In this study, we used a hue scaling technique to examine human color constancy performance in simulated three-dimensional scenes. These scenes contained objects of various shapes and materials and a matte test patch at the center of the scene. Hue scaling settings were made for test patches under five different illuminations. Results show that subjects had nearly stable hue scalings for a given test surface across different illuminants. In a control experiment, only the test surfaces that belonged to one illumination condition were presented, blocked in front of a black background. Surprisingly, the hue scalings of the subjects in the blocked control experiment were not simply determined by the color codes of the test surface. Rather, they depended on the sequence of previously presented test stimuli. In contrast, subjects' hue scalings in a second control experiment (with order of presentations randomized) were completely determined by the color codes of the test surface. Our results show that hue scaling is a useful technique to investigate color constancy in a more phenomenological sense. Furthermore, the results from the blocked control experiment underline the important role of slow chromatic adaptation for color constancy.

At this match point, however, the test and the match surfaces looked different, and the observers felt as if further adjustments of the match surface should produce a better correspondence. Yet turning any of the knobs or combinations of knobs only increased the perceptual difference (Brainard, Brunt, & Speigle, 1997, p. 2098).

^{1}corresponding to the locations of the observer's eyes in the virtual scene ( Figure 1). The scenes differed in the chromaticity of the test patch and in the color of the punctate source.

*u*′

*v*′ diagram ( Figure 3). We used this set of test patches in each of the three experiments.

Munsell notation | x | y | L | u′ | v′ |
---|---|---|---|---|---|

5R7/4 | 0.357 | 0.333 | 18.62 | 0.228 | 0.477 |

10R7/4 | 0.366 | 0.346 | 19.15 | 0.228 | 0.485 |

5YR7/4 | 0.373 | 0.362 | 18.82 | 0.226 | 0.494 |

10YR7/4 | 0.375 | 0.383 | 18.83 | 0.219 | 0.504 |

5Y7/4 | 0.369 | 0.397 | 18.37 | 0.210 | 0.509 |

10Y7/4 | 0.360 | 0.405 | 18.74 | 0.201 | 0.511 |

5GY7/4 | 0.341 | 0.400 | 17.88 | 0.192 | 0.506 |

10GY7/4 | 0.313 | 0.387 | 18.31 | 0.178 | 0.496 |

5G7/4 | 0.290 | 0.365 | 17.97 | 0.170 | 0.483 |

10G7/4 | 0.281 | 0.353 | 18.36 | 0.168 | 0.476 |

5BG7/4 | 0.271 | 0.338 | 17.96 | 0.166 | 0.467 |

10BG7/4 | 0.265 | 0.323 | 18.12 | 0.167 | 0.458 |

5B7/4 | 0.262 | 0.307 | 18.24 | 0.170 | 0.449 |

10B7/4 | 0.272 | 0.301 | 18.36 | 0.179 | 0.446 |

5P7/4 | 0.304 | 0.296 | 18.56 | 0.205 | 0.448 |

5RP7/4 | 0.337 | 0.314 | 18.26 | 0.222 | 0.464 |

*L*(

*λ*) from a Lambertian surface

*S*(

*λ*) that is illuminated by a diffuse source

*E*

_{D}(

*λ*) and a punctate source

*E*

_{P}(

*λ*) is given by

*λ*indexes the wavelength of light in the visible spectrum and

*θ*is the angle between the incident light from the punctate source and the surface normal. In our case,

*θ*was always set to zero. The reflectance functions of the surfaces are based on spectral reflectance measurements made with a spectrophotometer on 1,269 color chips from the 1976 Munsell Book of Color at a 1-nm resolution from 380 to 800 nm. This data set was obtained from http://spectral.joensuu.fi/.

*xy*and

*u*′

*v*′ chromaticities of the punctate sources are given in Table 2. For the five punctate sources, spectral energy distributions were computed from the CIE daylight basis functions (Wyszecki & Stiles, 1982). We calculated the light signal that reached the eye of the observer from the test patch using these distributions and the reflectance functions of the Munsell surfaces. The virtual punctate source was simulated to be behind the observer. The distance between the test patch and the punctate light source was 670 cm. The position of the punctate source was held constant throughout all experiments. The punctate–total luminance ratio was always

*π*= 0.67 (see Boyaci et al., 2003).

