panels and sunlight in the bottom panels), projected onto an equiluminant plane of MB-DKL space. These points are coded according to an observer’s classifications (as red or green in the left-hand plots and as yellow or blue in the right-hand plots). Black lines are examples of the intersection of fitted classification boundaries and the mean-luminance equiluminant plane. The chromaticity at which the red-green and blue-yellow classification boundaries intersect locates the chromaticity that is equally likely to be classified as red, green, yellow or blue. We infer this to be an observer’s achromatic point.

Figure 4

Migration of the achromatic point in all experimental conditions. Each panel shows a section of the MacLeod-Boynton Chromaticity Diagram and indicates the path taken by the achromatic point as it moved following a change of illuminant from skylight to sunlight (orange lines) and sunlight to skylight (blue lines). The squares show the position measured in the trial immediately after the switch, and the circles show the position in the tenth trial after the switch. Data are shown in separate plots for each of the three observers (KAD: left column, RJL: middle column, WS: right column), in each of the three experimental conditions (global: top row, isolated: middle row, inconsistent: bottom row). The crosses show the position of the achromatic point measured in the steady-state conditions under one illuminant (orange: sunlight, blue: skylight).

Figure 5

Chromaticity coordinates of the simulated CIE Illuminant C (grey symbols), sunlight (orange symbols), skylight (blue symbols) illuminants and of the achromatic points measured in our steady-state conditions, under prolonged viewing of constant illumination conditions over the whole stimulus by each of the three observers. The chromaticities of the sunlight and skylight illuminants are joined with a dashed line to indicate the vector along which colour constancy is calculated (described in text).

Figure 6

Data from the global condition. Colour constancy index C, calculated along a vector joining the steady-state achromatic points for the two illuminants, plotted against number of trials since an illuminant shift t (2.1s inter-trial interval). The colour of the symbols and lines represents the illuminant chromaticity relative to which the constancy index was calculated: sunlight (yellow) or skylight (blue). Filled symbols indicate the constancy index calculated relative to the illuminant chromaticity used on that trial, and open symbols represent the index calculated relative to the other illuminant, for comparison. The shaded regions of the plot indicate the time-course of the illuminant switch: sunlight (yellow) or skylight (blue). Presentations are labelled such that A_n is the nth trial after a change in simulated illuminant to sunlight, and B_n is the nth trial after a change in simulated illuminant to skylight.

Figure 7

Data from the isolated condition. Colour constancy C index plotted against t, as in Figure 6. The colour of the shaded background now indicates the simulated illuminant over the test patch only.

Figure 8

Data from the inconsistent condition. Colour constancy C index plotted against t, as in Figure 6. The colour of the shaded background indicates the simulated illuminant over the test patch, whilst the illuminant over the background ellipses was Illuminant C. The green horizontal lines show the relative location of the steady-state achromatic point measured under Illuminant C, relative to the steady-state achromatic point measured under either sunlight or skylight as indicated by the shaded background.

Figure 9

Amplitudes (top panel) and phases (bottom panel) of the first fundamental Fourier components of the measured constancy indices, relative to sunlight, over the course of the 20 possible temporal positions (C_A(t)).