“Fractional gaussian fields for modeling and rendering of spatially-correlated media” by Guo, Chen, Hu, Yan, Guo, et al. …

  • ©Jie Guo, Yanjun Chen, Bingyang Hu, Ling-Qi Yan, Yanwen Guo, and Yuntao Liu




    Fractional gaussian fields for modeling and rendering of spatially-correlated media

Session/Category Title: Advanced Volume Rendering



    Transmission of radiation through spatially-correlated media has demonstrated deviations from the classical exponential law of the corresponding uncorrelated media. In this paper, we propose a general, physically-based method for modeling such correlated media with non-exponential decay of transmittance. We describe spatial correlations by introducing the Fractional Gaussian Field (FGF), a powerful mathematical tool that has proven useful in many areas but remains under-explored in graphics. With the FGF, we study the effects of correlations in a unified manner, by modeling both high-frequency, noise-like fluctuations and k-th order fractional Brownian motion (fBm) with a stochastic continuity property. As a result, we are able to reproduce a wide variety of appearances stemming from different types of spatial correlations. Compared to previous work, our method is the first that addresses both short-range and long-range correlations using physically-based fluctuation models. We show that our method can simulate different extents of randomness in spatially-correlated media, resulting in a smooth transition in a range of appearances from exponential falloff to complete transparency. We further demonstrate how our method can be integrated into an energy-conserving RTE framework with a well-designed importance sampling scheme and validate its ability compared to the classical transport theory and previous work.


    1. Guillaume Bal and Wenjia Jing. 2011. Fluctuation theory for radiative transfer in random media. Journal of Quantitative Spectroscopy and Radiative Transfer 112, 4 (2011), 660 — 670.Google ScholarCross Ref
    2. H. W. Barker, J. N. S. Cole, J.-J. Morcrette, R. Pincus, P. Räisänen, K. von Salzen, and P. A. Vaillancourt. 2008. The Monte Carlo Independent Column Approximation: an assessment using several global atmospheric models. Quarterly Journal of the Royal Meteorological Society 134, 635 (2008), 1463–1478.Google ScholarCross Ref
    3. Benedikt M. Bitterli, Srinath Ravichandran, Thomas Müller, Magnus Wrenninge, Jan Novák, Steve Marschner, and Wojciech Jarosz. 2018. A radiative transfer framework for non-exponential media. ACM Trans. Graph. (2018). Google ScholarDigital Library
    4. Robert Cahalan. 1994. Bounded cascade clouds: Albedo and effective thickness. Nonlinear Processes in Geophysics 1 (01 1994).Google Scholar
    5. Eva Cerezo, Frederic Pérez, Xavier Pueyo, Francisco J. Seron, and François X. Sillion. 2005. A survey on participating media rendering techniques. The Visual Computer 21, 5 (01 Jun 2005), 303–328. Google ScholarDigital Library
    6. Subrahmanyan. Chandrasekhar. 1960. Radiative transfer. Dover.Google Scholar
    7. Anthony B. Davis. 2006. Effective Propagation Kernels in Structured Media with Broad Spatial Correlations, Illustration with Large-Scale Transport of Solar Photons Through Cloudy Atmospheres. In Computational Methods in Transport, Frank Graziani (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 85–140.Google Scholar
    8. Anthony B. Davis and Alexander Marshak. 2004. Photon propagation in heterogeneous optical media with spatial correlations: enhanced mean-free-paths and wider-than-exponential free-path distributions. Journal of Quantitative Spectroscopy and Radiative Transfer 84, 1 (2004), 3 — 34.Google ScholarCross Ref
