Efficient rendering of translucent objects using the diffusion approximation

Abstract

In translucent materials such as fruit and marble, light diffuses beneath the surface, creating a distinct appearance. I t is impossible to capture this using traditional reflection models, and requires computation of subsurface light transport. Full simulation has proven intractable, fueling the development of more efficient models, capable of retaining the most salient visual qualities. In this dissertation, we will explore the direction of approximating light transport as a diffusion process, in order to achieve efficient and practical simulation of subsurface light transport. In seminal work by .Jensen et al. [JMLHOla], a simplified diffusion model was introduced: the fast dipole approximation. It reduces the simulation of subsurface light transport to the computation of a surface integral over the object of interest. We show that the dipole approximation is simple enough to achieve the goal of interactive rendering. Two novel integration schemes are developed , which are fast and flexible enough to interactively account for varying viewpoint, illumination and geometry. In this context, we contribute to the dipole model in several ways: an efficient integration procedure over polygons, an importance sampling scheme for Monte Carlo quadrature, and an adjustment for ensuring reciprocity of light transport. The dipole approximation sacrifices accuracy to increase performance. We will analyze the underlying assumptions, and assess the impact for computer graphics. Most importantly, we find that conservation of energy is not guaranteed, and certain geometry-dependent visual cues are missing. When interactivity is not the main concern, a more accurate simulation is possible. We introduce a volumetric diffusion method for arbitrarily shaped objects, based on the multigrid method [Hac85, Sta95]. Two important issues are solved. First, accurate representation of interactions near the object's surface, which is realized by applying the so-called embedded boundary discretization [DCL +gs, JC98]. Second, the solution adaptively refines where required, in order to improve efficiency and keep memory requirements feasible [B084, DeZ93, BBSW94]. Although this approach may be slower than dipole-based methods, it is capable of dealing with both homogeneous and heterogeneous materials, and more accurately reproduces the general appearance of translucent objects. Contrary to previous methods for dealing with similar cases, computation time is only a few minutes. The dipole approximation makes no allowance for radiometric accuracy, but enjoys the attractive property of not requiring a volumetric representation. Inspired by the traditional boundary element method [HP02, HASS03] , we show that a general exact boundary diffusion model can be formulated. We point out the relationship to the well-known radiosity problem [CW93] and our novel polygon integration technique. As a practical application, the boundary diffusion model is employed for experimental validation of the dipole approximation, which confirms the findings of our analysis.