Light scattering from human hair fibers

Abstract

Light scattering from hair is normally simulated in computer graphics using Kajiya and Kay's classic phenomenological model. We have made new measurements of scattering from individual hair fibers that exhibit visually significant effects not predicted by Kajiya and Kay's model. Our measurements go beyond previous hair measurements by examining out-of-plane scattering, and together with this previous work they show a multiple specular highlight and variation in scattering with rotation about the fiber axis. We explain the sources of these effects using a model of a hair fiber as a transparent elliptical cylinder with an absorbing interior and a surface covered with tilted scales. Based on an analytical scattering function for a circular cylinder, we propose a practical shading model for hair that qualitatively matches the scattering behavior shown in the measurements. In a comparison between a photograph and rendered images, we demonstrate the new model's ability to match the appearance of real hair.

Interactive hair rendering under environment lighting

“…The hair properties used in this paper, including the index of refraction and the longitudinal shifts and widths, are the same as those used in [Marschner et al 2003]. We only modify the absorption coefficient σ a to obtain hair with different colors.…”

“…The model has been widely used in games and movies due to its simplicity, although it fails to correctly predict the azimuthal dependence of the scattered intensity and its diffuse term often results in a flat hair appearance. Marschner et al [2003] proposed a more sophisticated lighting model based on measurements of light scattering from a single hair fiber. It identifies the major modes of reflection that have the greatest influence on the fiber's scattering properties and takes into account the Fresnel factor and volume absorption to give a more convincing prediction of the fiber's reflectance.…”

“…Following the definition of curved intensity in [Marschner et al 2003], we write the single scattering integral under incident environment lighting L(ω i ) as follows: …”

“…Fortunately, we can leverage the symmetry of the scattering function to reduce the dimensionality of this sample space. Marschner et al [2003] decomposes the bidirectional scattering function into three major components, each of which is further factorized into a longitudinal function and an azimuthal function:…”

“…For each SRBF light, we factor out the effective transmittance to represent the radiance integral as the product of two terms: the transmittance and the convolution of the SRBF light and the scattering function. Observing that the convolution term is independent of the hair geometry, we precompute it for the two commonly-used scattering models, one by Kajiya and Kay [Kajiya and Kay 1989] and the other by Marschner et al [Marschner et al 2003], and reduce the run-time computation to table lookups. We further propose a technique, called the convolution optical depth map, to efficiently approximate the effective transmittance by filtering the optical depth maps generated at the center of the SRBF using a depth-dependent kernel.…”