    9. Anthony B. Davis and Mark Mineev-Weinstein. 2011. Radiation propagation in random media: From positive to negative correlations in high-frequency fluctuations. Journal of Quantitative Spectroscopy and Radiative Transfer 112 (2011), 632–645.Google ScholarCross Ref
    10. Anthony B. Davis and Feng Xu. 2014. A Generalized Linear Transport Model for Spatially Correlated Stochastic Media. Journal of Computational and Theoretical Transport 43 (2014), 474–514.Google ScholarCross Ref
    11. Anthony B. Davis, Feng Xu, and David J. Diner. 2018. Generalized radiative transfer theory for scattering by particles in an absorbing gas: Addressing both spatial and spectral integration in multi-angle remote sensing of optically thin aerosol layers. Journal of Quantitative Spectroscopy and Radiative Transfer 205 (2018), 148 — 162.Google ScholarCross Ref
    12. Eugene d’Eon. 2014. Computer graphics and particle transport: our common heritage, recent cross-field parallels and the future of our rendering equation. In Digital Production Symposium 2014.Google Scholar
    13. Eugene d’Eon. 2018a. A reciprocal formulation of non-exponential radiative transfer. 1: Sketch and motivation. arXiv:1803.03259 https://arxiv.org/abs/1803.03259.Google Scholar
    14. Eugene d’Eon. 2018b. A reciprocal formulation of non-exponential radiative transfer. 2: Monte Carlo estimation and diffusion approximation. arXiv:1809.05881 https://arxiv.org/abs/1809.05881.Google Scholar
    15. Eugene d’Eon and Geoffrey Irving. 2011. A Quantized-diffusion Model for Rendering Translucent Materials. In ACM SIGGRAPH 2011 Papers (SIGGRAPH ’11). 56:1–56:14. Google ScholarDigital Library
    16. Adrian Doicu, Dmitry S. Efremenko, Diego Loyola, and Thomas Trautmann. 2014. Approximate models for broken clouds in stochastic radiative transfer theory. Journal of Quantitative Spectroscopy and Radiative Transfer 145 (2014), 74 — 87.Google ScholarCross Ref
    17. Craig Donner and Henrik Wann Jensen. 2005. Light Diffusion in Multi-layered Translucent Materials. In ACM SIGGRAPH 2005 Papers (SIGGRAPH ’05). 1032–1039. Google ScholarDigital Library
    18. Bertrand Duplantier, Rémi Rhodes, Scott Sheffield, and Vincent Vargas. 2017. Log-correlated Gaussian Fields: An Overview. Springer International Publishing, 191–216.Google Scholar
    19. Jonathan Dupuy, Eric Heitz, and Eugene d’Eon. 2016. Additional Progress Towards the Unification of Microfacet and Microflake Theories. In Eurographics Symposium on Rendering – Experimental Ideas & Implementations, Elmar Eisemann and Eugene Fiume (Eds.). The Eurographics Association. Google ScholarDigital Library
    20. P. Flandrin. 1989. On the spectrum of fractional Brownian motions. IEEE Transactions on Information Theory 35, 1 (1989), 197–199. Google ScholarDigital Library
    21. Julian Fong, Magnus Wrenninge, Christopher Kulla, and Ralf Habel. 2017. Production Volume Rendering: SIGGRAPH 2017 Course. In ACM SIGGRAPH 2017 Courses (SIGGRAPH ’17). 2:1–2:79. Google ScholarDigital Library
    22. Jeppe Revall Frisvad, Toshiya Hachisuka, and Thomas Kim Kjeldsen. 2014. Directional Dipole Model for Subsurface Scattering. ACM Trans. Graph. 34, 1, Article 5 (Dec. 2014), 12 pages. Google ScholarDigital Library
    23. Toshiya Hachisuka, Wojciech Jarosz, Iliyan Georgiev, Anton Kaplanyan, and Derek Nowrouzezahrai. 2013. State of the Art in Photon Density Estimation. In ACM SIGGRAPH Asia Courses. Google ScholarDigital Library
    24. Eric Heitz, Jonathan Dupuy, Cyril Crassin, and Carsten Dachsbacher. 2015. The SGGX Microflake Distribution. ACM Trans. Graph. 34, 4 (July 2015), 48:1–48:11. Google ScholarDigital Library
