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

As on-line purchases is activated, customers' demand increases for the realistic and accurate digital information of a product design. In this paper, we propose a practical method that can generate a realistic 3D model of a real product using a 3D geometry obtained by a 3D scanner and its photographic images. In order to register images to the 3D geometry, the camera focal length, the CCD scanning aspect ratio and the transformation matrix between the camera coordinate and the 3D object coordinate must be determined. To perform this 2D-3D registration with consideration of computational complexity, a three-step method is applied, which consists of camera calibration, determination of a temporary optimum translation vector (TOTV) and nonlinear optimization for three rotational angles. A case study for a metallic coated industrial part, of which the colour appearance is hardly obtained by a 3D colour scanner has performed to demonstrate the effectiveness of the proposed method.