A Reflectance Model for Metallic Paints Using a Two-Layer Structure Surface with Microfacet Distributions

Abstract

SUMMARYWe present a new method that can represent the reflectance of metallic paints accurately using a two-layer reflectance model with sampled microfacet distribution functions. We model the structure of metallic paints simplified by two layers: a binder surface that follows a microfacet distribution and a sub-layer that also follows a facet distribution. In the sub-layer, the diffuse and the specular reflectance represent color pigments and metallic flakes respectively. We use an iterative method based on the principle of Gauss-Seidel relaxation that stably fits the measured data to our highly non-linear model. We optimize the model by handling the microfacet distribution terms as a piecewise linear non-parametric form in order to increase its degree of freedom. The proposed model is validated by applying it to various metallic paints. The results show that our model has better fitting performance compared to the models used in other studies. Our model provides better accuracy due to the non-parametric terms employed in the model, and also gives efficiency in analyzing the characteristics of metallic paints by the analytical form embedded in the model. The non-parametric terms for the microfacet distribution in our model require densely measured data but not for the entire BRDF(bidirectional reflectance distribution function) domain, so that our method can reduce the burden of data acquisition during measurement. Especially, it becomes efficient for a system that uses a curved-sample based measurement system which allows us to obtain dense data in microfacet domain by a single measurement. key words: metallic paint, reflectance modeling, multi-layer surface, measure-and-fit, non-parametric basis function

Simulation of Light Scattering in Automotive Paints: Role of Particle Size

“…Their model provides visually satisfactory results in the appearance of multilayer automotive paint, if one is to ignore sparkling. Accurate representation of the reflectivity of metallic paint using a two-layer model with sample distribution functions of microfacets was proposed in [9]. This model provides better accuracy due to the use of the nonparametric terms and allows the analysis of the characteristics of metal particles using the analytical form built into the model.…”

“…where α(Z) ≡ 2Z 0 Ds(l)dl = 2Z 0 ( D(S)s(l, S)dS)dl Z ≡ cz 2 (9) Let us calculate the above α, which in view of (7) and recalling that R = √ S/π can be written as…”