Gloss is an attribute of visual appearance that originates from the geometrical distribution of the light reflected by the surface. We used the maximum likelihood difference scaling (MLDS) procedure (L. T. Maloney & J. N. Yang, 2003) to estimate gloss scales over an extended range. Observers’ judgments were obtained for a series of 10 black, coated samples for two directions of illumination, in binocular and monocular vision. The results showed a nonlinear relation between gloss percept and instrumental specular gloss values. Sensitivity is higher at extreme scale values than in the middle. In binocular vision, the sensitivity to gloss is higher than in monocular vision exclusively for high gloss levels. Lastly, we found that gloss difference scales, when expressed in terms of the samples rather than the photometric characteristics, vary little with the direction of illumination. Gloss scaling thus seems to be independent of the geometrical variations of the luminous flux at the surface of the sample. By analogy with the term “color constancy,” we call this property “gloss constancy.”

*n*= 1.567 (Budde, 1980). Specular gloss measurements at 60° were made using a Zethner glossmeter on the samples from four sets of the series to control isotropy and homogeneity of the samples. The specular gloss values measured from the series at 60° range from 1 to 90 gloss units (gu), as reported in Table 1. Specular gloss values did not vary significantly from one set to another. Isotropy was assessed for each of the samples of the four sets by measuring specular gloss at five different positions. The variances of these measures are also listed in Table 1.

Sample | Specular gloss at 60° mean value | Specular gloss at 60° variance | Specular gloss at 20°mean value | Specular gloss at 20°variance |
---|---|---|---|---|

N001 | 90.9 | 0.5 | 63.3 | 1.7 |

N002 | 75.9 | 0.7 | 34.2 | 1.0 |

N003 | 61.6 | 1.2 | 23.0 | 0.3 |

N004 | 51.3 | 1.0 | 13.2 | 0.4 |

N005 | 47.2 | 1.4 | 11.0 | 0.3 |

N006 | 36.0 | 1.1 | 6.1 | 0.2 |

N007 | 24.5 | 0.7 | 3.1 | 0.04 |

N008 | 11.8 | 0.4 | 1.5 | 0.05 |

N009 | 4.6 | 0.1 | 0.8 | 0 |

N010 | 1.3 | 0.1 | 0.5 | 0.05 |

*x*,

*y*,

*z*,

*θ*, and

*φ*). The prop allows free and accurate positioning of the samples between the lamp and the observer. According to the angular configuration tested, it can be moved and tilted in the booth. Moreover, so that all the samples are seen in the same situation by observers, it was essential to ensure a fixed angle between pairs (see Figure 1). The observer’s head was fixed by a chin-rest, which guaranteed that the visual direction was in the specular direction.

*i*,

*j*,

*k*, and

*l*, is sampled from the full set. These are presented to the observer as two pairs, (

*i*,

*j*), (

*k*,

*l*), one pair chosen randomly to be placed above the other. The observer’s task is to select the pair whose elements display the greater difference in appearance. If the pair (

*i*,

*j*) is selected, the quadruplet is assigned the value

*R*= 0, otherwise

*R*= 1. With a collection of

*N*stimuli, it is possible to present

*N*!/((4)!(

*N*− 4)!) paired-comparisons. For example, for a collection of 10 samples, 210 non-overlapping quadruplets can be formed.

*i*,

*j*,

*k*, and

*l*, generate in the observer a response indicated as

*ψ*

_{i},

*ψ*

_{j},

*ψ*

_{k}, and

*ψ*

_{l}, respectively. These perceptual values are unknown, but it is supposed that they satisfy if and only if the pair (

*i*,

*j*) is judged to display a greater difference between its elements than the pair (

*k*,

*l*).

*i*,

*j*), otherwise the other pair. The MLDS procedure permits the estimation of a perceptual scale that predicts the relative magnitudes of differences between pairs. With

*ψ*

_{0}and

*ψ*

_{9}fixed at values of 0 and 1, respectively, the values

*ψ*

_{i},

*i*= 1 – 8 are estimated by maximizing the likelihood, where Φ is the cumulative normal distribution function,

*q*=

*ijkl*and

*s*is the standard deviation of the observer’s judgments. Including the value of

*s*, 9 parameters in total are estimated based on the 210 judgments. In practice, the logarithm of the likelihood is computed and its negative minimized. All calculations were performed in the Matlab computing environment.

*m*× 9 parameters, where

*m*is the number of conditions). The test can be described as where

*l*

_{i}is the log likelihood under the hypothesis of a single perceptual scale,

*i*= 0, or multiple perceptual scales,

*i*= 1, and the difference is distributed as

*χ*

^{2}with 9 (

*m*− 1) deg of freedom.

*p*< .001. Nevertheless, the similarity of the scales with viewing condition given the differences in the physical stimuli, from Table 1, is striking. Thus, in what follows, we will plot the visual gloss judgments as a function of the specular gloss measurements at 60°, even if the judgments were obtained at 20°.

Observer | χ^{2} | df | p |
---|---|---|---|

AM | 106 | 9 | 9.0 · 10^{−19} |

FV | 20 | 9 | 1.6 · 10^{−2} |

GO | 16 | 9 | 6.8 · 10^{−2} |

MH | 90 | 9 | 1.4 · 10^{−15} |

PT | 142 | 9 | 3.7 · 10^{−26} |

TP | 40 | 9 | 8.7 · 10^{−6} |