The human visual system has the ability to perceive approximately constant surface colors despite changes in the retinal input that are induced by changes in illumination. Based on computational analyses as well as psychophysical experiments, J. Golz and D. I. MacLeod (2002) proposed that the correlation between luminance and redness within the retinal image of a scene is used as a cue to the chromatic properties of the illuminant. However, J. J. Granzier, E. Brenner, F. W. Cornelissen, and J. B. Smeets (2005) found that the spatial extent in the field of vision that is relevant for the effect of the luminance-redness correlation on color appearance is very local and therefore questioned whether this scene statistic is used for estimating the illuminant. Here, I present evidence that the spatial extent is substantially more global than claimed by Granzier et al. and consistent with the hypothesis that this scene statistic is used for estimating the illuminant. It is further shown for two figural parameters of the stimuli that they influence the spatial extent and hence could have contributed to an underestimation of the spatial extent by Granzier et al. Finally, it is shown that the spatial extent relevant for the effect of mean surround chromaticity on color appearance is very similar to that found for the luminance-redness correlation.

Stimulus parameter | Experiment 1 | Granzier et al. (2005) |
---|---|---|

Size of display (width × height) | 40° × 31° | 16° × 16° (Experiment 1) 11° × 16° (Experiment 2) |

Size of surround elements | 1.5° (diameter) | 0.42° (edge length) |

Surround colors | >2000 different chromaticities | 2 different chromaticities |

Surround structure | Overlapping circles | Disjoint squares |

Relation test field/surround elements | Same form and size | Different form and size |

*l*,

*s*, luminance) of MacLeod and Boynton (1979) was used for representing the chromatic properties of the stimuli. The chromaticity values

*l*and

*s*are the luminance-normalized excitations of L and S cones respectively. The units for L, M, and S cone excitations were chosen such that

*l*= 0.7 and

*s*= 1.0 for an equal-energy white (see Golz & MacLeod, 2003). By luminance-redness correlation, the correlation between

*l*and luminance is meant.

*l*and luminance (for which the size of the inner region with a value of 0.8 and the outer region with a value of 0.0 varied as the experimental conditions), all statistics were equal for the inner and the outer region. The values were chosen to resemble the chromatic statistics of natural scenes (Ruderman, Cronin & Chiao, 1998) under daylight of 7000 K color temperature. In order to calculate the color codes for variegated surrounds with the intended chromatic statistics, the same algorithm as in our previous work on chromatic scene statistics (which is similar to the algorithm described in Mausfeld & Andres, 2002) was used, the only modification being that the algorithm now allows for different statistics within an inner and outer region of the surround. For each region, the colors of the circles belonging to that region (i.e., circles for which the center lies within that region) are chosen to produce the intended chromatic statistics. All pixels of a particular circle are assigned the same color even if that circle reaches partially into the other region. The chromatic statistics of each region are not calculated on the basis of individual circles but on the basis of all individual pixels that lie within that region. Note that the circular border between the inner and outer region of the surround is only virtual in that the algorithm ensures that for both regions the chromatic statistics calculated over all pixels within the respective region have the intended values while a particular circle in the surround can lie across this border without being split with regard to its color. (Therefore, the border between the two regions is visually not salient in the stimuli, a point that becomes important in Experiment 3.)

Chromatic statistic | Value | |
---|---|---|

Mean of chromaticity l | 0.6877 | |

Mean of chromaticity s | 1.1466 | |

Mean of luminance | 20 cd/m ^{2} | |

Standard deviation of l | 0.005 | |

Standard deviation of s | 0.1536 | |

Standard deviation of luminance | 5.0 | |

Correlation l and luminance | Inner region: | Outer region: |

0.8 | 0.0 | |

Correlation s and luminance | −0.1153 | |

Correlation l and s | −0.2133 |

*l*,

*s*, and luminance less than 4.4e−6, 3.0e−5, and 9.0e−4, respectively).

*l*,

*s*) of MacLeod and Boynton (1979) while the luminance was fixed at 20 cd/m

^{2}(this value corresponds to the mean luminance of the surround). In order to indicate that they were content with the adjustment, subjects pressed a key and the next trial started with a new stimulus. The initial color of the adjustable disk was randomly chosen. After dark adapting for 5 min and viewing the first stimulus for 2 min, subjects made a total of 80 settings (16 repetitions × 5 conditions) within a single session. In order to balance potential carry-over effects between conditions, 8 settings for each of the 5 conditions in the order of 0°, 2°, 4°, 8°, “all” were collected first and then another 8 settings for each condition in reversed order. (However, in the analysis of the results no indications of systematic carry-over effects were found.) For all conditions, the same four different spatial layouts for the placement of the circles in the surround were used, so for each condition each of the four layouts was collected four times.

