Eugene d'Eon

A layered, heterogeneous reflectance model for acquiring and rendering human skin

We introduce a layered, heterogeneous spectral reflectance model for human skin. The model captures the inter-scattering of light among layers, each of which may have an independent set of spatially-varying absorption and scattering parameters. For greater physical accuracy and control, we introduce an infinitesimally thin absorbing layer between scattering layers. To obtain parameters for our model, we use a novel acquisition method that begins with multi-spectral photographs. By using an inverse rendering technique, along with known chromophore spectra, we optimize for the best set of parameters for each pixel of a patch. Our method finds close matches to a wide variety of inputs with low residual error. We apply our model to faithfully reproduce the complex variations in skin pigmentation. This is in contrast to most previous work, which assumes that skin is homogeneous or composed of homogeneous layers. We demonstrate the accuracy and flexibility of our model by creating complex skin visual effects such as veins, tattoos, rashes, and freckles, which would be difficult to author using only albedo textures at the skins outer surface. Also, by varying the parameters to our model, we simulate effects from external forces, such as visible changes in blood flow within the skin due to external pressure.

A quantized-diffusion model for rendering translucent materials

We present a new BSSRDF for rendering images of translucent materials. Previous diffusion BSSRDFs are limited by the accuracy of classical diffusion theory. We introduce a modified diffusion theory that is more accurate for highly absorbing materials and near the point of illumination. The new diffusion solution accurately decouples single and multiple scattering. We then derive a novel, analytic, extended-source solution to the multilayer search-light problem by quantizing the diffusion Greens function. This allows the application of the diffusion multipole model to material layers several orders of magnitude thinner than previously possible and creates accurate results under high-frequency illumination. Quantized diffusion provides both a new physical foundation and a variable-accuracy construction method for sum-of-Gaussians BSSRDFs, which have many useful properties for efficient rendering and appearance capture. Our BSSRDF maps directly to previous real-time rendering algorithms. For film production rendering, we propose several improvements to previous hierarchical point cloud algorithms by introducing a new radial-binning data structure and a doubly-adaptive traversal strategy.

Efficient rendering of human skin

Existing offline techniques for modeling subsurface scattering effects in multi-layered translucent materials such as human skin achieve remarkable realism, but require seconds or minutes to generate an image. We demonstrate rendering of multi-layer skin that achieves similar visual quality but runs orders of magnitude faster. We show that sums of Gaussians provide an accurate approximation of translucent layer diffusion profiles, and use this observation to build a novel skin rendering algorithm based on texture space diffusion and translucent shadow maps. Our technique requires a parameterized model but does not otherwise rely on any precomputed information, and thus extends trivially to animated or deforming models. We achieve about 30 frames per second for realistic real-time rendering of deformable human skin under dynamic lighting.

A comprehensive framework for rendering layered materials

We present a general and practical method for computing BSDFs of layered materials. Its ingredients are transport-theoretical models of isotropic or anisotropic scattering layers and smooth or rough boundaries of conductors and dielectrics. Following expansion into a directional basis that supports arbitrary composition, we are able to efficiently and accurately synthesize BSDFs for a great variety of layered structures. Reflectance models created by our system correctly account for multiple scattering within and between layers, and in the context of a rendering system they are efficient to evaluate and support texturing and exact importance sampling. Although our approach essentially involves tabulating reflectance functions in a Fourier basis, the generated models are compact to store due to the inherent sparsity of our representation, and are accurate even for narrowly peaked functions. While methods for rendering general layered surfaces have been investigated in the past, ours is the first system that supports arbitrary layer structures while remaining both efficient and accurate. We validate our model by comparing to measurements of real-world examples of layered materials, and we demonstrate an interactive visual design tool that enables easy exploration of the space of layered materials. We provide a fully practical, high-performance implementation in an open-source rendering system.

Multiple-scattering microfacet BSDFs with the Smith model

Modeling multiple scattering in microfacet theory is considered an important open problem because a non-negligible portion of the energy leaving rough surfaces is due to paths that bounce multiple times. In this paper we derive the missing multiple-scattering components of the popular family of BSDFs based on the Smith microsurface model. Our derivations are based solely on the original assumptions of the Smith model. We validate our BSDFs using raytracing simulations of explicit random Beckmann surfaces. Our main insight is that the microfacet theory for surfaces with the Smith model can be derived as a special case of the microflake theory for volumes, with additional constraints to enforce the presence of a sharp interface, i.e. to transform the volume into a surface. We derive new free-path distributions and phase functions such that plane-parallel scattering from a microvolume with these distributions exactly produces the BSDF based on the Smith microsurface model, but with the addition of higher-order scattering. With this new formulation, we derive multiple-scattering micro-facet BSDFs made of either diffuse, conductive, or dielectric material. Our resulting BSDFs are reciprocal, energy conserving, and support popular anisotropic parametric normal distribution functions such as Beckmann and GGX. While we do not provide closed-form expressions for the BSDFs, they are mathematically well-defined and can be evaluated at arbitrary precision. We show how to practically use them with Monte Carlo physically based rendering algorithms by providing analytic importance sampling and unbiased stochastic evaluation. Our implementation is analytic and does not use per-BSDF precomputed data, which makes our BSDFs usable with textured albedos, roughness, and anisotropy.

Importance sampling for physically-based hair fiber models

We present a new strategy for importance sampling hair reflectance models. To combine hair reflectance models with increasingly popular physically-based rendering algorithms, an efficient sampling scheme is required to select scattered rays that lead to lower variance and noise. Our new strategy, which is tied closely to the derivation of physically-based fiber functions, works well for both smooth and rough fibers based on the Marschner et al. model and also for Lambertian fibers. It should be directly usable with future hair reflectance models that allow for more general cross-sections and more complex surface properties, provided the lobes are derived in a similar, separable fashion. Our strategy includes lobe selection and can efficiently sample complex lobe shapes like the Marschner TRT function. The scheme is easy to implement and requires no precomputation, allowing fully heterogeneous variation of all fiber parameters.

A zero-variance-based sampling scheme for Monte Carlo subsurface scattering

We simulate subsurface scattering using a Monte Carlo random walk in the volumetric medium under the surface. The simulation involves two steps: transition distance sampling and direction sampling. Traditionally, the pdfs used for this purpose emulate the underlying physical processes (exponential law for distance sampling pd(s) = σt e−sσt , phase function pph(ωo|ωi) for direction sampling). However, this sampling is purely local as it has no information about where the important parts of the entire domain are. In subsurface scattering simulation it is not useful to explore the medium far from the boundary, given that we are interested in paths that make it back out of the medium. This idea can be formalized using the notion of the importance function: A zero-variance estimator can be constructed by sampling paths proportionately to the product of the importance function and the classical pdfs [Hoogenboom 2008], and an approximation of this zerovariance ideal yields estimators with low variance. Dwivedi [1982] exploited this idea in deep-penetration transport problems such as reactor shielding. We show how this work can be adapted to reduce variance of subsurface scattering simulation.

A system for efficient rendering of human skin

Figure 1: We project multi-layer diffusion profiles onto a sumof-Gaussians basis to enable realistic rendering of human skin at 30 frames per second on a modern GPU. From left to right: Albedo (1st) and irradiance (2nd) combine to give subsurface irradiance which is then convolved with each Gaussian basis profile (3rd through 7th) and combined in a final render pass with specular (8th) to produce the final image (9th). Convolutions are performed in off-screen 2D textures but shown here mapped onto the face.

A fiber scattering model with non-separable lobes

Figure 1: Glossy reflections from fibers exhibit a lightand view-dependent lobe tightening similar to surface reflectance that previous analytic fiber models lack (a,c). We derive new non-separable fiber-scattering lobes that exhibit this and additional behaviours seen in ground-truth simulation of rough dielectric fiber scattering. Parameter tweaking of previous models can produce results similar to (d), but no previous model with fixed settings can simultaneously produce both (b) and (d). We found that ground-truth renders using explicit cylindrical geometry with Cook Torrance reflectance to be indistinguishable from (b) and (d) (upon convergence, which required significantly more samples per pixel). The difference between the old and new models is further illustrated in (e) by visualizing the R lobe of a circular fiber with Beckmann micro roughness and tilted scales (black hair). In the backlit case (c,d) light grazes the edges of fibers and exhibits the brighter more focused response (seen in (e) where the lobe compresses and brightens for high |φ |).

Additional progress towards the unification of microfacet and microflake theories

We study the links between microfacet and microflake theories from the perspective of linear transport theory. In doing so, we gain additional insights, find several simplifications and touch upon important open questions as well as possible paths forward in extending the unification of surface and volume scattering models. First, we introduce a semi-infinite homogeneous exponential-free-path medium that (a) produces exactly the same light transport as the Smith microsurface scattering model and the inhomogeneous Smith medium that was recently introduced by Heitz et al, and (b) allows us to rederive all the Smith masking and shadowing functions in a simple way. Second, we investigate in detail what new aspects of linear transport theory enable a volume to act like a rough surface. We show that this is mostly due to the use of non-symmetric distributions of normals and explore how the violation of this symmetry impacts light transport within the microflake volume without breaking global reciprocity. Finally, we argue that the surface profiles that would be consistent with very rough Smith microsurfaces have geometrically implausible shapes. To overcome this, we discuss an extension of Smith theory in the volume setting that includes NDFs on the entire sphere in order to produce a single unified reflectance model capable of describing everything from a smooth flat mirror all the way to a semi-infinite isotropically scattering medium with both low and high roughness regimes in between.