Judgments about the intensity of the illumination are influenced by the association between colour and luminance in the scene

In order to judge whether a surface that one is looking at is white or grey, one needs to consider the intensity of the illumination. We here show that people do not simply use the maximal luminance in the light from the scene as a measure for the intensity of the illumination but also consider how luminance and chromaticity are associated. We suggest that they take into account that there are physical limitations to the luminance that reflecting surfaces can achieve at high chromatic saturation. These limitations arise because chromaticity is the result of surfaces selectively reflecting light of different wavelengths, so that the luminance of the illumination must be higher than that of the brightest patch in the scene if that patch is not white. Introduction In daily life we are normally more interested in judging surface reflectance than in judging the intensity of the illumination. For judging chromaticity and saturation an emphasis on the ratio of stimulation of different kinds of cones helps remove influences of the intensity of the illumination [1][2]. Contrasts between adjacent surfaces are also insensitive to changes in the level of illumination, but for judging a surface’s lightness we need to somehow consider the intensity of the illumination. How could we otherwise tell whether the walls of our room are white and the illumination is dim, or the walls grey and the illumination bright? In simple displays we cannot: the brightest surface is simply perceived as white (e.g. [3]). However, in complex scenes it is not always that simple [4][5]. We here examine one potential factor in retrieving the intensity of the illumination: the chromaticity of the brightest surfaces. Previous studies have shown that the correlation between luminance and chromaticity is used to account for the colour of the illumination [6][7], the reasoning being that surfaces that reflect the colour of the illumination well are likely to reflect a lot of light. At the extreme, white objects, if present, would reflect all of the light falling on them, and would therefore not only have the highest luminance but the light they reflect would provide a direct estimate of the illumination at that position. We here examine a similar issue in judging the intensity of the illumination. A coloured surface is one that selectively reflects certain parts of the spectrum whereas a white surface is one that reflects as much light as possible. Since reflection can only reduce the intensity of the light at each wavelength, very bright surfaces are unlikely to have very saturated colours, because for any given illumination there is a physical limit to the combinations of luminance and chromaticity that can arise by diffuse reflection alone. The colours on this limit form a closed surface in colour space and are normally referred to as the optimal colours [8]. The constraints on the possible relationships between luminance and chromaticity should influence our judgments. If the highest luminance in the light reflected from a scene is from a surface that is clearly white, the luminance of the light reflected from that surface provides a reasonable estimate of the intensity of the illumination. However, if the highest luminance from the scene is from a surface that is, for instance, clearly blue, the intensity of the illumination must be higher than the luminance of the light reflected from that surface, because the surface does not reflect all the light falling on it at longer wavelengths (which is why it is blue). In other words, the maximal perceived saturation for purely reflecting surfaces can only be obtained for middle lightness, so the luminance of saturated coloured surfaces in a complex scene can be used to judge the level of illumination even when such surfaces do not have the highest luminance in the scene, and reliable estimates can be obtained even when there is no truly white surface available. We test whether the relationship between luminance and chromaticity influences our judgments of surface lightness by determining the luminance at which subjects report a transition between grey and white for scenes with identical distributions of luminance and chromaticity, but different relationships between luminance and chromaticity. We find differences, showing that subjects do consider this factor. Methods Observers sat at a distance of 183 cm from a 48 by 31 cm screen (Sony GDM-FW900 Trinitron CRT; 1280 by 1024 pixels; 100 Hz; 8 bits per gun; calibrated with a Minolta CS100A Chroma Meter). The screen was filled with a regularly tiled background of 12 by 8 squares, each with sides of about 1 deg. On each trial, one of three sets of specially selected patterns of colour and luminance was assigned to the squares. We will refer to the selected set as the pattern, but note that the images varied across instances of the same pattern because the colours and luminances were assigned to the individual