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# An empirical BSSRDF model

ACM Trans. Graph., no. 3 (2009): 1-10

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Abstract

We present a new model of the homogeneous BSSRDF based on large-scale simulations. Our model captures the appearance of materials that are not accurately represented using existing single scattering models or multiple isotropic scattering models (e.g. the diffusion approximation). We use an analytic function to model the 2D hemispherical ...More

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Introduction

- The authors present a new model of the homogeneous BSSRDF based on large-scale simulations. The authors' model captures the appearance of materials that are not accurately represented using existing single scattering models or multiple isotropic scattering models (e.g. the diffusion approximation).
- The authors use an analytic function to model the 2D hemispherical distribution of exitant light at a point on the surface, and a table of parameter values of this function computed at uniformly sampled locations over the remaining dimensions of the BSSRDF domain
- This analytic function is expressed in elliptic coordinates and has six parameters which vary smoothly with surface position, incident angle, and the underlying optical properties of the material.
- Rendering a single material requires only about 100KB to represent the BSSRDF

Highlights

- We present a new model of the homogeneous BSSRDF based on large-scale simulations
- Based on an analysis of this simulated data, we propose an analytic function expressed in elliptic coordinates with six fit parameters that accurately captures the features of these hemispherical distribution functions
- We propose the following analytic function of these 2D exitant distributions: H(ωo ; ωpeak, sp, ks| Γ ) = ks e−keμ − kc χ Ft, (8)
- We found that general non-linear optimization routines were unnecessarily complex and often produced noisy fits which undermines our goal of smoothly interpolating these values over the full BSSRDF domain
- We presented an empirical model of the BSSRDF that is valid over a far wider range of angular configurations and material properties than existing analytic models. Our model captures both nearsource and directional effects including the important contribution of low-order scattering. This model was derived from a large-scale simulation of the hemispherical distribution of light leaving a material’s surface over a range of positions from the source, incident angles and underlying optical properties
- We presented an analytic function to approximate these hemispherical functions which is expressed in elliptic coordinates and has six parameters

Methods

- The authors' photon tracing algorithm relies on sampling the probable paths of light within a material.
- The authors emit photons along a collimated beam incident on the slab from direction −ωi, such that it makes angle θi with the surface normal n.
- These photons refract into the material and propagate a distance d before being scattered or absorbed: d = −log ξ , (3).

Results

- All of the results in this paper were rendered on an Intel R Xeon R 2.33GHz Quad-Core processor and those produced with the model required less than one hour of processing time.

Figure 1 compares renderings of orange juice produced using the method to those produced with Monte Carlo path tracing and the diffusion dipole combined with a single scattering term [Jensen et al 2001]. - High-order multiple scattering is not a dominant effect and the image rendered using the diffusion dipole is too dark.
- This is because the dipole model assumes that anisotropic scattering is balanced by many scattering events.
- Because the model more accurately captures these low order scattering events, it matches the reference path traced image, but requires significantly less time to compute

Conclusion

- The authors presented an empirical model of the BSSRDF that is valid over a far wider range of angular configurations and material properties than existing analytic models
- The authors' model captures both nearsource and directional effects including the important contribution of low-order scattering.
- The authors estimated the best-fitting parameters for the simulated data
- Because these parameters vary smoothly with respect to the remaining degrees of freedom they may be interpolated between simulated locations to provide a compact yet continuous representation over the full BSSRDF domain.
- Many of the results the authors reported would have been impossible to render using diffusion based methods and much less efficient with more general numerical integration techniques

Summary

## Introduction:

The authors present a new model of the homogeneous BSSRDF based on large-scale simulations. The authors' model captures the appearance of materials that are not accurately represented using existing single scattering models or multiple isotropic scattering models (e.g. the diffusion approximation).- The authors use an analytic function to model the 2D hemispherical distribution of exitant light at a point on the surface, and a table of parameter values of this function computed at uniformly sampled locations over the remaining dimensions of the BSSRDF domain
- This analytic function is expressed in elliptic coordinates and has six parameters which vary smoothly with surface position, incident angle, and the underlying optical properties of the material.
- Rendering a single material requires only about 100KB to represent the BSSRDF
## Objectives:

The authors' goal is to model the 2D distribution of exitant light of the BSSRDF over the possible range of geometric and optical parameters.## Methods:

The authors' photon tracing algorithm relies on sampling the probable paths of light within a material.- The authors emit photons along a collimated beam incident on the slab from direction −ωi, such that it makes angle θi with the surface normal n.
- These photons refract into the material and propagate a distance d before being scattered or absorbed: d = −log ξ , (3).
## Results:

All of the results in this paper were rendered on an Intel R Xeon R 2.33GHz Quad-Core processor and those produced with the model required less than one hour of processing time.

Figure 1 compares renderings of orange juice produced using the method to those produced with Monte Carlo path tracing and the diffusion dipole combined with a single scattering term [Jensen et al 2001].- High-order multiple scattering is not a dominant effect and the image rendered using the diffusion dipole is too dark.
- This is because the dipole model assumes that anisotropic scattering is balanced by many scattering events.
- Because the model more accurately captures these low order scattering events, it matches the reference path traced image, but requires significantly less time to compute
## Conclusion:

The authors presented an empirical model of the BSSRDF that is valid over a far wider range of angular configurations and material properties than existing analytic models- The authors' model captures both nearsource and directional effects including the important contribution of low-order scattering.
- The authors estimated the best-fitting parameters for the simulated data
- Because these parameters vary smoothly with respect to the remaining degrees of freedom they may be interpolated between simulated locations to provide a compact yet continuous representation over the full BSSRDF domain.
- Many of the results the authors reported would have been impossible to render using diffusion based methods and much less efficient with more general numerical integration techniques

- Table1: Notation used in this paper

Related work

- Numerical techniques such as Monte Carlo path tracing [Kajiya 1986; Jensen et al 1999] are capable of simulating general BSSRDFs. However, these methods are expensive, often requiring hours to days of processing. Scattering equations may also be used in this context [Pharr and Hanrahan 2000], but are computationally expensive to evaluate. Photon mapping [Jensen 1996] can render many BSSRDFs but becomes expensive in both time and space for highly scattering materials. Furthermore, these techniques do not explicitly model the BSSRDF. Rather, determining the fraction of light that is transported between any pair of points requires a complete simulation.

Funding

- This work was supported in part by NSF grant 05-41259 on Fast and Accurate Volumetric Rendering of Scattering Phenomena in Computer Graphics, as well as NSF grants 03-25867, 04-46916, 07-01775, 07-01992, ONR Young Investigator Awards N00014-07-1-0900 and N00014-09-1-0741, and a Sloan Research Fellowship
- Jason Lawrence acknowledges a NSF CAREER award 07-47220, NSF grant 08-11493 and an NVIDIA Professor Partnership Award

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