In everyday life, the visual system is remarkably good at recognizing materials across a wide range of viewing conditions. This paper addresses the problem of identifying real samples of materials from appearance. Here, we consider gloss as an appearance attribute that could reveal certain information about object properties. We prepared twelve samples of glass and PMMA and eroded these using different agents. The gloss and haze of the samples were measured at 60 degrees via a gloss meter. For all samples, the surface roughness properties were measured. Microfacet distributions were derived from measured BRDFs using an inverted microfacet model. We conducted a visual ranking experiment using the pair comparison method. The psychophysical gloss ratings correlate well with the 60 degrees gloss index. Principal component analysis of the psychophysical results revealed a somewhat more complicated picture in which three components seem to play a role. We conclude that observers can apprehend the physical nature of the surface of real objects from features that are included in the BRDF and available in the gloss appearance.

*L*

_{ R }exiting the surface to the incident irradiance

*E*

_{ I }, for given incident direction

**I**and exiting direction

**R**(cf., Equation 1 and Figure 1):

*T*≈ 10

^{−5}). Four raw black glass samples of equal dimensions to the PMMA pallets were eroded using random polishing to obtain a mirror-like appearance and then submitted to repeated alumina-eroding treatments. These samples are labeled Gl1 to Gl4 from the rougher to the glossier.

*n*= 1.567 (ISO 2813, 1978). Specular gloss measurements at 60° were made using a ZLR 1050 Zethner gloss meter upon ten different points of the plates.

*is, for a specified specular angle, the ratio of flux reflected at a specified angle (or angles) from the specular direction to the flux similarly reflected at the specular angle by a specified gloss standard*.

^{2}) is illuminated under oblique incidence (about 46°) by p-polarized monochromatic light (wavelength,

*λ*= 632.8 nm). Then, measurements of the angular distribution of the scattered light are made at several sites within the plane of incidence on the sample surface (see Figure 5). By using the angle-resolved scattering theory (Elson & Bennett, 1979; Kröger & Kretschmann, 1970), this distribution is related to the surface roughness (through the power spectral density—PSD).

- Regarding the polished glass and the P-PMMA scales, the number of alumina-eroding cycles increases the surface roughness. The result of this process can be seen as similar to white noise acting over all spatial angular frequencies and shifting the PSD curves up (black and green curves in Figure 6). We note that the PSD slopes of the P-PMMA and glass scales are quite similar, marking the signature of the eroding process.
- Regarding the C-PMMA samples, the curvature of the PSD function is accentuated by the chemical erosion and no obvious shift of the PSD curve is observed for high spatial angular frequencies. This is because the treatment favors certain frequencies over others. Indeed, for spatial angular frequency above 10
^{−2}nm^{−1}, the chemical process has no effect on the superficial surface (blue curves in Figure 6).

^{−4}sr depending on the direction of observation. This system is based on a combination of Fourier Optics and a cooled CCD sensor head (Moreau, Curt, & Leroux, 2000). For a given incident direction, the EZ-Contrast records the luminance in the directions (

*θ, ϕ*), with 0° <

*θ*< 80° and 0° <

*ϕ*< 360° in one shot.

*θ*and

*ϕ*vary with a step of 0.4°. As our samples are assumed to be isotropic, we used only one azimuth of illumination. Unfortunately, the equipment does not provide the illumination. Thus, we do not measure the BRDF rigorously, but only the distribution of the luminance, for a given illumination (unknown but constant).

*ψ*= 20°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65°, 70°). We performed 4 repetitions on different areas of the sample. An example of this measurement can be seen in Figure 7.

*E*

_{ I }(

*ψ*) is the illumination at the zenithal angle

*ψ, L*

_{spec}(

*ψ, θ, φ*) is the luminance in the direction

**R**(

*θ, φ*) coming from the specular component, and

*L*

_{diff}(

*ψ*) is the luminance in the direction

**R**(

*θ, φ*) coming from the diffuse component.

*E*

_{0}is the illumination along

**N**(see Figure 1); Ω is the collection solid angle;

*F*(

*n, ψ*′) is the Fresnel factor depending on

*n*(the refractive index of the material) and

*ψ*′ (the angle of incidence of the light on the microfacet);

*G*(

*ψ, θ, α, ψ*′) is a function that takes into account the masking/shadowing of the adjacent facets;

*P*(

*α*) is the microfacet angular distribution function.

*P*(

*α*) describes the probability of finding a facet oriented with a given normal

**F**. As our surfaces are isotropic, the probability depends only on the zenith

*α*. The choice of the function to be used has been discussed several times (Blinn, 1977; Cook & Torrance, 1982; Obein, Leroux, Knoblauch, & Viénot, 2001). All these propositions are mathematical functions that are independent of the material. In our model, we use a function that is derived from the BRDF measurements, by inverting the model. The method is described below.