*l*values) for the gray settings of subjects. Because the absolute

*l*values of gray settings can differ systematically between subjects even for the same condition, the values of each subject are normalized to yield values relative to the range of values for that subject. These relative values are easier to compare and are presented in all following figures. A relative value of 0.0 corresponds to the mean of the condition with the lowest

*l*values, 1.0 corresponds to the mean of the condition with the highest

*l*values. The absolute

*l*values of these minimum and maximum means used for the normalization are given for all subjects in Table 3. The minimum means arise from the 0° condition for all subjects and the maximum means arise either from the 8° or the “all” condition. (In the discussion of Experiment 4, these values are further commented on in comparison with the corresponding values of that experiment.)

Subject | Minimum mean of l | Maximum mean of l |
---|---|---|

AG | 0.6870 | 0.6889 |

BJ | 0.6781 | 0.6797 |

CB | 0.6881 | 0.6904 |

DS | 0.6866 | 0.6885 |

IG | 0.6692 | 0.6733 |

JF | 0.6763 | 0.6810 |

JG | 0.6849 | 0.6882 |

KM | 0.6829 | 0.6864 |

NS | 0.6801 | 0.6834 |

SA | 0.6889 | 0.6918 |

Subject | AG | BJ | CB | DS | IG | JF | JG | KM | NS | SA | Mean |
---|---|---|---|---|---|---|---|---|---|---|---|

75% | 5.0 | 3.9 | 2.9 | 1.6 | 4.4 | 5.8 | 4.8 | 5.4 | 5.3 | 4.3 | 4.3 |

90% | 6.6 | 4.2 | 5.1 | 2.3 | 5.4 | 10.7 | 6.3 | 6.7 | 6.9 | 7.8 | 6.2 |

*F*(1,4) > 3.7,

*p*< 0.01, respectively]. The increase of the effect when enlarging the inner region beyond 2° toward 8° is statistically significant for all but one subject [

*t*(30) > 2.2,

*p*< 0.05, one tailed, respectively] and the increase when enlarging the inner region beyond 4° toward 8° is statistically significant for five of ten subjects [

*t*(30) > 2.0,

*p*< 0.05, one tailed, respectively]. The decrease of the effect when the inner region is enlarged from 8° to the entire surround (“all”) is statistically significant for five of ten subjects [

*t*(30) > 2.4,

*p*< 0.05, one tailed, respectively].

*l*,

*s*, luminance) space are the same for both regions. In particular, both regions are equated with respect to the mean of the chromaticity coordinate

*l*(hereinafter referred to as the “unweighted mean”). But there is a different measure for the average redness that could be used and this measure differs for the two regions with different luminance-redness correlation even if the unweighted mean redness does not differ: The

*l*coordinates of a region are averaged after each of these values are weighted by the corresponding luminance (and divided by the average luminance of the region to make the weighting factors sum up to 1.0). This so calculated measure (hereinafter referred to as the “luminance weighted mean”) is equivalent to calculating the average redness by first averaging the coordinates in the (L, M, S) cone excitation space and then projecting the resulting mean values onto the MacLeod–Boynton chromaticity plane (

*l*,

*s*). So, if one uses the same luminance weighted mean redness for both regions, the two are equated on the level of cone excitations, but if one uses the same unweighted mean, the two regions are equated on the opponent level of the MacLeod–Boynton measures. In Golz (2005), I have shown that the basic effect of the luminance-redness correlation holds no matter which of the two measures for the mean is used, so this effect is not merely a consequence of equating the average redness on the wrong level. Furthermore, Granzier et al. (2005) did not find substantial differences for the spatial extent relevant for the effect of the luminance-redness correlation when equating in these two different ways (which they called “matched ratio method” and “matched sum method” for their situation with only two different chromaticities in each region). And finally, in an additional (not presented) experiment analogous to Experiment 1 but with stimuli equated for the luminance weighted mean redness the results were very similar to those presented above. So, the method chosen for equating the average redness does not seem to be critical for the spatial extent relevant for the effect of the luminance-redness correlation.

*t*(14) > 2.0,

*p*< 0.05, one tailed, respectively] and for three subjects still at 4° [

*t*(14) > 2.0,

*p*< 0.05, one tailed, respectively]. Figure 5 shows the result for the average observer established by averaging the relative values of all subjects.

- “non-salient” (same as in Experiment 1): The circular border is only virtual in that the algorithm for determining the color codes of the circles in the surround ensures that for both regions the chromatic statistics have the intended values, but all circles are painted homogenously even those of the inner region that extend beyond this virtual border into the outer region (see Figure 6b).
- “color change”: Circles crossing the border are still drawn with an intact circular form but not painted homogenously—the color of each circle differs on either side of the border (see Figure 6c).
- “form change”: The outlines of circles are truncated at the border and different circles with different colors are painted on the other side of the border, so the outlines do not match across the border (see Figure 6d).

*t*(110) = 3.48,

*p*< 0.001, one tailed] but neither for the “color change” nor the “form change” condition. Furthermore, at 8° the relative effect is significantly lower compared to the “non-salient” condition for the “color change” condition [

*t*(110) = 2.74,

*p*< 0.01, one tailed] as well as for the “form change” condition [

*t*(110) = 2.68,

*p*< 0.01, one tailed].

