Multiple-Scattering Microfacet BSDFs with the Smith Model

Key Takeaways

in this paper we address an important open problem in material modeling what happens when light scatters multiple times on rough material surfaces in image synthesis accurately describing light matter interactions is important for materials to obtain a realistic look however the multiple light matter interactions that we can see in this figure are absent from many surface appearance models here's an example of this problem rendering white glass should be simple but we can see that the raw for the glass is the darker its appearance becomes even though it should be simple modeling the appearance of glass that is at the same time rough and white is almost impossible with the current material models many material models such as those rough dialectric plates are called microfacet materials because the underlying mathematical model assumes that their interfaces are made of microscopic imperfections that we call facets those facets are too small to be visible but the way they are statistically oriented change the way light interacts with the material causing its rough appearance many rendering systems model only the contribution of the first bounce of light the contribution of multiple bounces is unknown and it is simply set to zero as if it were neglectable however on very rough micros surfaces the amount of light that scatters multiple times is significant and should not be neglected to avoid energy loss and the noticeable darkening of the material appearance in summary modeling rough materials correctly with with multiple scattering is a challenging problem our multiple scattering model presented in this paper opens up the possibility of modeling rough materials correctly in a practical manner Beyond fixing the darkening problem our goal is to derive a physically based model that is able to make accurate predictions compared to reference data more specifically we derived the multiple scattering component of a specific kind of microsurface the Smith microsurface model because it is based on simple assumptions and makes accurate predictions for single scattering it has received widespread industrial adoption and is considered the academic state-of-the-art in computer graphics for modeling many materials but can we extend this model for multiple scattering and could it be practically incorporated into a classic bsdf plugin these are the questions we are interested in our main Insight is to transform this surface scattering problem into a volume scattering problem which is easier to solve to achieve that we show that the Smith microsurface model can be derived as a special case of the microflame theory for volumes we reformulate the Smith microsurface as a volume with additional constraints to enforce the presence of a Sharp interface this volumetric analogy is very convenient because we know how to compute the light scattering in volumes it depends on two functions that we derve for this new kind of volume the first one is the free path distribution which tells us how long a rate can travel in a medium before finding an intersection on the micros surface the equivalent question is what is the height of the next intersection once an intersection is found we need to know in which direction the light is scattering again this is given by a volumetric phase function which depends on both the base material of the surface and the distribution of the micr faets we derived the phase function for three different surface materials diffuse conductive and dialectric and common microf faet distributions such as Beckman and ggx now that we know the free path and the phas function of this volumetric model we know exactly how the light scatters in the medium from the light propagated in this medium emerges a distribution that has all the expected properties of a classic surface bsdf it is energy conserving and reciprocal furthermore it is exactly the classic single scattering bsdf based on the Smith microsurface model but with the addition of higher order scattering now that we know that the model is mathematically correct we are interested in its predictive power how accurate is this new model to answer this question we need some reference data to compare the predictions of the model two a common way to validate models is to compare their predictions to simulated data obtained by R tracing triangulated surfaces contrary to real world acquisition the surface used in the simulation has known material and statistics and the collected data are free of noise there is thus no decrease of Freedom left to match the parameters of the model to the simulation this is why this validation procedure is widely used in the field of optical physics and therefore we chose this to validate our model we generated random surfaces with known bman statistics and did a r tracing simulation on them by comparing the predictions of our multiple scattering model to the results of the rate racing simulation we found our bsdf model to accurately predict both the albo and angular distribution of the excitant energy among the scattering orders and this for a large variety of materials roughnesses and isotropy and inclinations in our supplemental material we provide an exhaustive set of such validation results to make the model practical we Implement two procedures evaluation and import sampling since the bsdf is the expectation of all the paths that can be traced on the microsurface important sampling can be done straightforwardly by generating One path we construct an unbiased tastic estimate by tracing One path and evaluating the phase functions at each intersection with next event estimation as in classical path tracing with important sampling and this stochastic evaluation we have everything requir re ired to implement a classic bsdf plug-in furthermore our implementation is analytic and does not use per bsdf precomputed data which makes RB sdfs usable with textured albos roughness and an isotropy in the supplemental materials we provide a document describing a tutorial implementation for various materials and ready to use plugins for the mitsuba physically based renderer now let's have a look at some results this image shows a collection of bottles with microfacet materials the energy loss is significant if multiple scattering is neglected especially on dial electrics without multiple scattering rough transmittance appears unnatural which is hard to compensate for by tuning parameters with our multiple scattering model we simulate the expected appearance of rough glass and metals without tuning any parameters our model is robust and behaves as expected even with high roughness values we can see that the model avoids the darkening effects and even produces interesting emerging effects like color saturation this can be observed on this rough diffus material since the absorption spectrum of the material is repeatedly multiplied after each bounce on the microsurface the reflected color appears more saturated after multiple bounces this emerging effect can also be seen on this gold conductor material the unsaturated single scattering gold conductor appears strangely dull thanks to our model the introduction of multiple scattering restores the shiny appearance expected from gold note that since our model is parametric and does not depend on any precomputed data we fully support textured input which is important for creating visually Rich images as an example this is a dialectric with textured roughness and anisotropy thanks for watching