Illumination | x | y | u′ | v′ |
---|---|---|---|---|

Neutral (D65) | 0.313 | 0.329 | 0.198 | 0.468 |

Blue (D10) | 0.279 | 0.292 | 0.188 | 0.442 |

Yellow (D40) | 0.382 | 0.384 | 0.224 | 0.505 |

Red | 0.354 | 0.313 | 0.234 | 0.466 |

Green | 0.268 | 0.347 | 0.162 | 0.471 |

*none*) to 6 (

*very saturated*). The active scale was presented monocularly as the number of the current value in the respective color of the scale. The subject saw this number to the right of the fused image. At any given time, only one hue scale was active. The subject could increase or decrease the value of the active scale by pressing the left or the right mouse button, respectively. The subject moved to a different scale by scrolling the mouse wheel up or down. The settings of one trial were confirmed by pressing the mouse wheel.

^{2}In the experiments, different illuminant conditions were blocked into different sessions. Each session started with 16 training trials. These training trials were prepended to the experimental trials to allow subjects to practice hue scalings as well as to stabilize the adaptational state of the subject. In each trial, the scene was presented to the subject and the subject carried out the task described above. Between two trials, a black screen was presented to the subject for 1 s to reduce the influence of afterimages. Observers repeated hue scalings for each of the 16 test surfaces four times. Each subject made 80 settings in one session. There were no time constraints. One session took about 20 min on the average. Each experiment consisted of five sessions that corresponded to the five different punctate sources. The order of illuminant blocks was randomized and differed across subjects. Within one illuminant block, the test surface order was randomized and different subjects saw different randomizations.

*u*′

*v*′ chromaticity coordinates. This transformation makes it easier to compare our results with those from previous studies in terms of color constancy indices. The procedure we followed to obtain these indices is explained next.

*a*

_{BY}on a BY opponent scale that ran from −6 (blue) to 6 (yellow). If, for example, the subject's rating was 2.3 on the blue scale and 0 on the yellow, the rating on the opponent scale would become

*a*

_{BY}= −2.3. A rating of 1.7 on the yellow scale (with a rating of 0 on the blue) would become

*a*

_{BY}= 1.7. We similarly combined red and green hue ratings into a rating

*a*

_{RG}on a red–green opponent scale. An observer's mean hue ratings in any given condition are then summarized by the two-dimensional column vector

**a**= [

*a*

_{BG},

*a*

_{RG}]′ in a two-dimensional opponent space,

**A**.

**u**be the two-dimensional vector that denotes the

*u*′

*v*′ coordinates of a surface under the neutral illuminant. We assume that the mapping between the opponent space

**A**and

*u*′

*v*′ space is affine but perturbed by judgment error. That is, we assume that there is a 2 × 2 matrix

**M**and a column vector

**c**such that

*ɛ*∼

*Φ*(0,

*σ*

^{2}) is Gaussian judgment error with a mean of 0 and a variance of

*σ*

^{2}. The vector

**c**captures the shift of the achromatic point.

**M**and the two elements of

**c**) for each subject. We chose the set of parameters for which the sum of squared distances between

*u*′

*v*′ coordinates and predictions was minimized.

**M**and

**c**, determined by the observer's ratings under neutral illumination, was then used to compute

*u*′

*v*′ coordinates from hue scalings under other illuminations.

*any*surface (not just an achromatic surface) induced by the same change in illumination? Speigle and Brainard conclude that, although the transformations on all points in color space as measured by asymmetric matching are

*potentially*too complex to be predicted by knowledge of the transformation of the achromatic point, in

*reality,*they can be accurately predicted.

*i*to

*u*′

*v*′ using the specific transformation that was given by

**M**

_{ i}and

**c**

_{ i}. Then, we fitted optimal ellipses to the

*u*′

*v*′ data of each subject for each illuminant (Halir & Flusser, 1998). Finally, we compared the parameters of the ellipse for neutral illumination data with those of the ellipses for the chromatic illumination data. Analyzing the parameters of the ellipses is advantageous in that we can directly separate effects of color constancy from deviations from the Speigle–Brainard conjecture. If we analyze the ellipses for neutral and chromatic illumination, then differences in the centroids reflect incomplete color constancy. However, differences in area, eccentricity (shape), or orientation of the ellipses indicate deviations from the Speigle–Brainard conjecture. If their conjecture were valid, then changes in illuminant chromaticity would lead to simple translations of the ellipses in

*u*′

*v*′ space. They will not rotate, shrink or grow, or change shape. We next describe how we measure area, eccentricity, and orientation.