Chromatic statistic | Value | |
---|---|---|

Inner region: | Outer region: | |

Mean of chromaticity l | 0.69 | 0.685 |

Mean of chromaticity s | 1.14 | 1.27 |

Mean of luminance | 20 cd/m ^{2} | |

Standard deviation of l | 0.005 | |

Standard deviation of s | 0.1536 | |

Standard deviation of luminance | 5.0 | |

Correlation l and luminance | 0.0 | |

Correlation s and luminance | −0.1153 | |

Correlation l and s | −0.2133 |

*l*, 1.0 corresponds to the mean of the condition with the highest

*l*values. The absolute

*l*values of the minimum and maximum means used for this normalization are given for all subjects in Table 6.

Subject | Minimum mean of l | Maximum mean of l |
---|---|---|

AG | 0.6846 | 0.6883 |

BJ | 0.6859 | 0.6903 |

DW | 0.6810 | 0.6847 |

JG | 0.6860 | 0.6884 |

KR | 0.6798 | 0.6836 |

LT | 0.6810 | 0.6837 |

NS | 0.6795 | 0.6841 |

Subject | AG | BJ | DW | JG | KR | LT | NS | Mean |
---|---|---|---|---|---|---|---|---|

75% | 5.2 | 2.9 | 2.0 | 5.4 | 5.7 | 5.5 | 1.9 | 4.1 |

90% | 9.0 | 5.3 | 2.6 | 8.6 | 8.2 | 12.5 | 2.5 | 7.0 |

*F*(1,4) > 7.5,

*p*< 0.001, respectively]. The increase of the effect when enlarging the inner region beyond 2° toward 8° is statistically significant for all but one subject [

*t*(30) > 1.9,

*p*< 0.05, one tailed, respectively]. The increase when enlarging the inner region beyond 4° toward 8° is statistically significant for three subjects [

*t*(30) > 1.76,

*p*< 0.05, one tailed, respectively].

*l*values have been transformed into relative values by a subject-wise normalization (as described in the result section of Experiment 1). In absolute terms, the size of the effect on gray settings resulting from differences in mean chromaticity measured in Experiment 4 as well as the size of the effect resulting from differences in luminance-redness correlation measured in Experiment 1 is relatively small compared to the inter-individual differences of the gray settings. To illustrate this, the minimum and maximum means of the subject-wise normalization in Experiment 1 and 4 (given in Table 3 and Table 6) are plotted in Figure 11. Panel a shows the data for all subjects in Experiment 1, panel b for all subjects in Experiment 4. The lower horizontal end of the marker indicates for the respective subject the minimum mean and the upper horizontal end indicates the maximum mean. The vertical lengths of the markers correspond to the size of the effect of the tested scene statistic (i.e., the luminance-redness correlation in Experiment 1 and the mean chromaticity in Experiment 4) and differences between subjects in the vertical position of the markers correspond to inter-individual differences in the location of the subjective gray point.

*l*value of the gray settings in Experiment 1 is small and ranges across subjects from 0.00161 to 0.00469 with an average of 0.00294. Note, for comparison, that the standard deviation of

*l*in the variegated stimuli used in the experiments is 0.005 (which equals the average standard deviation in the natural scenes of Ruderman et al., 1998). This size of the effect of the luminance-redness correlation found in Experiment 1 is in good agreement with the size of the effect found in previous studies (Golz, 2005; Golz & MacLeod, 2002). In Golz and MacLeod (2002), we have shown that the size of the effect of the luminance-redness correlation is roughly consistent with the size of the effect that would be expected based on an optimal observer computation of the weight that should be given to the luminance-redness correlation in estimating the illuminant in the natural scenes of Ruderman et al. (1998). The size of the effect measured in Experiment 1 results from stimuli that differ in luminance-redness correlation by 0.8 (see Table 2). This value is comparable to the range of luminance-redness correlation values occurring in natural scenes.

*l*value of the gray settings in Experiment 4 ranges across subjects from 0.00242 to 0.00458 with an average of 0.00362. The difference in mean chromaticity of the stimuli from which this size of the effect results (see Table 5) is comparable in size to the difference in chromaticity between a 7000 K daylight and a 8000 K daylight. The use of larger differences in mean chromaticity was not possible due to constraints of the algorithm used to find colors for the circles in the surround with the intended chromatic statistics for the two different regions. Because some circles reached into both regions but had to be painted with one homogeneous color the realizable difference of the mean chromaticity between the two regions was limited.

*l*values of gray settings in the 0° stimuli where the entire surround has a luminance-redness correlation of 0.0 (i.e., the standard deviation of the minimum means plotted as the lower horizontal end of the markers in Figure 11a) is 0.00630. In Experiment 4, the standard deviation (across the 7 subjects) of the mean

*l*values of gray settings in the 0° stimuli where the entire surround has a mean chromaticity of (

*l*,

*s*) = (0.69, 1.14) (i.e., the standard deviation of the minimum means plotted as the lower horizontal end of the markers in Figure 11b) is 0.00284. These inter-individual differences are in the range of differences found in previous studies measuring gray settings with the same type of stimuli manipulating various scene statistics (Golz, 2005; Golz & MacLeod, 2002).