    25. Wenzel Jakob. 2010. Mitsuba renderer. http://www.mitsuba-renderer.org.Google Scholar
    26. Wenzel Jakob, Adam Arbree, Jonathan T. Moon, Kavita Bala, and Steve Marschner. 2010. A Radiative Transfer Framework for Rendering Materials with Anisotropic Structure. ACM Trans. Graph. 29, 4 (July 2010), 53:1–53:13. Google ScholarDigital Library
    27. Adrian Jarabo, Carlos Aliaga, and Diego Gutierrez. 2018. A Radiative Transfer Framework for Spatially-correlated Materials. ACM Trans. Graph. 37, 4 (July 2018), 83:1–83:13. Google ScholarDigital Library
    28. Wojciech Jarosz, Derek Nowrouzezahrai, Iman Sadeghi, and Henrik Wann Jensen. 2011. A Comprehensive Theory of Volumetric Radiance Estimation Using Photon Points and Beams. ACM Trans. Graph. 30, 1 (Feb. 2011), 5:1–5:19. Google ScholarDigital Library
    29. Henrik Wann Jensen and Per H. Christensen. 1998. Efficient Simulation of Light Transport in Scenes with Participating Media Using Photon Maps. In Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’98). 311–320. Google ScholarDigital Library
    30. Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan. 2001. A Practical Model for Subsurface Light Transport. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). 511–518. Google ScholarDigital Library
    31. J. T. Kajiya and T. L. Kay. 1989. Rendering Fur with Three Dimensional Textures. In Proceedings of the 16th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’89). 271–280. Google ScholarDigital Library
    32. Pramook Khungurn, Daniel Schroeder, Shuang Zhao, Kavita Bala, and Steve Marschner. 2015. Matching Real Fabrics with Micro-Appearance Models. ACM Trans. Graph. 35, 1 (Dec. 2015), 1:1–1:26. Google ScholarDigital Library
    33. Alexander B. Kostinski. 2001. On the extinction of radiation by a homogeneous but spatially correlated random medium. J. Opt. Soc. Am. A 18, 8 (Aug 2001), 1929–1933.Google ScholarCross Ref
    34. Jaroslav Křivánek, Iliyan Georgiev, Toshiya Hachisuka, Petr Vévoda, Martin Šik, Derek Nowrouzezahrai, and Wojciech Jarosz. 2014. Unifying Points, Beams, and Paths in Volumetric Light Transport Simulation. ACM Trans. Graph. 33, 4 (July 2014), 103:1–103:13. Google ScholarDigital Library
    35. Mateusz Kwaśnicki. 2017. Ten equivalent definitions of the fractional laplace operator. Fractional Calculus and Applied Analysis 20, 1 (2017).Google Scholar
    36. Edward W. Larsen and Richard Vasques. 2011. A generalized linear Boltzmann equation for non-classical particle transport. Journal of Quantitative Spectroscopy and Radiative Transfer 112, 4 (2011), 619 — 631.Google ScholarCross Ref
    37. Michael L. Larsen and Aaron S. Clark. 2014. On the link between particle size and deviations from the Beer Lambert Bouguer law for direct transmission. Journal of Quantitative Spectroscopy and Radiative Transfer 133 (2014), 646 — 651.Google ScholarCross Ref
    38. Asad Lodhia, Scott Sheffield, Xin Sun, and Samuel S. Watson. 2016. Fractional Gaussian fields: A survey. Probability Surveys 13 (2016), 1–56.Google ScholarCross Ref
    39. B. Mandelbrot and J. Van Ness. 1968. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Rev. 10, 4 (1968), 422–437.Google ScholarDigital Library
    40. Johannes Meng, Marios Papas, Ralf Habel, Carsten Dachsbacher, Steve Marschner, Markus Gross, and Wojciech Jarosz. 2015. Multi-scale Modeling and Rendering of Granular Materials. ACM Trans. Graph. 34, 4 (July 2015), 49:1–49:13. Google ScholarDigital Library