*E*

_{0}, the absolute value of the illumination. Furthermore, the value of the solid angle Ω by which 1 pixel of the CCD is seen by the surface is not well known. However, we know that

*E*

_{0}and Ω are independent of the directions of illumination and reflection. We define

*C*

_{spec}by

*C*

_{spec}is a constant of the equipment.

*P*(

*α*),

*C*

_{spec}, and

*n*are unknown.

*Step 1: Adjustment of the refractive index n from the measurements made in the plane of incidence.*

*C*

_{spec}·

*P*(

*α*) according to the measurements and an arbitrary refractive index, for each direction of illumination where the measurements were performed. As

*P*(

*α*) is a characteristic of the sample and

*C*

_{spec}is a constant of the equipment, the product

*C*

_{spec}·

*P*(

*α*) should be independent of the direction of illumination.

*C*

_{spec}·

*P*(

*α*) for the different incidences. The refractive index obtained is not necessarily the optical refractive index of the material. It should be considered as an effective refractive index

*n*

_{eff}that allows the modeling of the surface with a microfacet model. Figure 8 illustrates the adjustment of the effective refractive index

*n*

_{eff}.

*n*

_{eff}of the surface.

*Step 2: Fitting the facet normal distribution function P(α) and the constant C*

_{ spec }.

*P*(

*α*) is a distribution function. Its integral on the half-space must be equal to 1. Now that we know the effective refractive index of the surface, we can express

*C*

_{spec}·

*P*(

*α*) for each of the 4 repetitions on different areas of the sample and the 10 angles of illumination. We have 40 measurements of the function

*C*

_{spec}·

*P*(

*α*). We average the 40 measurements and we separate

*C*

_{spec}and

*P*(

*α*) by normalizing

*P*(

*α*) to 1.

*Step 3: Validation of the model by reconstruction of the luminance in the plane of incidence.*

*C*

_{spec}·

*P*(

*α*) and

*n*

_{eff}by a confrontation of the luminance calculated with the model and the measurement for different directions of illumination (Figure 9).

*P*(

*α*) is a function of real BRDF measurements. It is determined by fitting unknowns from the Cook–Torrance model to measurements. Increasing the number of measurements by changing illumination direction is a way to increase the model ability to predict BRDF in every possible direction. Averaging measurements from different parts of the samples adds reliability to the luminance reconstruction obtained in the last stage of the inversion.

*R*

^{2}is equal to 0.93 indicating a good correlation between appearance and optical measurements.

Samples | F1 | F2 | F3 | F4 |
---|---|---|---|---|

Gl1 | 0.700 | −0.149 | −0.372 | 0.308 |

Gl2 | 0.623 | 0.244 | −0.313 | 0.555 |

Gl3 | 0.793 | −0.410 | 0.223 | −0.295 |

Gl4 | 0.887 | −0.220 | 0.268 | −0.221 |

P1 | −0.476 | −0.792 | 0.176 | 0.111 |

P2 | −0.680 | −0.458 | 0.314 | 0.347 |

P3 | −0.610 | 0.400 | 0.500 | 0.317 |

P4 | −0.105 | 0.869 | 0.270 | −0.066 |

C1 | −0.478 | −0.749 | −0.395 | −0.014 |

C2 | −0.666 | −0.340 | −0.416 | −0.324 |

C3 | −0.334 | 0.705 | −0.496 | 0.081 |

C4 | −0.362 | 0.635 | −0.109 | −0.410 |

Samples | F1 | F2 | F3 | F4 |
---|---|---|---|---|

Gl1 | 11.457 | 0.612 | 9.883 | 9.004 |

Gl2 | 9.067 | 1.637 | 7.026 | 29.140 |

Gl3 | 14.701 | 4.627 | 3.571 | 8.264 |

Gl4 | 18.379 | 1.329 | 5.139 | 4.643 |

P1 | 5.287 | 17.283 | 2.207 | 1.159 |

P2 | 10.795 | 5.784 | 7.047 | 11.384 |

P3 | 8.703 | 4.418 | 17.895 | 9.486 |

P4 | 0.256 | 20.814 | 5.224 | 0.408 |

C1 | 5.337 | 15.482 | 11.188 | 0.019 |

C2 | 10.361 | 3.185 | 12.396 | 9.958 |

C3 | 2.602 | 13.709 | 17.573 | 0.625 |

C4 | 3.055 | 11.120 | 0.849 | 15.909 |

*α*.