squares at random on each trial. A target square that was perceived to be achromatic (CIExy = [0.291, 0.328]; variable luminance) and that had the same dimensions as the tiles in the background was superimposed on the tiles 2s after the new colours and luminances were assigned to them. Subjects had to indicate whether the target square was grey or white by pressing the ‘g’ or ‘w’ key of a computer keyboard. A separate staircase procedure was used to estimate the luminance at which subjects’ judgments switched from grey to white for each of three kinds of patterns (the patterns are described in the next CGIV 2012 Final Program and Proceedings 321 paragraph). The room was dark except for the light from the screen. In order to understand how the luminances and chromaticities of our three patterns were designed it is easiest to start with the pattern in which there were coloured squares of maximal luminance (test condition; Figure 1). For the 24 squares of maximal luminance, one gun was set to maximum and the other two to zero (8 squares for each of the three possible combinations). The CIExyY coordinates of the three colours were [0.622, 0.347, 18.24 cd/m], [0.287, 0.595, 63.99 cd/m] and [0.144, 0.069, 8.68 cd/m], for red, green and blue squares, respectively. Another 24 squares had the same colours, but 1/3 of the luminance (again 8 per colour). The remaining 48 squares were grey (CIExy = [0.291, 0.328]) and had a luminance of 2/3 of the maximal luminance of one of the three colours (16 each). The second pattern (baseline condition) was matched to the first pattern both in luminance and chromaticity. This was achieved by switching between coloured and grey squares without changing the luminance. Thus there were squares with six grey levels (matching the coloured squares with maximum and 1/3 of the maximum luminance) and three kinds of coloured squares (each with 2/3 of the maximal luminance of the gun in question). In this way, both patterns had exactly the same distribution of luminance values and both had 16 red, 16 green, 16 blue and 48 grey squares. The third pattern (darker condition) was identical to the second, but the whole pattern was 5% darker (the luminance of each square was 95% of that in the baseline condition). Thirteen subjects (including one of the authors) each took part in one session that was divided into 30 blocks of 10 trials: 10 blocks for each condition. The blocks of the three conditions were presented in random order. Each block started with a 10 second presentation of the pattern without the target, but with the text “short break’ printed in black letters across the centre of the screen instead. The target was centred at one of the central grid of 5 by 3 intersections of four squares. Separate staircases were used to sample the appropriate target luminance for each condition. Each staircase started at a luminance of 63.6 cd/m. If the subject pressed the ‘w’ key the target’s luminance on the next presentation within the block (or on the first presentation of the next block for that condition) was decreased by 7%. If the subject pressed the ‘g’ key the luminance was increased accordingly. The main question was whether subjects would assume that the illumination was more intense in the test condition than in the baseline condition. In order to make sure that our method works, which would be especially relevant if we were to find no difference in the previous comparison, we also compared the baseline condition with the darker condition. For each subject and condition we determined the border between what he or she considered grey and what he or she considered white. To do so, we took all the data of the subject and condition in question and fit a cumulative normal distribution to the proportion of ‘white’ responses as a function of luminance. The fit was done more or less as proposed by Wichmann and Hill [9], but we removed the 2% least likely responses from each set to account for stimulus-independent errors, rather than fitting an additional parameter. The mean of the fit distribution indicates at what target luminance the transition from grey to white occurs. We evaluated whether subjects assumed that the illumination was more intense in the test condition than in the baseline condition by testing whether the transition was at a higher value in the former. We evaluated whether our method works by testing whether the transition was at a higher value for the baseline condition than for the darker condition. Both comparisons were done with paired, one-tailed t-tests. Results Figure 2 shows an example of one subject’s data with the fit cumulative normal distributions. The curve for the test condition is clearly shifted to the right with respect to the curve for the baseline condition (by about 4.5 cd/m), indicating that for this subject a higher target luminance was required for the target to appear to be white in the test condition. This is consistent with assuming that the illumination is more intense in the test condition. Similarly, the curve for the baseline