    41. Jonathan T. Moon, Bruce Walter, and Stephen R. Marschner. 2007. Rendering Discrete Random Media Using Precomputed Scattering Solutions. In Proceedings of the 18th Eurographics Conference on Rendering Techniques (EGSR’07). 231–242. Google ScholarDigital Library
    42. Thomas Müller, Marios Papas, Markus Gross, Wojciech Jarosz, and Jan Novák. 2016. Efficient Rendering of Heterogeneous Polydisperse Granular Media. ACM Trans. Graph. 35, 6 (Nov. 2016), 168:1–168:14. Google ScholarDigital Library
    43. Jan Novák, Iliyan Georgiev, Johannes Hanika, and Wojciech Jarosz. 2018. Monte Carlo Methods for Volumetric Light Transport Simulation. Computer Graphics Forum (Proceedings of Eurographics – State of the Art Reports) 37, 2 (may 2018).Google ScholarCross Ref
    44. E. Perrin, R. Harba, C. Berzin-Joseph, I. Iribarren, and A. Bonami. 2001. nth-order fractional Brownian motion and fractional Gaussian noises. IEEE Transactions on Signal Processing 49, 5 (May 2001), 1049–1059. Google ScholarDigital Library
    45. Matthias Raab, Daniel Seibert, and Alexander Keller. 2008. Unbiased Global Illumination with Participating Media. In Monte Carlo and Quasi-Monte Carlo Methods 2006, Alexander Keller, Stefan Heinrich, and Harald Niederreiter (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 591–605.Google Scholar
    46. I. S. Reed, P. C. Lee, and T. K. Truong. 1995. Spectral representation of fractional Brownian motion in n dimensions and its properties. IEEE Transactions on Information Theory 41, 5 (1995), 1439–1451. Google ScholarDigital Library
    47. L. F. Rojas-Ochoa, J. M. Mendez-Alcaraz, J. J. Sáenz, P. Schurtenberger, and F. Scheffold. 2004. Photonic Properties of Strongly Correlated Colloidal Liquids. Phys. Rev. Lett. 93 (2004), 073903. Issue 7.Google ScholarCross Ref
    48. Gennady Samorodnitsky. 2007. Long Range Dependence. Foundations and Trends in Stochastic Systems 1, 3 (2007), 163–257. Google ScholarDigital Library
    49. Kai Schröder, Reinhard Klein, and Arno Zinke. 2011. A Volumetric Approach to Predictive Rendering of Fabrics. In Proceedings of the Twenty-second Eurographics Conference on Rendering (EGSR ’11). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 1277–1286. Google ScholarDigital Library
    50. Kai Schröder, Arno Zinke, and Reinhard Klein. 2014. Image-Based Reverse Engineering and Visual Prototyping of Woven Cloth. IEEE Transactions on Visualization and Computer Graphics PP, 99 (2014).Google Scholar
    51. Raymond A Shaw, Alexander B Kostinski, and Daniel D Lanterman. 2002. Super-exponential extinction of radiation in a negatively correlated random medium. Journal of Quantitative Spectroscopy and Radiative Transfer 75, 1 (2002), 13 — 20.Google ScholarCross Ref
    52. Leung Tsang, Jin Au Kong, Kung-Hau Ding, and Chi On Ao. 2002. Scattering of Electromagnetic Waves: Numerical Simulations. John Wiley & Sons.Google Scholar
    53. Eric Veach. 1997. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation. Stanford, CA, USA. Google ScholarDigital Library
    54. Magnus Wrenninge, Ryusuke Villemin, and Christophe Hery. 2017. Path Traced Subsurface Scattering using Anisotropic Phase Functions and Non-Exponential Free Flights. Pixar Technical Memo 17–07. Pixar Inc.Google Scholar
    55. Jiahua Zhang, G. Baciu, Dejun Zheng, Cheng Liang, Guiqing Li, and Jinlian Hu. 2013. IDSS: A Novel Representation for Woven Fabrics. IEEE Transactions on Visualization and Computer Graphics 19, 3 (2013), 420–432. Google ScholarDigital Library
    56. Shuang Zhao, Wenzel Jakob, Steve Marschner, and Kavita Bala. 2011. Building Volumetric Appearance Models of Fabric Using Micro CT Imaging. ACM Trans. Graph. 30, 4 (July 2011), 44:1–44:10. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: