Subsurface scattering

Abstract: The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or micro-facets. Diffuse reflection is generally considered to result from multiple scattering either from a rough surface or from within a layer near the surface. Accounting for diffuse reflection by Lambert’s Cosine Law, as is universally done in computer graphics, is not a physical theory based on first principles. This paper presents a model for subsurface scattering in layered surfaces in terms of one-dimensional linear transport theory. We derive explicit formulas for backscattering and transmission that can be directly incorporated in most rendering systems, and a general Monte Carlo method that is easily added to a ray tracer. This model is particularly appropriate for common layered materials appearing in nature, such as biological tissues (e.g. skin, leaves, etc.) or inorganic materials (e.g. snow, sand, paint, varnished or dusty surfaces). As an application of the model, we simulate the appearance of a face and a cluster of leaves from experimental data describing their layer properties. CR Categories and Subject Descriptors: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism.

Abstract: We present fast methods for separating the direct and global illumination components of a scene measured by a camera and illuminated by a light source. In theory, the separation can be done with just two images taken with a high frequency binary illumination pattern and its complement. In practice, a larger number of images are used to overcome the optical and resolution limitations of the camera and the source. The approach does not require the material properties of objects and media in the scene to be known. However, we require that the illumination frequency is high enough to adequately sample the global components received by scene points. We present separation results for scenes that include complex interreflections, subsurface scattering and volumetric scattering. Several variants of the separation approach are also described. When a sinusoidal illumination pattern is used with different phase shifts, the separation can be done using just three images. When the computed images are of lower resolution than the source and the camera, smoothness constraints are used to perform the separation using a single image. Finally, in the case of a static scene that is lit by a simple point source, such as the sun, a moving occluder and a video camera can be used to do the separation. We also show several simple examples of how novel images of a scene can be computed from the separation results.

Abstract: We estimate surface normal maps of an object from either its diffuse or specular reflectance using four spherical gradient illumination patterns. In contrast to traditional photometric stereo, the spherical patterns allow normals to be estimated simultaneously from any number of viewpoints. We present two polarized lighting techniques that allow the diffuse and specular normal maps of an object to be measured independently. For scattering materials, we show that the specular normal maps yield the best record of detailed surface shape while the diffuse normals deviate from the true surface normal due to subsurface scattering, and that this effect is dependent on wavelength. We show several applications of this acquisition technique. First, we capture normal maps of a facial performance simultaneously from several viewing positions using time-multiplexed illumination. Second, we show that highresolution normal maps based on the specular component can be used with structured light 3D scanning to quickly acquire high-resolution facial surface geometry using off-the-shelf digital still cameras. Finally, we present a realtime shading model that uses independently estimated normal maps for the specular and diffuse color channels to reproduce some of the perceptually important effects of subsurface scattering.

Abstract: We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of per-point weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results per-point (on the GPU). Since the output of the matrix is lower-dimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.