*a*be the semimajor axis and

*b*be the semiminor axis of an ellipse. Then, the eccentricity

*e*of the ellipse is given by

*θ*between the major axis of the ellipse and the

*x*-axis. The area

*A*of an ellipse is defined as

*A*=

*πab*.

*u*′

*v*′ coordinates of the scalings under test illumination should completely overlap with those under neutral illumination. If a subject has no constancy, the

*u*′

*v*′ coordinates of the scalings under test illumination coincide with the coordinates of the test surfaces under this illumination.

*u*′

*v*′ chromaticities of all surfaces under neutral illumination was almost identical to the centroid of the predicted coordinates. Therefore, we used the centroids of test surfaces and settings in

*u*′

*v*′ to calculate color constancy indices. The indices have the form

**m**

_{D65}is the centroid of the surfaces under neutral illumination,

**m**

_{test}is the centroid of the surfaces under test illumination, and

**m**

_{data}is the centroid of the transformed hue scalings of the subject. This index is 1 in case of perfect constancy and 0 in case of no constancy. By design, it is directly comparable to Brunswik ratios typically reported in studies of color constancy (Arend, Reeves, Schirillo, & Goldstein, 1991; Brunswik, 1929; Thouless, 1931).

*θ*should be interpreted with care as the estimated ellipses of one subject (X.H.) were almost circular, which resulted in unreliable estimates of

*θ*. In general, we found small systematic deviations for the orientation of the ellipse in the yellow and green illuminant conditions ( Figure 7C). The analysis of the ellipses indicates that the Speigle–Brainard conjecture holds also for hue scaling data.

Illumination | A.H.R. | A.S.T. | L.G.S. | X.H. | A.L.L. | ||
---|---|---|---|---|---|---|---|

Blue (D10) | Experiment 1 | 0.74 | 0.71 | 0.67 | 0.91 | 0.69 | |

Experiment 2 | 0.72 | 0.50 | 0.59 | 0.73 | 0.75 | ||

Experiment 3 | 0.17 | −0.18 | 0.34 | 0.68 | 0.08 | ||

Yellow (D40) | Experiment 1 | 0.70 | 0.63 | 0.62 | 0.76 | 0.64 | |

Experiment 2 | 0.29 | 0.56 | 0.23 | 0.18 | 0.38 | ||

Experiment 3 | −0.04 | 0.13 | 0.06 | −0.23 | −0.05 | ||

Red | Experiment 1 | 0.65 | 0.58 | 0.58 | 0.85 | 0.75 | |

Experiment 2 | 0.16 | 0.46 | 0.37 | 0.63 | 0.46 | ||

Experiment 3 | 0.06 | 0.21 | 0.22 | 0.05 | 0.03 | ||

Green | Experiment 1 | 0.75 | 0.65 | 0.73 | 0.73 | 0.68 | |

Experiment 2 | 0.60 | 0.42 | 0.72 | 0.44 | 0.57 | ||

Experiment 3 | 0.07 | −0.04 | 0.49 | −0.01 | −0.11 |

^{1}We used, as a standard, an interocular distance of 6.3 cm in rendering. This separation has proven to be sufficient for subjects in these and previous experiments using the same apparatus. The normal human range of interocular distances is 6.0 to 7.0 cm (French, 1921). We checked whether subjects could achieve fusion, and, had any subject reported difficulty with stereo fusion, we would have excluded them from further participation in the experiment.

^{2}In the training session, subjects repeated hue scaling settings for 16 surfaces under neutral illumination five times. For each subject, we transformed all pairwise correlations between repeated measurements using Fisher's r-to-z transformation. The subject's reliability was defined as the correlation corresponding to the mean of the transformed values. We did not measure consistency of hue scalings over time (like over a few days). However, Boynton and Gordon (1965) report that their subjects made very reliable settings with mean correlation coefficients of 0.96.